United States

Department

of Agriculture

Forest Service

Rocky Mountain

Research Station

General Technical

Report RMRS-GTR-56

October 2000

Wilderness Recreation Use

Estimation: A Handbook of

Methods and Systems

Alan E. Watson

David N. Cole

David L. Turner

Penny S. Reynolds
Rocky Mountain Research Station

324 25th Street

Ogden, UT 84401

The Authors ____________________

Alan E. Watson is Research Social Scientist with the

Aldo Leopold Wilderness Research Institute on the University of Montana campus, Missoula. Dr. Watson’s

academic training was with the School of Forestry and

Wildlife Resources, Virginia Polytechnic Institute and

State University, including a Ph.D. degree in 1983. His

research interests are primarily in the area of wilderness

experience quality, including influences of conflict, solitude, and visitor impacts.

David N. Cole is Research Biologist with the Aldo

Leopold Wilderness Research Institute, Missoula, MT.

Dr. Cole received his B.A. degree in geography from the

University of California, Berkeley, in 1972. He received

his Ph.D. degree, also in geography, from the University

of Oregon in 1977. He has written many papers on

wilderness management, particularly the ecological effects of recreational use.

David L. Turner is Mathematical Statistician with the

Rocky Mountain Research Station in Logan, UT. Dr.

Turner received his education at Colorado State University, Fort Collins, including a Ph.D. degree in statistics in

1975.

Abstract _________________________________________

Watson, Alan E.; Cole, David N.; Turner, David L.; Reynolds, Penny S. 2000. Wilderness recreation

use estimation: a handbook of methods and systems. Gen. Tech. Rep. RMRS-GTR-56. Ogden,

UT: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station. 198 p.

Documented evidence shows that managers of units within the U.S. National Wilderness

Preservation System are making decisions without reliable information on the amount, types, and

distribution of recreation use occurring at these areas. There are clear legislative mandates and

agency policies that direct managers to monitor trends in use and conditions in wilderness. This

report is specifically designed as a convenient resource for wilderness managers and others who

have the responsibility of monitoring and describing visitor use in wilderness. It is a comprehensive

manual on estimation techniques and procedures that are essential to appropriately and accurately

measure visitor use-related characteristics and conditions. Guidelines enable the manager to

evaluate options and decide on a use estimation system that meets the needs of a specific area and

set of circumstances. This handbook provides, in a single source, all relevant information on setting

objectives, making decisions about what to monitor, developing a sampling plan, collecting the

needed information, and computing basic statistics to provide input into management decisions. The

user should have mathematical abilities at least through algebra; knowledge of statistics and

calculus would be helpful.

Keywords: National Wilderness Preservation System, visitation, visitor use, visitor use estimation

Penny S. Reynolds is Assistant Professor of Comparative Physiology at the University of Richmond, VA.

Dr. Reynolds has a B.Sc. degree in wildlife biology and an

M. Sc. degree in zoology, both from the University of

Guelph, and an M.S. degree in biometry, and a Ph.D.

degree in zoology with a statistics minor (1992) from the

University of Wisconsin-Madison.

Acknowledgments ______________

The authors gratefully acknowledge cooperation and

support of the Southern Region of the USDA Forest

Service for providing the opportunity to work closely with

managers of that Region’s Cohutta Wilderness and Mount

Rogers National Recreation Area, and to explore in depth

the challenges of wilderness use estimation. Specific

acknowledgements go to Larry Phillips of the Southern

Region Office; Bill Black, Larry Thomas, and Mike Davis

of the Cohutta District of the Chattahoochee National

Forest; Tim Eling, Mike Evans and Steve Sherwood of

the Mount Rogers National Recreation Area, Jefferson

National Forest; and Harry Fisher of the Forest

Supervisor’s Office, Jefferson National Forest.
Wilderness Recreation Use

Estimation: A Handbook of

Methods and Systems

Alan E. Watson

David N. Cole

David L. Turner

Penny S. Reynolds

Contents__________________________________________

Page

Introduction ........................................................................................................................1

The Problem: Inadequate Wilderness Use Data ............................................................2

What is a Wilderness Use Estimation System? .............................................................. 2

Handbook Organization .....................................................................................................3

Part I: Elements of a Use Estimation System ................................................................5

Chapter 1: Visitor Use Characteristics ...............................................................................7

Objectives ..........................................................................................................................7

Identification of Visitor Use Characteristics ........................................................................9

Visit Counts ...................................................................................................................10

Individual Visits ..........................................................................................................10

Group Visits ...............................................................................................................10

Visit Attributes ...............................................................................................................11

Method of Travel ........................................................................................................11

Group Size.................................................................................................................12

Use of Commercial Services .....................................................................................12

Activity Participation ..................................................................................................13

Length of Stay ...........................................................................................................13

Temporal Use Distribution .........................................................................................14

Spatial Use Distribution ............................................................................................. 14

Conditions and Visitor Perceptions............................................................................14

Miscellaneous Visit Characteristics ........................................................................... 15

Visitor Attributes ............................................................................................................15

Sociodemographics ...................................................................................................15

Past Experience ........................................................................................................16

Visitor Knowledge ......................................................................................................17

Visitor Attitudes and Preferences ..............................................................................17

Summary-Use Statistics ...............................................................................................18

Visitors .......................................................................................................................18

Visitor-Day .................................................................................................................18

Visitor-Hours ..............................................................................................................18

Overnight Stays .........................................................................................................19

Recreation Visitor-Days ............................................................................................. 19

Chapter 2: Visitor Use Estimation Techniques.................................................................20

External Visual Observations ...........................................................................................20

Internal Visual Observations: Stationary .......................................................................... 23

Internal Visual Observation: Roaming..............................................................................24

Mechanical Traffic Counters ............................................................................................24

Registration ......................................................................................................................29

Permits ............................................................................................................................32

Visitor Surveys .................................................................................................................36

Indirect Estimation............................................................................................................39

Aerial Surveys ..................................................................................................................41

Chapter 3: Sampling Methods..........................................................................................43

Convenience or Judgment Sampling ............................................................................... 43

Statistical Sampling Designs ............................................................................................44

Why Use Statistical Sampling? .....................................................................................44

What is a Good Sampling Design? ............................................................................... 44

Sample Size Determination..............................................................................................45

Defining the Sampling Unit ...........................................................................................45

Sample Size ..................................................................................................................46

Sampling Designs ............................................................................................................57
Simple Random Sampling ............................................................................................ 47

How to Obtain a Random Sample .............................................................................47

Procedure for Random Sampling .............................................................................. 47

Advantages of Random Sampling .............................................................................49

Disadvantages of Random Sampling ........................................................................ 49

Systematic Sampling ....................................................................................................49

Procedure for Systematic Sampling .......................................................................... 49

Advantages of Systematic Sampling ......................................................................... 49

Disadvantages of Systematic Sampling .................................................................... 49

Computations for Systematic Samples ......................................................................50

Multiple Systematic Sampling .................................................................................... 50

Computations for Multiple Systematic Samples ........................................................ 50

Stratified Sampling ........................................................................................................ 52

Procedure for Stratified Sampling .............................................................................. 53

Choosing Stratum Sample Size ................................................................................. 53

Advantages of Stratified Sampling ............................................................................ 53

Disadvantages of Stratified Sampling........................................................................ 53

Computations for Stratified Samples ......................................................................... 54

Cluster Sampling ..........................................................................................................54

Procedure for Cluster Sampling ................................................................................ 55

Advantages of Cluster Sampling ............................................................................... 55

Disadvantages of Cluster Sampling .......................................................................... 55

Effects of Sample Design on Use Estimates: A Case Study ........................................ 55

Field Sampling Strategies ............................................................................................. 57

Scheduling “Observer” Rotation Across Trailheads .................................................. 57

Scheduling Observer Effort ....................................................................................... 59

Calibration .................................................................................................................59

Compliance Estimates ............................................................................................... 60

Visitor Selection ......................................................................................................... 61

Part II: Selecting and Building a Use Estimation System .......................................... 63

Introduction ......................................................................................................................65

System A: Mechanical Counters With Visual Calibration ................................................. 68

System Description ..........................................................................................................68

Operational Procedures ................................................................................................... 68

Step 1: Decide on Use Characteristics ......................................................................... 68

Step 2: Decide on Counter Type ..................................................................................68

Step 3: Decide on the Number of Counters Needed .................................................... 70

Step 4: Choose the Calibration Method ........................................................................ 70

Step 5: Develop a Sampling Plan ................................................................................. 71

Step 6: Purchase Equipment ........................................................................................71

Step 7: Install Equipment ..............................................................................................71

Step 8: Collect Calibration Data .................................................................................... 72

Step 9: Collect Counter Data ........................................................................................73

Step 10: Estimate Use .................................................................................................. 73

System B: Mechanical Counters With Observer Calibration and

Sample Observations ................................................................................................79

System Description ..........................................................................................................79

Operational Procedures ................................................................................................... 79

Step 1: Decide on Use Characteristics ......................................................................... 79

Step 2: Decide on Counter Type ..................................................................................80

Step 3: Decide on the Number of Counters Needed .................................................... 81

Step 4: Choose the Calibration Method ........................................................................ 81

Step 5: Develop a Sampling Plan ................................................................................. 82

Step 6: Purchase Equipment ........................................................................................82

Step 7: Install Equipment ..............................................................................................82

Page
Step 8: Collect Calibration Data ....................................................................................83

Step 9: Collect Count Data ...........................................................................................84

Step 10: Estimate Use ..................................................................................................85

System C: Mechanical Counters With Observer Calibration and Sample Interviews ...... 90

System Description ..........................................................................................................90

Operational Procedures ...................................................................................................90

Step 1: Decide on Use Characteristics to Measure ......................................................90

Step 2: Decide on Counter Type ..................................................................................91

Step 3: Decide on the Number of Counters Needed ....................................................92

Step 4: Develop a Sampling Plan .................................................................................92

Step 5: Purchase Equipment ........................................................................................92

Step 6: Install Equipment ..............................................................................................92

Step 7: Collect Counter Data ........................................................................................93

Step 8: Select and Train the Interview Team ................................................................93

Step 9: Collect Calibration and Interview Data .............................................................94

Step 10: Estimate Use ..................................................................................................96

System D: Visitor Registration System With Checks For Registration Rate .................. 101

System Description ........................................................................................................101

Operational Procedures .................................................................................................101

Step 1: Decide on Use Characteristics to Measure ....................................................101

Step 2: Decide on Registration Form .......................................................................... 102

Step 3: Decide on Number of Registration Stations ...................................................102

Step 4: Decide on Method of Estimating Registration Rates ...................................... 102

Step 5: Develop a Sampling Plan ...............................................................................103

Step 6: Purchase Equipment ......................................................................................103

Step 7: Construct the Registration Stations ................................................................103

Step 8: Install Equipment ............................................................................................104

Step 9: Collect Registration Data ................................................................................105

Step 10: Obtain Registration Rate Data ..................................................................... 105

Step 11: Estimate Use ................................................................................................106

System E: Visitor Registration System With Registration Rate Checks and

Sample Interviews ...................................................................................................110

System Description ........................................................................................................110

Operational Procedures .................................................................................................110

Step 1: Decide on Use Characteristics to Measure ....................................................110

Step 2: Decide on Registration Form .......................................................................... 111

Step 3: Decide on Number of Registration Stations ...................................................111

Step 4: Develop Sampling Plan ..................................................................................111

Step 5: Construct the Registration Stations ................................................................113

Step 6: Install Registration Stations ............................................................................114

Step 7: Select and Train the Interview Team. ............................................................. 114

Step 8: Collect Registration Rate and Interview Data ................................................. 115

Step 9: Estimate Use ..................................................................................................117

System F: Permit System With Compliance Checks .....................................................121

System Description ........................................................................................................121

Operational Procedures .................................................................................................121

Step 1: Decide on Use Characteristics .......................................................................121

Step 2: Decide on a Permit Form ...............................................................................121

Step 3: Establish a Permit-Issue Procedure ............................................................... 122

Step 4: Decide on Method of Implementing Compliance Checks ............................... 123

Step 5: Purchase Equipment ......................................................................................124

Step 6: Estimate Use ..................................................................................................124

System G: Permit System With Compliance Checks and Sample Interviews ...............128

System Description ........................................................................................................128

Operational Procedures .................................................................................................128

Page
Step 1: Decide on Use Characteristics .......................................................................128

Step 2: Decide on a Permit Form ...............................................................................129

Step 3: Establish a Permit-Issue Procedure ............................................................... 129

Step 4: Develop Sampling Plan ..................................................................................130

Step 5: Purchase Equipment ......................................................................................132

Step 6: Select and Train the Interview Team .............................................................. 132

Step 7: Collect Compliance Rate and Interview Data ................................................. 132

Step 8: Estimate Use ..................................................................................................134

System H: Permit System With Compliance Checks and Mailback Questionnaires...... 138

System Description ........................................................................................................138

Operational Procedures .................................................................................................138

Step 1: Decide on Use Characteristics to Measure ....................................................138

Step 2: Decide on a Permit Form ...............................................................................139

Step 3: Establish a Permit-Issue Procedure ............................................................... 139

Step 4: Develop the Mailback Questionnaire .............................................................. 140

Step 5: Develop Sampling Plan for Survey .................................................................144

Step 6: Purchase Equipment and Supplies ................................................................144

Step 7: Obtain Mailback Responses ...........................................................................144

Step 8: Estimate Response Rates, Compliance Rates, and Use ............................... 145

System I: Indirect Counts ...............................................................................................150

System Description ........................................................................................................150

Operational Procedures .................................................................................................150

Step 1: Decide on Use Characteristics .......................................................................150

Step 2: Select the Appropriate Predictor Variable ...................................................... 151

Step 3: Select a Direct Counting Method ....................................................................151

Step 4: Develop a Sampling Plan for Direct Counting ................................................151

Step 5: Install Equipment for Indirect Counts (If Applicable) ...................................... 152

Step 6: Collect Direct Count Data ...............................................................................152

Step 7: Collect Predictor Variable Data ......................................................................155

Step 8: Estimate Use ..................................................................................................156

System J: General Visitor Surveys................................................................................. 157

System Description ........................................................................................................157

Operational Procedures .................................................................................................157

Step 1: Decide on Use Characteristics to Measure ....................................................157

Step 2: Decide on Survey Method ..............................................................................157

Step 3: Formulate the Survey .....................................................................................158

Step 4: Select and Train the Interview Team .............................................................. 162

Step 5: Develop a Sampling Plan ...............................................................................163

Step 6: Purchase Supplies .........................................................................................163

Step 7: Collect Interview or Questionnaire Data ......................................................... 163

Step 8: Obtain Mailback Responses ...........................................................................164

Step 9: Estimate Use ..................................................................................................164

Appendices ...................................................................................................................171

Appendix A: References ................................................................................................173

Appendix B: Data and Data Analysis .............................................................................175

Variables ........................................................................................................................175

Populations and Samples ..............................................................................................175

Descriptive Statistics: Data Plots ...................................................................................176

Stem-and-leaf Displays ...............................................................................................176

Histograms and Bar Charts ........................................................................................177

Scatterplots .................................................................................................................179

Time Plots ...................................................................................................................179

Descriptive Statistics: Continuous Data .........................................................................180

Measures of Central Tendency ...................................................................................180

Measures of Variability ...............................................................................................181

Page
Descriptive Statistics: Categorical Data .........................................................................184

Binomial Data .............................................................................................................184

Multinomial Data .........................................................................................................185

Differences Between Variables ......................................................................................186

One-Sample Tests ......................................................................................................187

Comparing Two Samples ...........................................................................................188

Comparing More Than Two Samples .........................................................................189

Association of Two Variables .........................................................................................193

Regression ..................................................................................................................193

Correlation ..................................................................................................................196

Calibration ...................................................................................................................196

Page
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 1

Introduction ______________________________________________________

As stipulated by the Wilderness Act of 1964 (PL 88-577), the National

Wilderness Preservation System (NWPS) is established “...to secure for the

American people of present and future generations the benefits of an

enduring resource of wilderness.” This legislation now applies to more than

625 separate areas in 44 states, comprising nearly 105 million acres.

The goal of the Act may be stated briefly as the mandate to manage

wilderness areas so as to leave them unimpaired for future use and enjoyment as wilderness. Each individual area is to be managed to maintain

natural conditions and provide opportunities for “solitude” or “primitive and

unconfined” recreation experiences. However, it is apparent that these two

responsibilities of management may become contradictory: to maintain or

minimize loss of ecological integrity (and ensure quality solitude experiences), while simultaneously providing access for human use and enjoyment

for unconfined experiences.

Although human use is part of the wilderness mandate, human use

nevertheless results in unavoidable impact on the resource. Even at low use

levels, visitors cause substantial disturbance, both to the wilderness resource itself, and to the wilderness experiences of others. Because recreational use of wilderness continues to increase (Cole 1996), the potential for

disturbance and wilderness degradation is very great. It follows that:

(1) the management of wilderness visitors is a priority, and

(2) in order to make effective management decisions, the manager must

have reliable information about visitor use of wilderness (Watson 1990).

Monitoring wilderness status is mandated in the Act, with the primary

goals being to (1) improve wilderness management, (2) improve the acquisition and use of knowledge from wilderness, and (3) improve assessment of

status and trends. Managers must monitor wilderness use through a systematic description. In general, use measurement has two aspects: first, the

inventory of human uses that provide a baseline for planning and management, and second, a means of determining how human use and resource

conditions of the wilderness are changing. Evaluation of standards may be

performed by cataloging real and potential threats to the resource, and by

monitoring trends in condition and changes in demand and use (Landres and

others 1994). At the same time, management techniques must not detract

from “primitive and unconfined” types of experience (Cole 1995). Therefore,

empirical studies are required for both deciding upon, and verifying, the most

effective management techniques for (1) resolving a given management

problem, and (2) reducing visitor burden.

Wilderness Recreation Use

Estimation: A Handbook of

Methods and Systems

Alan E. Watson

David N. Cole

David L. Turner

Penny S. Reynolds
2 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The Problem: Inadequate Wilderness Use Data

Unfortunately, wilderness use has been, and continues to be, inadequately

measured and described. A recent survey of wilderness managers (comprising

423 out of a total of 440 wilderness areas) reported that 63 percent relied on

“best guesses” to estimate visitor use. Only 16 percent reported that they used

any sort of systematic procedure for determining amount of use; an additional

22 percent reported that they made estimates based on “frequent field

observation” (McClaran and Cole 1993).

There are several reasons why wilderness use is not assessed adequately:

 1. Difficulty in quantifying and measuring wilderness use. Lack of funding

is the most common problem facing managers. Apart from financial considerations, logistic problems result from the size of the area, number of access

points and relative ease of accessibility, the amount of visitor use (for

example, low numbers are difficult to detect), the type of visitor use, and the

amount of resources (personnel, time) available to monitor use.

 2. Little or no coordination across wilderness areas. NWPS comprises

extremely diverse units, that vary in ecosytem type, geographical location,

unit size, use, and perceived benefits. Furthermore, administration is divided

among four different federal agencies: the Forest Service in the Department

of Agriculture, and the National Park Service, Bureau of Land Management,

and the Fish and Wildlife Service in the Department of The Interior. As a

result, there is a lack of unanimity in purpose; perceived management goals

will differ widely between units.

 3. Lack of quantitative and practical skills. Managers have no training on

techniques and processes available for collecting and analyzing data.

 4. Lack of decision-making and judgment skills. Employment of any given

technique requires that the manager decide between competing restrictions

and priorities with respect to study objectives, desired level of accuracy,

availability of personnel, time commitment, acceptable visitor burden, and

cost. Managers may lack knowledge of the various options available for the

most appropriate and cost-effective techniques.

With little or no reliable wilderness use information, managers cannot

adequately judge resource condition trends. Visitor opinions alone are inadequate for evaluation purposes; there may be little agreement between visitor

perceptions and the actual condition of the resource, or even on the conditions

that determine “primitive and unconfined” experiences. Quality wilderness

use information is absolutely essential for examining and testing the various

tenets, principles, and dogmas of wilderness management; for optimal management of the resource, it is critical to distinguish management principles

which have been empirically verified from those which have never been

tested, and are based on nothing more than “authoritative opinions” (Cole

1995).

What is a Wilderness Use Estimation System?

To many managers, a use estimation “system” is nothing more than some

kind of measurement technique: a mechanical counter, a permit, or a selfregistration station. Measurement techniques alone do not constitute a use

estimation system. Instead, a use estimation “system” is a conceptual structure, comprising five essential steps:
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 3

1. A statement of objectives.

2. Identification of the specific use characteristics to be measured.

3. Choice of appropriate wilderness visitor use measurement techniques.

4. Choice of the appropriate strategy for sampling.

5. Choice of a specific technique and/or procedure for data analysis and

summary.

If any of these elements is missing from the system, the exercise of data

collection is of little or no value. Given the investment in data collection, it

is important to derive the maximum value from the data, and to avoid

inappropriate analyses which will generate misleading conclusions. Reliable

and high-quality data (“good” data) are obtained, not only by the type of

information collected, but also by the relevance of that information to the

study objectives, and the accuracy of the techniques used in data collection.

Handbook Organization ____________________________________________

This report is specifically designed as a convenient resource for wilderness

managers and others who have the responsibility of monitoring and describing visitor use in wilderness areas. It also should be more broadly of value to

any manager or planner trying to monitor human use of any type of

nonroaded, nonmotorized protected areas. It is a comprehensive manual on

estimation techniques and procedures that are essential to appropriately

and accurately measure visitor use-related characteristics and conditions.

Guidelines are presented that enable the manager to evaluate options and

decide on a use estimation system that meets the needs of a specific area and

set of circumstances.

This handbook is divided into two organizational units. Part I: Elements

of a Use Estimation System, consists of three chapters introducing the

fundamental components of a use estimation system. These chapters provide

the basic information necessary to adequately and reliably describe visitor

use. Chapter 1: Visitor Use Characteristics, details the types of visitor

use data that can be measured, together with methods of reporting such data

and specific areas of application. Because the selection of use characteristics

to be measured must be determined a priori in accordance with the goals of

the study, we present general guidelines for formulating study objectives. In

Chapter 2: Visitor Use Estimation Techniques, we describe specific

measurement techniques and equipment used in data collection. Also specified are the types of visitor use information that can be obtained with each

technique, estimates of relative accuracy, visitor burden, and associated

management costs. Chapter 3: Sampling Strategies, describes practical

and systematic methods of developing statistically based and field-oriented

strategies of data collection. Specific statistical methods required for elementary data analysis are included in the appendix section.

Part II: Selecting and Building a Use Estimation System, presents

the basic criteria for the evaluation, design, and step-by-step implementation of 10 major use estimation systems. The information presented in each

section should enable the reader to quickly evaluate each system in the

context of management objectives set on a case-by-case basis.
4 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 5

Part I: Elements of a Use

Estimation System
6 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 7

Chapter 1: Visitor Use

Characteristics

The two aspects to the initial formulation of a use estimation system are:

1. The statement of objectives

2. Identification of the specific use characteristics to be measured

Objectives _______________________________________________________

The statement of objectives is a justification or outline of the reasons for

collecting a specific set of information; in other words, why wilderness use

measurement and monitoring are to be performed. A clearly defined objectives statement directs the entire course of the project by determining both

the type of information that needs to be collected and the purpose for which

it is collected. However, all phases of the objectives statement may be

progressively updated and revised as the planning process continues.

It is important to emphasize that the objective is not accumulation of use

information for its own sake; nor are objectives defined in terms of methods,

numerical goals or quotas, or specific measurement techniques. Instead, a

statement of objectives involves the identification of a specific wilderness

management “problem” in terms that allow some assurance of its solution

(Ackoff 1953); the collection of visitor use data will be essential to resolving

the identified problem. A management “problem” exists where there are one

or more desired objectives.

The objectives statement consists of six components (Ackoff 1953):

 1. Potential participants

 2. Their respective goals

 3. Prioritization of the respective goals

 4. Alternatives

 5. Practical applications

 6. The scope of inference of the intended study

 1. Participants.—These involve all individuals or groups associated with

a particular use problem. At the very least, these will include the manager

and the various types of wilderness visitors. Participants outside this

immediate loop include the relevant agency, special-interest groups, legislators and congressional representatives, and so on.

 2. Goals.—Goals are defined in terms of some thing, some motivation, or

some end, to be attained. Goals of the wilderness manager can be summarized as: the collection of “basic” information; identification of constraints

(finances, time, labor), which may prevent or hinder data collection; and the

practical application of this information.
8 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

(a) “Basic” information may be collected in response to an immediate

problem perceived by the manager, or in accordance with one or more

wilderness directives. Such directives may result from legislative mandates,

agency reporting requirements, the requirement for feasible management

objectives, or the need to associate funding levels, maintenance, and educational programs with amounts and types of clientele served (Watson 1990).

Regardless of directive origin, “basic” information conforms to one or more of

the following categories (Landres and others 1994):

(1) Descriptors. These data constitute the basic supply side of the

NWPS. Examples include the number of miles of trail, number of visitors per

day or season in a given area, and so on. In addition, “background” description data may be critical in formulating and clarifying management objectives. Background information includes such descriptors as the number and

description of major ecosystem types, the number and location of endangered

species, and specific area issues and concerns identified by managers and

various public groups.

(2) Threats. A threat is any significant potential agent of change to

the wilderness resource. Relevant information includes identification of the

specific threat, how that agent threatens wilderness attributes, the attributes under threat, specifics of impact (type, amount, and time frame),

potential areas or specific resources most susceptible to damage, long-term

versus short-term threats, and so forth

(3) Trends in condition. Monitoring of both resource condition and

use patterns over time are essential for evaluating and directing effective

wilderness management (Cole 1989; Stankey and others 1985). Unfortunately, monitoring is performed relatively rarely, although information on

some types of monitoring procedures is available (Cole 1989; McClaran and

Cole 1993).

(4) Demands and uses may be categorized as either expressed, that

is, use and use applications that are actually performed, or latent, those uses

that are desired but not achieved. This information is critical for predicting

patterns of use and potential impact.

(5) Societal values and benefits. Public input is important in identifying potential problems and formulating management decisions about

which impacts are potentially significant, which characteristics should be

monitored, what constitutes the limits of acceptable change, what are

appropriate management strategies, and what methods of strategy implementation should be utilized. Public involvement is critical in identifying

potential sources of conflict between managers and users, and between

different user groups (McClaran and Cole 1993).

(b) Constraints, or potential limiting factors, on the amount of information that can be collected, include finances, time, labor, and potential visitor

burden. The motivation to save time and money is almost always operative

in the selection of the methods used to collect data. The budget should be

formulated with contingency planning incorporated in the event of unexpected expenses or budget cutbacks. The potential visitor burden must also

be assessed as a constraint; the use variables to be measured must always be

selected with the goal of placing little or no burden on the visitor.

 3. Prioritization.—There is no management “problem” if there are no goals

to be attained, or no alternative courses of action available. However, it is

inevitable that goals will vary from group to group. For example, the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 9

manager’s first priority may be to protect the resource, whereas visitors,

although agreeing in principle with the concept of wilderness protection, may

nonetheless resent restrictions on their own wilderness experiences. Other

groups may be actively hostile to the entire wilderness concept, or conversely,

they may advocate wholesale wilderness protection at the expense of even

mandated recreational opportunities.

 4. Alternatives.—As a consequence of competing goals, and because of

constraints on finances, time, and other resources for accomplishing the

necessary work, the various objectives will have to be prioritized. Priorities

will be partially determined by the alternative courses of action available for

attaining the objectives. Available courses of action that will be open to the

investigator will be dictated by considering the relative efficiency of each

means, as well as the specific goals to be addressed.

 5. Practical Application.—How the information will be used in the context

of the study should be clearly stated and given a practical working definition.

An example of a general application statement is the manager’s wish to

“learn more about visitor preferences and expectations so that responses to

management changes can be anticipated.” “Learning more” and “anticipating visitor response” are too vague to be useful. A practical redrafting of this

objective would involve:

(a) Identifying one or more specific visitor responses.

(b) Listing the methods of evaluating response.

(c) Setting practical guidelines for identifying changes in response

(that is, some baseline level would have to be identified).

(d) Identifying what management actions could be implemented if the

response is affected.

 6. Scope of Inference.—The scope of the project describes the extent to

which the results can be applied and the future implications of the results.

Identification of Visitor Use Characteristics ____________________________

Once the primary objectives of the study are clearly established, the

investigator must decide on the kinds of observations that must be made. The

use characteristics chosen must adequately characterize wilderness “use” as

defined by the study objectives.

In general, visitor use data may be either quantitative or categorical.

Strictly quantitative data are usually compiled in the form of visit counts.

Count data provide a tally, or overall census, of the number of times an

individual or a group passes a specific site during a certain time period. In

contrast, other types of visitor use data may be a combination of categorical

and quantitative information. These data describe some feature or attribute

of (1) the visit, (2) the visitor, or (3) some aggregate feature of the visit, visitor,

or both. Visit attribute data describe relevant characteristics of visits, such

as length of stay, number of people per group, and activities participated in.

Visitor attributes describe traits characterizing wilderness visitors, such

as experience, demographics, and preferences. Finally, summary use statistics describe aggregate attributes; these provide an additional perspective on total amount of use by combining characteristics of the visit with visit

counts.

In this section we describe several of the most commonly used types of

observations obtained in wilderness use measurement. Data are described in
10 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

terms of their working definitions, methods of reporting, the practical

applications of specific types of data, and, when applicable, the advantages

and disadvantages of certain methods of categorization.

Visit Counts

Visit counts may be recorded as either individual visits or group visits.

Individual Visits

The individual visit count is defined as the total number of single-person

visits made by people that enter (or leave) a given area during a specified time

period, without regard for length of stay. For example, a person making a 2-

week trip into the area is counted as one visit, two people in a group entering

the area for a single visit are counted as two visits, and so on. Conversely, a

person camping outside the area who takes two single-day trips into the

wilderness is counted as two visits.

Reporting.—Typically, individual count data are reported on a per-area

and per-time basis. Individual visits may be tallied for portions of areas. For

example, if there is particular interest in the number of visits along a specific

trail or at a specific destination area, counts of individuals can be confined to

those sites. Similarly, individual visit data may be obtained for relatively

short time periods; for example, on a per-hour, per-weekend, or per-season

basis. Alternatively, individual count data may be combined over areas or

time periods to form aggregate counts. For example, the total number of

visits to wilderness was reported to be approximately 5 million in 1986

(Lucas 1990).

Applications.—Individual visit data are required for devising site-specific

management plans. Since management emphasis is on areas of heavy use,

and use often occurs sporadically during the year, visit counts may be

necessary only during high-use periods, such as the summer season or

holiday weekends. In areas with high day use, the measurement period may

be only in peak periods.

Individual visit totals aggregated at the regional and national level provide

a gross estimate of participation levels. Such estimates provide effective

descriptions of agency output, and are important for monitoring societal

trends and developing demand/supply comparisons. These data may be

critical in regional economic analyses where it is necessary to estimate the

total effect of visitor influx and expenditures on local economies (Cordell and

others 1992).

The individual visit count is the simplest method of obtaining quantitative

data on visitor use. No additional information is required about either the

nature of the visit or the visitor. However, because such factors as length of

stay are ignored, the amount of use occurring in an area may be underestimated.

These data should be combined with other measures of visit information.

Group Visits

A group is defined as a collection of individuals taking a wilderness trip

together. It is implicit in this definition that travel and camping are shared

to some extent by members of the party. This does not preclude separate

travel arrangements to and from the wilderness site (more than one vehicle

could have transported the group to the site, different members of the group

may have originated from different places, arrival and departure times may
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 11

differ), nor does it imply that all members of the group will necessarily be

together the whole time in the wilderness. However, if camping, members of

the group usually share a common site, and much of the traveling time is

spent together.

A group visit count is defined as the total number of single-group visits

made by groups that enter (or leave) a given area during a specified time

period, without regard for length of stay. The working definition is essentially that of the individual count, except that the unit considered is the group

rather than the individual.

Reporting.—As with individual visit counts (see above).

Applications.—Group visit data are relevant if use is heavily oriented

toward organized groups. These data will be of particular interest to management if use-rationing is contemplated, with the objective of limiting the

number of groups allowed access. Restricting access on the basis of groups,

rather than on the basis of individuals, will be appropriate in many cases

because the number of groups is the primary influence on demand for

campsites and influences visitor perceptions of solitude (Roggenbuck and

others 1982).

Visit Attributes

Observations describing attributes of each visit may be either quantitative

(such as group size, length of stay), or qualitative (such as method of

travel, use of commercial services, types of activity, use distribution

patterns, wilderness conditions, visitor perceptions, and so forth).

Various miscellaneous concerns, such as degree of compliance with lowimpact regulations, may also be documented.

Method of Travel

Although a few wilderness areas permit motorized terrestrial and waterbased transport and aircraft landings, these are rare exceptions (Browning

and others 1989). In general, transport in wilderness areas is nonmechanized.

Hiking is by far the most common method of wilderness travel. Ski and

snowshoe travel may be included with hiking (as a form of self-propelled

transport), or documented in separate categories. In many wilderness areas,

other forms of nonmotorized transport, such as canoeing, rafting, and

horseback riding, may approach or exceed hiking. Packstock (for example,

horses, llamas, and goats) are commonly used in wilderness travel.

Reporting.—Specific categories of travel are usually reported as a percentage, or proportion, of the total number of groups or individuals surveyed. If

these data are used to develop population estimates, estimates of the sample

mean should be accompanied by the sample size and an estimate of variation—all of which can be used to express a confidence interval.

Applications.—Both the location and nature (social and physical) of impact

problems will change with major shifts in travel method. Thus, need for

adjustments in management strategies and priorities in a given area may be

acquired by documenting trends in travel methods. For example, repeated

visitor surveys in the Bob Marshall Wilderness revealed that mode of travel

had shifted from predominantly horse use prior to 1970, to predominantly

hiker use by the 1980’s (Lucas 1985).
12 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Group Size

This refers to the number of individuals in a group (or party) of visitors; as

defined above, a group includes all individuals visiting the wilderness as a

unit.

Reporting.—Group size may be treated as either a quantitative or a

categorical variable. As a quantitative variable, group size is usually reported as an average (together with some measure of variation). The most

common (mode) and maximum group sizes are also sometimes reported.

Alternatively, the data set can be partitioned into several group-size classes;

the number of observations in each size class can be used to calculate the

relative proportion of groups in each class. For example, a study of visitors

entering the Bob Marshall Wilderness in 1982 reported a mean group size of

4.7; 61 percent of all groups consisted of two to four people, while only 8

percent comprised more than 10 people (Lucas 1985).

Applications.—Group size data are important for evaluating impact on

wilderness areas, and for the planning, implementation, and assessment of

management strategies for specific groups and types of activities. Information about maximum group size may be valuable in determining if facilities

can accommodate the largest groups. For example, groups travelling with

recreational packstock are generally larger than hiking groups (Watson and

others 1993). Restrictions applying specifically to packstock use may be

necessary because of trail degradation and erosion, and conflict with other

users. Many wilderness areas do not offer sufficient grazing to accommodate

“large” numbers of stock. Thus, reliable information is required to set

reasonable limits to packstock access.

Use of Commercial Services

This information indicates whether the services of an outfitter were used

on the trip and the nature of services provided. Types of service provided vary

greatly between commercial outfits. Many outfitters provide all-inclusive

packages consisting of transportation, equipment, and guides. More limited

services may be provided, consisting only of shuttle service to trailheads,

transportation of gear to a base camp, equipment rentals, or guides. It is

useful to differentiate between the major categories of commercial services

prevalent in any area, and classify groups according to the type of commercial

service utilized.

Reporting.—Data may be reported as either categorical or quantitative.

Categorical information recorded includes type of commercial service provided, extent of services, target groups, major activity of target group, and so

forth. Quantitative information may be appended with categorical data—

proportion of groups utilizing various services, average group size, time of

year, length of stay. For example, hunters use outfitters more than twice as

frequently as nonhunters do; thus, much outfitter use is concentrated in the

fall. However, in other areas, and during warm-weather seasons, river-float

operators will be more prevalent.

Applications.—These data are useful for monitoring outfitter service

allocations and for evaluating the relative necessity for, and impact of,

outfitter services. In addition, these data provide a means of determining the

magnitude of visitor impact on local economies in terms of visitor expenditures, employment opportunities, and income generated (Bergstrom and

others 1990; Watson and Cordell 1990).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 13

Activity Participation

The types of activities visitors engage in while visiting the area are critical

for evaluating consumer use patterns, and potential impact on wilderness.

Examples are on-trail hiking, off-trail hiking, horseback riding, hunting,

fishing, mountain climbing, rock climbing, photography, nature study,

swimming and sunbathing, collecting berries or mushrooms, and spending

time in camp. Less common activities (such as cave exploration, nude

sunbathing, athletic training, and survival training, for example) may be of

sufficient magnitude and impact to warrant documentation and monitoring.

Reporting.—Data are generally presented in a combined format of qualitative and quantitative information. Subclasses may be identified by such

categories as reasons for visit and range of activities engaged in; the number

of observations in each category are used to compute proportion of visitors in

each category. For example, a survey of wilderness visitors in the Bob

Marshall and Linville Gorge Wilderness areas determined the proportion of

visitors participating in hunting and nature study. In the Bob Marshall

survey, the proportion of visitors in each category was 16 percent and 28

percent respectively; in contrast, for the Linville Gorge area, these proportions were 3 percent and 41 percent (Roggenbuck and Lucas 1987).

Applications.—Information on type of activity is important for characterizing differential effects of visitor-expenditure patterns. Specifically, economic impact analysis determines the effect of changes in final demand on

specified economies; the change in final demand is often expressed as a

change in numbers of a certain type of recreation visitor. To date, most

analyses characterize visitor “type” in terms of activities participated in. For

example, short-term users, such as those camping at developed or improved

sites and resort customers making day trips into a wilderness, exhibit

different expenditure patterns (and thus have different impacts on the local

economy) than relatively long-term users do who stay in wilderness areas for

long periods (Watson and others 1989).

Length Of Stay

Length of stay is defined as the total amount of time spent within the

wilderness area boundaries on each trip. It may be calculated by reporting

the date and hour of entrance and exit, or by reporting the total number of

time units spent in the area (hours, days, nights, and so forth).

Reporting.—Length of stay is a quantitative variable; therefore, any

convenient measure of location and variation can be calculated (mean,

median, mode, variance, and so forth). Alternatively, observations can be

partitioned into various time classes (for example: day trip, 2 to 4 days, more

than 4 days, and so forth), and proportions of visits calculated for each

category. For example, a survey of visitors to the Bob Marshall Wilderness

Complex reported a mean length of stay of 4.7 days, and 54 percent of all trips

lasted for 4 days or longer; in contrast, a survey of visitors to the Mission

Mountains Wilderness reported an average length of stay of 1.7 days, with

62 percent of all visits being day trips (Roggenbuck and Lucas 1987).

Applications.—Length of stay can be used as a crude measure of success in

attracting the public to recreation sites (Collings and Grayson 1977). Campsite demand may be assessed by calculating the proportion of visitors that

camp overnight. Relative impact may be assessed by evaluating the proportion of visitors taking long trips of a week or more versus the proportion of
14 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

users making only day trips. Finally, trends in length of stay measures

indicate the need to revise or implement area management strategies.

Temporal Use Distribution

The distribution of use through time measures the extent to which “use” is

concentrated in certain seasons, certain days of the week, or during certain

times of the day. Measures of use distribution can be obtained by reporting

date and time of entry of the individual or group, then categorizing by season,

day of the week, or period of the day.

Reporting.—Use distribution may be reported as the proportion of total

visitation that occurs in each time period (for example, per season, or on

weekends as opposed to weekdays). Alternatively, patterns may be determined by plotting use data in time order.

Applications.—Understanding temporal use distribution is important for

directing management decisions concerning the placement of survey and

maintenance personnel in the field. Data on temporal use are critical in

assessing and predicting rates of deterioration, and formulating strategies to

shift use patterns in time, thus minimizing impact due to temporal crowding.

Spatial Use Distribution

The distribution of use across the area is a measure of the extent to which

it is concentrated on certain trails or destinations. The simplest and most

commonly recorded information is the entry and exit point for each visitor or

group. An alternative is specification of the primary destination for the trip.

Detailed information on internal use distribution may be obtained by

subdividing areas into zones and reporting the time spent in each zone by an

individual or group; alternatively, visitors may provide maps of trip routes

with each campsite noted.

Reporting.—Spatial distribution is reported as area-specific proportion of

total use; for example, the proportion of users in a wilderness area that enters

(or exits) at a specific trailhead. Information on destination may be used to

compute the proportion of visitors that go to particular destinations within

the wilderness.

Applications.—This information can be useful in setting management

priorities and evaluating the extent of use concentration. Educational

messages may be targeted on trailheads that account for a large proportion

of use. Use concentration problems are likely to be particularly severe where

a few trailheads account for a large proportion of total use; these trailheads

will receive priority for development and maintenance. Mapping the amount

of use for specific zones, routes, and campsites within the wilderness is useful

in devising site-specific management plans, predicting spatial distribution

patterns of impact, and anticipating the effect of changes in specific areas on

other sites.

Conditions and Visitor Perceptions

Measures of “conditions” include information on number of encounters

with groups, individuals, or packstock along trails or at campsites; amount

of litter seen; number of encounters with wildlife; and the physical condition

of trails and campsites. Relevant measures of condition will vary from area

to area.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 15

Reporting.—Visitor perception of conditions, and their reactions to perceived conditions, are obtained retrospectively. This is performed via visitor

surveys in which visitors are asked for their subjective assessment of

conditions. Examples include ranking conditions from “very good” to “very

poor”; evaluating numbers of encounters in terms of “too many people,”

“about the right number,” or “too few”; evaluating certain factors, such as

amounts of horse manure on trails, as a “problem” or “acceptable.”

Applications.—This information is commonly collected by researchers in

visitor surveys, but has seldom been part of use estimation systems. However, visitor opinions on current conditions, and how conditions are perceived

to be changing over time, provide valuable auxiliary information for monitoring programs. Because such information provides a good perspective on the

extent to which problems are a concern to visitors, this information can be

used to direct management priorities and strategies.

Miscellaneous Visit Characteristics

Wilderness managers can collect a wide variety of additional information

pertaining to visits; the type of information collected, its relevance, and its

priority need to be carefully considered in the context of the stated objectives

of the study. One example of interest to managers is the assessment of

compliance with low-impact recommendations. Examples of compliance

measures include: the number of groups using stoves instead of campfires,

the proportion of groups with dogs visiting the wilderness, the incidence of

off-trail travel, the proportion of groups exceeding the maximum allowable

number per party, the proportion of packstock groups that hobble or picket

stock rather than tie animals to trees, and so on.

Visitor Attributes

The behavior of wilderness visitors is influenced by the type of activity

participated in, visitor origins and background, and visitor perceptions of

wilderness and its management. The attributes of targeted visitors will

determine certain management priorities, methods of communicating management information, and the relative effectiveness of education programs.

Specific visitor attribute data of interest commonly include sociodemographic characteristics (such as age, sex, ethnicity, and education), level

and type of past experience, knowledge of wilderness conditions and

regulations, and attitudes toward and preferences for management practices and environmental conditions encountered.

Sociodemographics

These variables describe visitors in terms of age, gender, ethnicity, education, occupation, income, and place of residence.

Reporting.—Sociodemographic data are usually collected by categorizing

each individual according to classes established for each of these variables,

and reporting the resulting proportion of visitors in each class. Comparisons

can be conducted with other areas within the wilderness or with other

wilderness areas. For example, a survey of visitor occupation conducted in

the Bob Marshall Wilderness Complex showed 37 percent of visitors were

professional or technical, 18 percent were craftsmen or operators, and 11

percent were students. In contrast, a survey of the Adirondack High Peaks
16 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Wilderness showed that students comprised 43 percent of the sample

(Roggenbuck and Lucas 1987).

Applications.—Management strategies for visitor contact and assessing

relative needs will be affected by the sociodemographic profile of the various

users groups. For example, local versus distant users will require different

methods of visitor contact; relative requirements for developed campsites

close to trailheads will also vary according to the proportion of nonlocal users

in the user population. It has been suggested that the generally high

educational levels of wilderness users should make it relatively easy to alter

behavior through education. This may not be true for a place where a large

proportion of visitors is unusually young and/or poorly educated. Place of

residence information enables managers to target specific populations for

news releases about upcoming management changes, educational programs,

or public meetings. A more general application is the economic assessment

of visitor contribution to the local economy. Economic assessments usually

exclude visitors who live inside the economic region of interest; expenditures

by “outsiders” are evaluated in the context of, for example, location of trip

expenditures, the distance traveled from place of residence to the recreation

site, and the geographic boundaries of the economic region (Bergstrom and

others 1990).

Past Experience

“Past experience” refers to the relative familiarity of the visitor with

wilderness areas and wilderness practices.

Reporting.—There has been little consensus about how to measure “past

experience.” For example, one optional question on the approved Forest

Service Visitor’s Permit (FS-2300-30) is “number of times you visited this

area in past 10 years.” Even without permit information, managers frequently categorize users as either “novice” or “highly experienced.”

Two separate domains, or classes, of experience are relevant: (1) experience

at a particular place, and (2) experience with a particular style of recreation

(Watson and Niccolucci 1992; Watson and others 1991). Within these classes,

experience may be measured in terms of length of time or frequency of visits.

The most commonly used measures of experience include:

(1) the length of time the visitor has been going to a specific wilderness area;

(2) the frequency of visits to the specific wilderness area (either the total

number of times or the typical number of times per year);

(3) the length of time the visitor has been going to any wilderness;

(4) the frequency of visits to any wilderness;

(5) the total number of wilderness areas visited.

Applications.—Visitor management strategies will differ according to user

experience. Experienced users may be more likely to exhibit appropriate lowimpact behaviors, and are therefore less in need of education or regulation.

They may also have more attachment to particular places, be more sensitive

to change, and be more tolerant of management practices involving curtailment of activities geared toward protection of the resource. More direct

management strategies may be needed with less-experienced visitors: safety

risks may be higher and high-impact behavior may be more prevalent.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 17

Visitor Knowledge

Visitor behavior is partially influenced by awareness of appropriate lowimpact practices, regulations, and rationale for management decisions

which may curtail visitor use. Knowledge does not necessarily translate into

practice; lack of compliance may be due to inappropriate behavior rather

than ignorance of appropriate behavior. Inappropriate behavior in defiance

of either regulations or expectations of appropriate behavior may stem from

lack of support for certain management directives. As a result, level of

support for potentially unpopular wilderness uses and practices must also be

assessed (Manfredo and others 1990)

Reporting.—Visitor knowledge may be assessed by questionnaires or

interviews. Visitors are questioned as to their awareness of (1) appropriate

low-impact practices, (2) regulations for the given wilderness area, and/or (3)

rationale for potentially controversial management decisions. Measures of

tolerance or level of support for certain practices or mandates is obtained by

asking visitors for their subjective assessment of each issue and ranking level

of tolerance (for example, “problem” versus “acceptable”; “do not support,”

“indifferent,” “strongly support”).

Applications.— Where levels of knowledge are low, it may be important to

increase education. The success of educational programs can be assessed by

periodic evaluations of visitor knowledge of appropriate low-impact practices

or regulations in the area. Knowledge of, and level of support for, appropriate

but unpopular management mandates (for example, domestic livestock

grazing, permitting certain fires to burn) are likewise important to assess on

a regular basis (Manfredo and others 1990).

Visitor Attitudes and Preferences

“Attitude” and “preference” information is a means of assessing (1) the

qualities and characteristics of the wilderness experience important to the

visitor, (2) how these expectations are met in practice, (3) current levels of

“satisfaction,” (4) “satisfaction” in comparison with previous visits to the

wilderness area or visits to other areas, and (5) perceived “defects” or causes

of dissatisfaction. Topics for assessment include both conditions encountered

in a specific wilderness setting and opinions on management.

Reporting.—Visitor attitudes and preferences may be assessed by questionnaires or interviews. There are three aspects to attitude/preference

information: (1) definition of the characteristic to be measured, (2) specification of alternatives, and (3) conflicts.

It is critical that intangibles such as “attitudes” and “preferences” are given

a concrete working definition in terms of a number of measurable attributes.

This will be accomplished within the context of the stated objectives of the

study. For example, visitors may place a high premium on the “quality” of a

wilderness experience. However, “quality” may be defined in a number of

ways. For example, “quality” may be expressed in terms of “solitude” (for

example, number of encounters per trip, number of groups camping within

sight or sound, visibility of lights originating from outside the wilderness

area), “lack of observed habitat degradation” (for example, number of

encounters with wildlife, amount of litter seen, perception of trampling

damage), “provision” of certain goods and services (for example, number of

designated campsites, number of stock corrals). Alternative attitudes and
18 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

preferences may be expressed negatively in terms of characteristics which

create dissatisfaction or are perceived as defects. Finally, a number of visitor

preferences and attitudes will likely conflict. Within a particular user group

certain characteristics may rank as desirable, whereas others will rank low;

for example, a wilderness area may be excellent from the standpoint of

“facilities” provided, but rank low from the standpoint of various measures

of solitude. Conflicting attitudes and preferences may exist between user

groups; for example, hikers may be relatively tolerant of llama users,

whereas horse users may not.

Applications.—Knowledge about attitudes and preferences gives valuable

information on both the motivation of the visitor and on possible courses of

action for management. These data can be used as valuable input to selection

of indicators and standards for conditions (Lucas and Stankey 1985). This

information can be used to design quality recreation experiences and to

identify and either avoid or predict response to management actions.

Summary-Use Statistics

Frequently, measures of visitor use are reported as a combination of

several different use measures, forming a new, aggregate variable.

Visitors

This refers to the total number of people that visit an area during some unit

of time, usually a year. One person would be recorded as one visitor,

regardless of how many times he or she visited the area during the year.

Reporting.—This index is difficult to calculate. A crude measure is the

count of all visits to the defined area, summed over the period of time of

interest. Alternatively, the total number of visitors to an area may be

estimated as the ratio of the total number of individual visits to the estimated

mean frequency of visits, if this information is available.

Applications.—This index is used as a measure of the proportion of either

a particular population, or of society in general, that derives recreational

benefits from a wilderness.

Visitor-Day

A visitor-day is defined as one 24-hour day spent by one visitor at a given

site.

Reporting.—A visitor-day is calculated as the product of the number of

visits and length of stay (in days); in effect, the visit count is weighted by the

time involved. If group counts are obtained, the visitor-day index can be

obtained if information on group size is available.

Applications.—To determine use by specific categories of interest, total

visitor-days may be categorized by user type, method of travel, activity, and

so on. This requires data on the proportion of time spent engaged in each

activity, as well as length of stay.

Visitor-Hours

This is calculated in a manner similar to visitor-days, in that 1 visitor-hour

is defined as 1 hour of recreation at the site. Thus, one person spending 12

hours onsite is recorded as having spent 12 visitor-hours, a two-person group

spending 1 hour at the area would be described as 2 visitor-hours, and so on.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 19

This index is not in common use. If length of stay can be measured to the

nearest hour, it may be a more accurate measure than visitor-days.

Overnight Stays

One overnight stay is defined as the presence of one visitor over one night.

The aggregate is the total number of nights spent by all individuals in the

area. This index is calculated as the product of the number of individual visits

and the number of nights spent during each visit. Day use does not contribute

to the calculation of overnight stays.

Reporting.—Calculation of this index is affected by the measurement

technique used to collect the data. If a mechanical counter or observer is used

to record individual visits, the resulting estimate of total visits is multiplied

by an estimate of the mean length of stay, expressed in number of nights.

(Day users are recorded as having stayed zero nights). If visits are recorded

by means of registration stations or permits, the number of nights per visit

may be obtained simultaneously. If each individual visit is recorded, the

aggregate measure is obtained by summing the data. If group data are

obtained, group size is multiplied by the number of nights the group stayed;

the resulting value is summed for all groups.

Applications.—This is the standard unit for backcountry and wilderness

use in the National Park Service. Information on overnight stays can be used

as a measure of campsite impact and usage. However, the proportion of day

excursions are common in many wilderness areas, and vary in frequency

between areas; thus the overnight stay may be an incomplete measure of

total use.

Recreation Visitor-Days

A recreation visitor-day is defined as 12 hours of recreation at the site. One

visitor-day can be one person inside a wilderness for 12 hours, or two persons

present for 6 hours, and so on.

Reporting.—As with overnight stays, both a measure of number of individual visits and a measure of length of stay are required. If mechanical

counters or observers are used, the number of individual visits is multiplied

by mean length of stay (expressed in 12-hour units). Alternatively, the mean

length of stay (in hours) is multiplied by the number of individual visits and

the product divided by 12 to get total recreation visitor-days. Where data are

recorded on registers or with permits, the number of visitor-days is recorded

for each trip and summed.

Recreation visitor-day measures may be combined with other visit characteristics. Examples include reporting the number of recreation visitor-days

by transportation method (for example, horse users or hikers), activity

categories (for example, hunting, skiing, or hiking), and type of commercial

service used (for example, fully outfitted trips, drop trips).

Applications.—This is the standard unit used by the Forest Service for all

types of recreational use. This index accounts for both day and overnight use,

and is therefore one of the better measures for comparing total amounts of

use.

A major source of inaccuracy is the difficulty of assessing lengths of stay

shorter than 12 hours. Where day use is common, estimates of visitor-days

may be highly inaccurate unless some means of reporting or estimating

length of stay (in hours) is built into the system.
20 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Chapter 2: Visitor Use

Estimation Techniques

After it has been decided what data are to be collected, the manager must

select a specific measurement technique and/or device for collecting those

data. The most appropriate data collection technique is one that is capable of

providing the data required with a sufficient level of accuracy while maintaining both management costs and visitor burden at acceptable levels.

This section discusses various techniques available for the systematic

collection of wilderness use data. A summary of use estimation techniques

and range of application are given in table 1. Nonsystematic techniques and

methods based primarily on guesswork are not included. Each technique is

described in terms of (1) specific methods and equipment required, (2)

visitor use characteristics (the type of data) that can be obtained, (3)

visitor burden, (4) management costs associated with equipment purchase and setup, and data collection, and (5) accuracy. Comments are

added as applicable.

External Visual Observations ________________________________________

Methods.—This technique involves the visual observation of individuals or

groups outside the wilderness area; that is, as they enter or leave. Human

observers can be stationed at, or close to, trailheads to observe visitors and

record visitor use characteristics required by the study. Direct observation is

most feasible for an area with (1) a small number of access points which

account for a large proportion of total use, or (2) a program in which visitors

are regularly contacted by agency or volunteer personnel at access points.

Indirect observation methods include movie cameras or video recorders

Table 1—Summary of visitor use estimation techniques.

Technique Use characteristicsa Visitor burden Management costs Accuracy

External visual observation 1 2 3 5 None High Variable

Stationary internal observation 1 2 3 5 6 None Variable Variable

Roaming internal observation 1 2 3 5 6 None Low Low

Mechanical counters 1, 6 None High High

Registration All Low Moderate Variable

Permits All Moderate to high Variable High

Surveys All Moderate High Variable

Indirect estimation 1, 5 High → low High → low Variable

Aerial surveys 1, 2?, 3?, 5?, 6? High High ?

a

Specific use characteristics are indicated as follows: 1 = Individual/group counts; 2 = Group size; 3 = Method of travel; 4 = Length of stay;

5 = Activity type; 6 = Use patterns; 7 = Nonobservable characteristics (sociodemographics, attitudes, experience, etc.); ? = Unknown
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 21

(modified to expose one frame at a time), or single lens reflex cameras

modified to shoot one frame either at pre-set intervals or when triggered by

visitor traffic. A mechanical counter may be used to signal visitor presence.

Observations are recorded by viewing the film in the office at a later date. An

example of a typical data sheet for reporting observations obtained from

either direct or indirect observations is shown in figure 1.

Systematic observations should be directed by a formal sampling plan.

Sampling may be randomized across access points; alternatively, stratified

sampling plans may be used, with strata consisting of access points or specific

time periods (for example, weekday/weekend or holiday/nonholiday). Care

must be taken to assure coverage of visitors entering (or leaving) in the very

early or late hours of the day.

Visitor Use Characteristics.—Data obtained by this method can include

the number of individual or group visits, group size, method of travel, location

of entry or exit, and date of entry or exit. Gender and age estimates may

occasionally be determined, but individuals may not always be distinguishable. Likewise, although day and overnight users can be distinguished by the

amount of gear carried, it is generally not possible to determine length of

stay.

Visitor Burden.—None. Visitors are not contacted, and may not be aware

that they are being observed.

Management Costs.—Relatively high. Substantial personnel time is required, regardless of whether cameras or human observers are used to

monitor visitor traffic. When human observers are used, the primary costs

are personnel time, wages, and transportation. Costs can be reduced somewhat if volunteer labor is available, or if personnel are able to combine

observations with other tasks in the vicinity of observation points. When

cameras are used, costs include equipment (cameras, traffic counters, batteries, a film editor, film), film processing, personnel and transportation costs

associated with locating, maintaining, and periodically moving the equipment, and costs associated with film viewing.

Accuracy.—Variable. Considerable sampling effort is required for even

modest levels of accuracy (Roggenbuck and Lucas 1987). Accuracy is reduced

if sampling intensity is low, the sampling plan is poor, or if there is no

commitment to following the plan. Because data obtained from human

observers are highly accurate, human observers are the preferred method of

data collection. Large variation in response and equipment failure reduces

the accuracy of mechanical counters; if mechanical counters are used, data

collected from human observers should always be used to assess the accuracy

of mechanical counters. Nonsystematic methods for obtaining observations

are used frequently; however, unknown sources of bias associated with

haphazard data collection result in data of dubious or no value.

Comments.—Possibly because of the expense involved, systematic visual

observation is not in common use. Nonsystematic visual observations are

used frequently; however, nonsystematic methods result in worthless data.

The most common mechanized method in use is a video- or camera-based

system triggered by a traffic counter. Limitations include high rates of

maintenance (for example, 35-mm cameras can provide a maximum of only

36 exposures per roll of film, thus requiring frequent visits to replace film),
22 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

WILDERNESS AREA

VISUAL OBSERVATION DATA SHEET

Date _______________________________________ Weather ________________________________________

Sample time _________________________________ Location ________________________________________

Observer ____________________________________ (Example of Observable Visitor Characteristics)

 Age (approx.)

Group Group Exit/ Overnight Mode of <= 17- 31- 46- Over

 # size Time Entera or day useb travelc # dogs 16 30 45 55 55

 1 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 2 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 3 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 4 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 5 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 6 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 7 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 8 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 9 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 10 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 11 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 12 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 13 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 14 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 15 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 16 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 17 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 18 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 19 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

 20 _____ ____ _____ ____ ____ ___ ___ ___ ___ ___ ____

____________________

a1 = Exit, 2 = Enter

b0 = Unsure, 1 = Day use, 2 = Overnight

c1 = Foot travel, 2 = Horse, 3 = Hike with packstock, 4 = Water craft

Figure 1—Sample data recording sheet for observable visitor characteristics.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 23

equipment obsolescence (for example, obtaining, developing, and viewing

film for 8-mm movie cameras is an increasing problem), and expense.

There are ethical, and sometimes legal, concerns about using cameras to

observe visitors. Privacy can be safeguarded by (1) adjusting distance or focus

so that individuals cannot be identified, and (2) destroying the film after

observations are recorded. In Canada there is a legal requirement to post a

notice that observation monitoring activities are occurring. Only public areas

through which visitors pass should be filmed, not campsites or swimming

areas (Lucas and Kovalicky 1981).

Internal Visual Observations: Stationary ______________________________

Methods.—Observations are taken only at specific locations within the

wilderness area. For example, if the objective is to assess visitor use along a

particular trail segment, or at a particular destination, cameras or human

observers are installed along the specific trail segment or at all entrances to

the destination area.

Visitor Use Characteristics.—Data include the number of individual or

group visits, group size, method of travel, and date of entry or exit. Additional

information such as gender and approximate age may be determined, but

individuals are not always distinguishable. Summary visitor use statistics,

such as overnight stays and recreation visitor-days, can be compiled for

destination areas. Examples of spatial use-pattern information that can be

obtained are (1) order in which available campsites are selected, and (2) use

intensity at specific target areas at destination sites (such as lakeshores).

Visitor Burden.—None. Privacy concerns must be considered because

observations are made at places where people expect privacy. When cameras

are used, they should be slightly out of focus and the film should be destroyed

after information is recorded.

Management Costs.—Variable. Costs may be relatively high if there are a

number of remote locations to be monitored; substantial transportation costs

are associated with maintaining cameras or observers in a number of remote

locations. However, if only a few sites are to be monitored, or sites are close

and popular, total costs may be relatively low. Use of observers is likely to be

more cost-effective than use of cameras; systematic observations by employees or volunteers located at a popular destination may add little additional

cost beyond normal operations.

Accuracy.—Variable. As with external observations, accuracy depends on

the adequacy of sampling. Although nonsystematic observations are commonly made, data collected haphazardly are biased, and therefore are of little

or no value. Mechanical equipment, such as cameras, are liable to failure;

equipment must be maintained, checked, and calibrated at regular intervals.

Comments.—Internal visual observation with human observers is in

relatively common use. If use is to be estimated for a few popular destinations, and personnel have other things to do, this technique can provide costeffective results. However, if visitors are relatively uncommon, observer

boredom and fatigue can be a problem; as a result, there may be no

consistency in sampling, or observers may fail to adhere to the study plan

after a time. Mechanical equipment, such as cameras, are liable to failure;
24 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

equipment purchase and setup can become prohibitively costly if more than

a few places need to be observed.

Internal Visual Observation: Roaming_________________________________

Method.—Visitors are observed during wilderness ranger patrols; patrols

are commonly scheduled for times or areas known to have heavy use.

Visitor Use Characteristics.—As above. The most useful application is to

obtain estimates of the number of overnight stays, tabulated by trail section

or destination area within the wilderness.

Visitor Burden.—None. Visitors are not contacted, and may not be aware

that they are being observed.

Management Costs.—Low. Data are collected during routine wilderness

ranger patrols.

Accuracy.—Low. Because scheduling is not random, but deliberately

selected to coincide with periods of heaviest use, this type of counting results

in highly biased measures of visitor use. Lucas and Oltman (1971) cautioned

that the “roaming technique” cannot yield a definable probability sample.

This is because the probability of any person being contacted depends on

where the observer travels, and these probabilities will generally be unknown to the observers. For example, if the observer is deep in the wilderness, there is zero probability of counting people who make short trips; the

probability of counting people who hike off trails is proportional to the

amount of time the observer spends offtrail; the probability that a user will

be enumerated is directly proportional to the length of time spent in a given

area, and so on. A reasonably accurate visitor count can be obtained if ranger

movement occurs in the reverse direction of anticipated traffic flow (Schreuder

and others 1975); however, such planning is generally impossible for wilderness areas.

Comments.—Techniques and strategies for observing visitors as an observer passes through the area have never been refined and tested. The

difficulties involved with counting mobile traffic with a roaming observer are

obvious. Systematic sampling strategies must be incorporated into this

method to obtain unbiased data. Further research as to appropriate strategies is required.

Mechanical Traffic Counters_________________________________________

Methods.—The three most commonly used types of trail-traffic counters

are photoelectric, sensor-plate, and loop-type counters. Detailed information

on suppliers, specifications, options, and prices (2000) is given in table 2.

1. Photoelectric counters consist of a scanner that emits an infrared beam,

and a reflector that returns the beam to the scanner; the counter is advanced

when the beam is interrupted (active infrared detection), or if the sensor

detects body heat and motion (passive infrared). Counts, and date and time

to the minute can be recorded. Group counts can be registered if counters

have a programmable delay that can be set to avoid multiple counts from one

group. Photoelectric counters may activate cameras; cameras may be used

either to record use directly or to calibrate the mechanical counters. Timers
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 25

Table 2—Specifications for trail traffic counters and associated equipment.

Type Supplier Model Specifications Cost

Photoelectric Diamond Traffic Products, TTC-442 Sensitivity: 110 ft Counter: $399

Oakridge, OR Power source: 4 D-cell batteries with 35-mm camera: $1215

(541) 782-3903 Operational Lifea: 12-15 months with video camera: $2245

Trailmaster TM-550 Weight: 12 oz. Counter: $180

Lenexa,, KS Sensitivity: 65 ft, width 150°, height 4°. Data collector: $250

(913) 345-8555 Temperature range: –40° to +120°F. Printer: $250

Power source: 4 C-cell batteries 35-mm camera: $290

Operational life: 1000 events, 1 year

TM-700V as above, range to 100 ft, Counter: $595

Activates video camera video camera: $1200

Power source: 4 C-cell batteries weatherproof housing for

Operational life: 3-6 months video camera: $950

TM-1000 Sensitivity: 90 ft Counter: $205

Temperature: –40° to +130°F

Power source: 4 C-cell batteries

Operational life: 1000 events, 30-90 days

TM-1500 as above

Compu-Tech Systems, PIR-70 Passive infrared sensor system CALL FOR PRICES

Bend, OR Size: 3" x 6"

(503) 389-9132 Sensitivity: 100' x 4' x 2'

Temperature: ?

Power source: 3 AA batteries

Operational life: up to 2 years

TR-41 series Counters

41IR Size: 4" x 5"

Power source: 2 N-cell batteries

Operational life: up to 4 years

41 Size: 4" x 6" CALL FOR PRICES

Power source: 4 D-cell batteries

Operational life: up to 1 year

Seismic Compu-tech Systems TSP-45 Weight: 3 lbs.; 3" x 10" CALL FOR PRICES

(pressure- Sensitivity: 100 yds.

sensitive) Temperature: ?

Power source: 8 AA batteries

Operational life: up to 3 months

Loop-type Interprovincial Traffic ADR-1000 Weight: 2.6 kg Counter: CAN $1150

Services, Sensitivity: Variable

Surrey, BC Temperature: –40° to +60°C

(604) 594-3488 Power source: 3 to 6 V rechargeable

sealed lead acid battery (solar power option)

Operational life: 40 days

ADR-2000 Data collector (include PC software) Collector: CAN $1095

Size: 0.75 kg; 10 x 20 x 5 cm (Price includes batteries,

Temperature: –20 to +50°C RS232 connector for

Power source: 1 to 9 V alkaline battery downloading to a microcomputer, computer software for calculating

summary statistics,

and shipping costs).

Spare battery: CAN $235

Battery charger: CAN $150

aOperational limit before unit must be reset, recalibrated, recharged, or resupplied.
26 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

may be set to take photographs automatically at specified time intervals

during the day.

Careful site selection and proper installation are critical to ensure accurate

counts (Deland 1976). Scanners and reflectors must be mounted at about

waist level, so there must be trees or posts on each side of the trail. Scenic

overlooks or level areas at the top of steep grades should be avoided; in these

areas people tend to stop and move back and forth across the beam of the

counter, resulting in inaccurate counts. If counts of individual visitors are

desired, it is important to select a place where trail users must pass single file

and cannot detour around the counter. It may also be important to place the

counter far enough along the trail to avoid the most casual visitors—those

who do not actually travel along the trail a significant distance.

Because visitors may tamper with, vandalize, or steal counters, counters

must be concealed and secured. There must be adequate cover to conceal or

camouflage the counter and the reflector. However, counter housing also

affects relative security. Counter housing varies with manufacturer; for

example, TrailMaster counters are housed in plastic exteriors mounted with

nylon straps, whereas Diamond Traffic Products counters are contained in

heavy steel exteriors. Securing the unit to trees with screws or bolts stabilizes

the equipment on the tree trunk and makes equipment more difficult to

remove, leaving only the plastic reflector susceptible to vandalism.

2. Sensor-plate counter (seismic sensors). Pressure-sensitive sensor plates

or mats are buried in the trail; sensors are connected to the counter unit

concealed off-trail. The sensor mat is installed 6" to 8" below the ground

surface; to ensure that visitors cross in single file, the sensor is located in a

narrow portion of the trail (36" to 40" wide) in an area that is relatively flat

and free of large rocks.

The counting unit should be concealed in a location where disturbance will

be minimal. The dust cover which fits over the liquid-crystal display of the

counter may be camouflaged with dirt and plant material. Connecting wires

(available in lengths up to 50 feet) must also be buried for concealment. The

counter must be adjusted for both sensitivity and length of delay between

readings; these must be set carefully to avoid multiple counts for people,

horses, or groups. Counters may activate cameras or be connected to other

sensors if other applications are desired. Different types of seismic sensors

may be required according to the type of ground cover. For example, sensors

used to detect cross-country skiers on snowpack will have different specifications from sensors used to monitor hikers on hard-packed dirt trails.

3. Loop-type counter. This is a relatively new type of mechanical counter

which employs microprocessor technology to store data. The counter is in the

form of a large loop (approximately 8" by 48"), which is concealed under a

layer of earth or snow (or any convenient form of covering) in the center of the

trail. Impulses triggered by visitors (hikers, horses, or skiers) passing over

the loop are stored as counts in the memory unit of the device; date and time

may also be recorded. Data may be retrieved, and the counter reset, by using

a radio transmitter and receiver, or stored.

In general, counters should be located such that travel time to and from the

counting location is minimized; however, it is also important to place the

counter far enough from the trailhead to be reasonably confident that

everyone who trips the counter actually enters the wilderness area. Initial

setup for both photoelectric and sensor-plate counters takes approximately

1 hour; this includes setting the sensitivity and time-delay, and concealing
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 27

Photo-electric counters emit an infrared beam, and a reflector returns the

beam to the scanner. Careful site selection and proper installation of photoelectric counters are critical to ensure accurate counts.
28 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

the unit. The units are battery-powered; therefore, primary maintenance

requirements will be battery replacement, and if camera attachments are

included, units will have to be checked for mechanical failure and film

replaced at regular intervals. The equipment is lightweight, reasonably easy

to conceal, has a reasonably long operational life, and functions under a wide

range of weather conditions.

Visitor Use Characteristics.—Data obtained from mechanical counters are

restricted to individual or group counts, and the location and extent of use

during a specified time period (between counter readings). However, when

combined with visual observations, data can be obtained for group size,

method of travel, approximate length of stay (overnight versus day use) and

gender and approximate visitor age. When counters are used near trailheads,

additional information will be required to estimate distances traveled and

use patterns within the wilderness area. For example, in the Great Smoky

Mountain National Park, only 25 percent of trail users counted with a

mechanical device hiked beyond 1⁄2 mile from the parking lot on one trail,

while more than 50 percent completed an 8-mile round trip on another trail

(Burde and Daum 1988).

Visitor Burden.—None. Visitors unknowingly trip the counting mechanism when passing the counter trigger.

Management Costs.—High. Equipment requirements and costs are outlined in table 2. Associated personnel costs (wages, time, and labor) are

incurred with installation, maintenance, and calibration of the counters.

Installation time will vary by the method selected. For example, selection of

an appropriate site depends on both the nature of the counter, as well as the

need for concealment; adjusting the aim of infrared beam is tricky. A possible

option to incurring the large initial expense of equipment purchase and

installation involves cooperation with state highway transportation departments. Because these departments already possess traffic counting equipment and experience with calibration and maintenance, managers may

prefer to explore this possibility rather than duplicate equipment and

training.

The greater the number of access points that need to be monitored, the

higher the cost is going to be for equipment and maintenance. Calibration is

expensive if performed on a regular basis; to check the validity of mechanical

counters, either human observers will have to periodically observe use, or

cameras will have to be installed and film viewed. Rarely, visitors or wildlife

may damage counter equipment, necessitating equipment replacement.

Accuracy.—High. However, accuracy is high only if care is taken in installation and calibration, and routine maintenance is performed. Accuracy is

seriously compromised if battery power runs low or other mechanical failure

occurs, or if calibration procedures are neglected. The sampling effort

required will be substantial because of high variability in certain classes of

visit and visitor characteristics (for example, group size or gender); accurate

estimates of such groups will require large sample sizes.

It is extremely important that units are calibrated on a regular basis.

Counter readings are subject to many sources of inaccuracy. For example,

wildlife using the trail may not be differentiated from people; passive

infrared counters may count even small animals which are not on the trail.

Sensitivity of sensor-plate counters, if set too high or too low, will over- or

underestimate use. Therefore, readings must be validated independently.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 29

Counter readings can be calibrated by visual observation, either by people or

with cameras. Use of field personnel has the advantage of making it possible

to derive additional information on visitor use. Counter sensitivity and delay

may be adjusted in some cases to match counter readings with observations.

Any residual difference will have to be accounted for through correction

factors.

Most operational problems are related to improper initial setup and

installation. Most devices are resistant to false tripping when correctly

installed. However, significant counter error associated with photoelectric

sensors may occur as an indirect result of various environmental factors: for

example, wind-induced sway of the tree on which the counter or reflector was

fastened, snow and fog, and falling leaves.

Comments.—Traffic counters are used relatively frequently; however,

calibration is usually sporadic at best. This is unfortunate because unless

equipment is calibrated against a known and accurate standard, use estimates will be highly inaccurate and misleading. Traffic counters may be

much less expensive than direct observation, but costs increase greatly with

the frequency of calibration.

Because of counter bias and errors induced by mechanical failures, use

estimates obtained from counter data are usually much less accurate than

those obtained by visual observation. A less-expensive and highly efficient

strategy combining both methods could employ visual observation at highuse areas, and mechanical counters (calibrated with cameras) at low-use

areas.

Registration ______________________________________________________

Methods.—Visitors voluntarily register by filling out survey cards before

entering the area, and use characteristics are obtained from the resulting

information. Registration stations are usually unstaffed and located at, or

close to, trailheads; registration stations may also be located at staffed visitor

centers or ranger stations.

The distinguishing feature of this technique is that registration is voluntary. However, the location, design, and maintenance of registration stations

all influence the likelihood of visitor registration. Stations located a mile or

two up the trail have considerably higher registration rates than stations at

trailheads (Petersen 1985). This observation suggests that criteria for a

“good” location include lack of competing information, a reduced concern

with packing up and getting on the trail, and opportunities to stop or rest.

Places where users are likely to stop are points of interest, a scenic view, a

stream crossing, the top of a hill, terrain allowing users (especially stock) to

stop safely and easily, or an area where the station is easily seen by

approaching visitors. Registration by stock users is difficult to obtain;

targeting stock users by installing registration stations at stock-unloading

facilities may increase registration rates.

Registration rates are increased if registration stations are marked by an

attractive sign. The message on the sign should (1) clearly and simply explain

the purpose of collecting information from visitors (Petersen 1985), and (2)

provide clear instructions as to what the visitor is expected to do. Registration stations should be maintained on a regular basis, keeping them supplied

with registration cards and pencils and collecting the completed cards.
30 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Figure 2—Voluntary registration card as used in the Bob Marshall Wilderness, MT.

One variation of the registration technique is to have visitors complete

registration cards both when they enter and when they leave the area. This

system has been tested in National Park backcountry and in some Forest

Service wilderness areas. Visitors pick up two cards when they enter the

area. They are asked to fill out and leave the first card when they pass the

registration station, and to complete the second card during their visit and

deposit it when they leave the area. One variation is to affix a postage stamp

to the second card so it can be sent in from the visitor’s home, if he or she

forgets to deposit it upon exit. More visit characteristic information can be

obtained by this method than by standard registration techniques; for

example, routes of travel, points of entry and exit, social and resource

conditions encountered, and reactions to those conditions, and more accurate

estimates of length of stay. Because many trips do not last as long as

originally expected (van Wagtendonk and Benedict 1980), length of stay is

usually overestimated when data are obtained from visitors before their

trips.

The disadvantages of this technique are that (1) registration rates would

likely vary for the two cards, and both would have to be estimated, (2)

clearance by the Office of Management and Budget (OMB) of any questions

not currently approved for visitor registration must be obtained, (3) this

technique is not in sufficient use to be evaluated rigorously. However, it

offers several advantages over standard registration formats. More information can be collected than with standard registration cards, at little added

cost to visitors or to managers. It seems to be particularly useful for more

remote places when managers are interested in getting information on

conditions that visitors encounter (such as the number of people they meet)

or in their satisfaction with conditions and/or management. It is a much
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 31

cheaper method of collecting this information than by the more commonly

used visitor surveys.

Estimation of registration rates remains a challenge, particularly at

remote places. However, pilot tests using cameras to estimate registration

rates have found sufficiently high rates of registration by hikers at remote

access points to allow highly accurate estimates of use.

Visitor Use Characteristics.—The types of information that can be collected are constrained only by what can be placed on a registration form.

Currently, the Forest Service uses a card that has been approved by the

Office of Management and Budget (OMB) (fig. 2). The OMB-approved Forest

Service visitor registration form (FS-2300-32) provides information on the

number of individual and group visits, group size, method of travel, length

of stay, entry and exit locations, destinations, dates of entry and exit, and

place of residence. The number of overnight stays can be calculated and

recreation visitor-days can be estimated.

Additional information may be collected for other purposes. If visit or

visitor characteristic data are required beyond what is on the registration

form, a sample of registrants could be asked the supplemental questions.

This information, in conjunction with an estimate of registration rate, would

allow the manager to predict these additional items for the population of

registrants. For example, suppose the manager wished to determine how

many visitors had made previous visits to the area, as a means of estimating

how many novice versus how many experienced visitors the area might be

expected to accommodate each year. A sample of registrants would be

surveyed. Then, if it were determined that, for example, 20 percent of hikers

and 60 percent of stock users had made previous visits, these data can be

applied to the larger population estimate of users to obtain an estimate of

novice versus experienced visitors of each use category which enter the area.

Variations in survey cards must receive prior approval from OMB. It

should be noted that registration rates are likely to decline if too much

information is requested.

Visitor Burden.—Low. Registration is voluntary, and it takes little time to

fill out a survey card. If the station is suitably placed at a point that visitors

would naturally stop, registration is more convenient. However, associated

visitor burden is higher than for visual observation or traffic counts.

Management Costs.—Moderate. Registration stations must be constructed

and installed. Location will influence registration rates (as indicated previously) as well as the relative incidence of vandalism; stations located a ways

up the trail from the trailhead have higher registration rates and are less

prone to vandalism. However, because transportation time increases, distant stations are more costly to maintain.

Stations must be maintained on a regular basis by supplying them with

cards and pencils, and collecting completed survey cards. Data must be

compiled on a regular basis. The time commitment is probably comparable

to that involving the use of traffic counters, and is less than that associated

with visual observation. Checking registration rates requires additional

time and equipment (if cameras are used); however, time and equipment

needs are not likely to be substantially higher than that required to calibrate

traffic counters.
32 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Accuracy.—Variable. The level of accuracy depends on maintenance of the

station and the adequacy of registration rate estimates. If funding is

insufficient to keep stations supplied with cards and pencils, the resulting

data will be of dubious value. However, estimation of rates of registration is

the most critical factor in the estimation of total visitor use.

Data will not be accurate if registration rates are unknown or only crudely

estimated. Estimates of registration rates are necessary because registration is voluntary and there is no official sanction against not registering;

therefore, a large and variable proportion of visitors do not register.

Registration rates vary greatly between location (for example, rates for dayuse horseback riders range from a low of 0 percent in the Bob Marshall

Wilderness (Lucas 1983) to 89 percent in the Rawah Wilderness (Roggenbuck

and Lucas 1987)), main activity (hunters register at a lower rate than

hikers; hikers register at higher rates than horse users), length of stay

(overnight users register more frequently than day users do), party size

(large parties have higher registration rates than small parties have), place

of residence (visitors who come from far away register more often than local

people do), time of day (those arriving after 6 p.m. were less likely to register

than those arriving at other times; Leatherberry and Lime 1981), season of

visit (spring and fall visitors were less likely to register than summer

visitors), and frequency of previous use of an area (Wenger and Gregerson

1964).

Registration rates can be determined in a number of ways, including

visual observation by human observers and the use of sensor-triggered

cameras. The most common and cost-effective techniques used in recent

years is a movie camera triggered by a photoelectric counter (Roggenbuck

and Lucas 1987), or human observers stationed at high-use entrances.

Estimates of registration rates used to correct for nonregistering visitors

are called the “expansion factor.” For example, if only 50 percent of users

register, registration data will need to be doubled to obtain a representative

visitor total; therefore, the expansion factor is 2. Accuracy is greatly

increased if separate registration rates and expansion factors are calculated

for different subgroups of the population. Alternatively, if it can be assumed

that the mix of visitors using a given trail is relatively stable, registration

rates and corresponding expansion factors can be calculated for each

separate trailhead.

Comments.—Registration is relatively inexpensive and places little burden on the visitor. The major consideration is the requirement for reliable

estimates of registration rates. Although methods of estimating registration

rates are neither highly complex nor expensive, many managers fail to

commit necessary resources. As a result, much registration data collected is

of unknown accuracy, and is therefore useless for estimating wilderness use.

Permits _________________________________________________________

Methods.—Permits are use-authorization forms issued by the agency. In

many cases, the available number of permits is limited to control amount of

use in a wilderness area. Permits may be obtained from the agency office, by

mail, over the phone, in person, or may be self-issued; self-issued permits are

usually obtained at the trailhead or immediately outside agency offices.

Visitors fill out the permit, leaving a copy at the station and taking the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 33

original with them on their wilderness visit. General permit categories are

summarized as follows:

1. Source of issue. Permits may be self-issued or issued only by agency

personnel.

2. Restrictions on type of use. Use allowed by permits may be either limited

or unlimited.

3. Restrictions on type of user. Permits can be required for all users, only

overnight users, only overnight users during high-use times (for example,

summer weekends). Combinations are also possible. For example, the Desolation Wilderness has a limited number of agency-issued permits for overnight users, whereas there is (currently) an unlimited number of self-issued

permits available for day users.

Permit format must be approved by OMB; Forest Service-issued visitor

permits are authorized under the same OMB clearance (0596-0019) as the

registration form.

Visitor Use Characteristics.—As with registration data, the information

that can be collected is constrained by what can be placed on the permit form.

A sample OMB-approved permit is shown in figure 3. Data obtained from

permits can include number of individuals/groups, group size, method of

travel, length of stay, entry and exit locations, destinations, routes of travel,

dates of entry and exit, and place of residence. This information may be

sufficient to estimate other categories of use, such as number of overnight

Figure 3—OMB-approved mandatory permit form.
34 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

stays and recreation visitor-days. Information on other types of visitor

characteristics, such as gender and age, can be obtained if permits are issued

at offices, or during compliance checks.

The Forest Service permit includes two optional questions which may be

completed if the permit is issued at the agency office. These are:

(A) “The number of times you visited this area in past 10 years”

(B) “Is visiting this area (1) the primary purpose of your trip away from

home, (2) one of several important things you planned to do on your trip, or

(3) something you decided to do after arriving near the area?”

The National Park Service backcountry use permit includes the same basic

information as the Forest Service visitor registration and visitor permit.

However, the Park Service requires more specific information on camping

locations; the two optional questions are not included.

Visitor Burden.—Relatively high. One component of burden may be the

perceived sense of regimentation and control implied by permits. Burden is

increased when visitors are required to visit agency offices. Office visits may

represent a logistic problem for some users; for example, groups that arrive

at trailheads after office hours will have difficulty complying with requirements to obtain an agency-issued permit. The self-issued permit will not be

as much of a problem for users if permits are made available at the trailhead;

in this case, visitor burden would not differ from that associated with

trailhead registration. However, this option can only be used where the

number of permits issued is unlimited. Alternatives which increase user

convenience include mail, telephone, and even private sector cooperators. In

general, visitor reactions to permits have been highly positive, as long as the

rationale for permit issuance is considered worthwhile (Lucas 1990).

Strategies for reducing visitor burden (Leonard and others 1980) include:

1. Publicizing requirements for permits in areas where users are known to

live or start their trips.

2. Ensuring that the potential user population is made aware of use limits

or restrictions that are enforced through the permit system.

3. Clarifying the type of use, or user, requiring a permit.

4. Minimizing (as far as possible) the amount of information required from

users.

5. Increasing the convenience in obtaining a permit.

Management Costs.—Variable. Management costs will vary greatly according to the type of permit system. For example, a system of unlimited selfissued permits is relatively inexpensive. Apart from the costs involved in

managing the registration system, additional costs are incurred by enforcement; however, these costs will be minimal if other enforcement duties and

field tasks can be performed simultaneously. In contrast, where the number

of permits are limited and demand for those permits is high, administrative

costs can be relatively expensive. (However, those costs do not result from the

use of permits as a use estimation system; they result from the use limitation

strategy). Where permits are agency-issued but unlimited, costs are moderate.

Office personnel must be available to issue permits. This might involve

directly issuing permits to visitors coming to the office, which requires a more

centralized distribution. In contrast, indirect methods may impose less

burden on both users and personnel, and less restrictions on location; these
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 35

include mailing out permits, or posting permits outside the office after hours

for late arrivals, or providing for permit issue on the basis of telephone

requests. In some cases, outfitters are allowed to issue agency permits for

their own trips; these permit receipts need to be retrieved periodically from

outfitter offices and checked for completeness and accuracy. Field personnel

are less involved in data collection than they would be with visual observation or traffic counter systems.

Accuracy.—Usually high. Permit systems differ from registration systems

in that permits are mandatory, rather than voluntary. Visitors must obtain

a permit to enter an area, otherwise they are in violation of regulations.

Accurate estimation of use characteristics from a permit system is reduced

by lack of compliance. When permit requirements are well enforced, compliance is usually relatively high. For example, compliance in a number of

National Park wilderness areas is more than 90 percent; compliance is more

variable with self-issue day-use permits, ranging from 53 percent in one area

(Lucas and Kovalicky 1981) to as high as 80 percent in other areas. Permit

compliance increases with increased levels of enforcement, increased publicity about permit requirements, and increased visitor awareness of requirements (Lime and Lorence 1974).

The level of accuracy depends primarily on the accuracy of estimated levels

of compliance. An estimate of compliance rates is required to correct for the

unknown proportion of visitors not in compliance; this is the “expansion

factor” similar to that determined for registration data. The compliance rate

(which is identical to a registration rate) is simply the proportion of all groups

encountered that have permits. It can be estimated by checking permits,

either systematically or randomly; checks can be performed by rangers on

patrol or stationed at or near trailheads. Ranger checks are most often

performed within the limits of a normal work schedule, often at high-use

times; however, reliability of compliance estimates can be increased if checks

are assigned randomly. Because of observed differences between different

types of users (Lime and Lorence 1974), expansion factors to account for

noncompliance rates should be calculated by user subgroup (for example,

horse users versus hikers, or day-users versus campers). Accuracy may also

be compromised by visitors changing their plans after obtaining their permit.

Such changes usually result because people overestimate their abilities, or

do not account for changes in weather. For example, at Yosemite National

Park, 62 percent of all groups deviated from their planned trip; as a result,

permit data overestimated use by 12.5 percent (van Wagtendonk and

Benedict 1980). Compliance with permit requirements by visitors to Sequoia

and Kings Canyon National Parks was 97 percent; however, changes in plans

resulted in overreporting of total visitors by 8 percent, and of visitor-nights

by 23 percent (Parsons and others 1982). The validity of permit data can be

checked by contacting a sample of visitors, either as they leave the area or at

their home after the trip, and asking them about their travel behavior.

Comments.—The use of permits is controversial (Behan 1974). Most of the

controversy stems from the use of permits as part of a use-limitation system.

This is unfortunate because permits have many positive attributes that do

not have to be coupled to a use-limitation system. For example, when

compliance is high, permits are a simple method of collecting accurate use

data; a large number of visitor use statistics can be gathered. Permit issuance
36 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

offers an opportunity for contact between visitors and agency personnel. This

can be used to increase visitor knowledge about regulations, recommended

low-impact behaviors, and potential hazards. It gives visitors a chance to

obtain information of interest to them, it increases the professional image of

the agency, and it may add an element of increased safety (Hendee and Lucas

1973).

In 1980, permit systems were in use in 69 wilderness areas. Of these areas,

17 limited use and 52 did not (Washburne and Cole 1983). Recent informal

surveys suggest that the number of wilderness areas that issue permits has

declined since that time. Approximately 50 areas currently require permits;

however, the number of areas that limit use has increased to about 25. Most

of these changes have occurred in areas managed by the Forest Service.

These findings suggest that use of permits as a tool for collecting visitor data

and communicating with the public is decreasing.

Visitor Surveys ___________________________________________________

Methods.—A visitor survey consists of two parts: (1) contacting a sample

of visitors (either at trailheads, within the wilderness, or at home); and (2)

obtaining visitor use information by either interviewing visitors or

asking them to respond to a questionnaire.

1. Visitor contact. Strategies of contacting visitors must identify the

sampling design to be used, the timing of visitor contact, and the location of

contact.

There are three principal types of sampling design used to obtain a

representative sample of visitors:

(a) Stratified samples of visitors at, or close to, trailheads.

(b) Random or systematic sampling of either permits or registration

forms, or both.

(c) Convenience sampling.

Stratified sampling involves the placement of personnel at or close to

randomly selected trailheads; the strata are time blocks selected from

available weekdays, weekends, and holiday periods. Visitors are interviewed

or asked to complete a questionnaire as they enter or leave the wilderness;

alternatively, personnel can obtain names of visitors who are then sent a

mailback questionnaire. Personnel could also ask visitors for information

regarding length of stay; this information can be used for estimating such

summary visitor use statistics as recreation visitor-days. Stratified sampling

is most efficient if observers can combine interviewing with counter validity

checks or monitoring registration rates.

Random or systematic sampling of permits may be used to obtain the names

and addresses of visitors; the visitors thus sampled are subsequently sent

mailback questionnaires. Sampling from permit lists is inexpensive. However, the information provided is usually restricted to the permit compliers,

group leaders, or whoever registers or fills out the permit. Information

regarding other party members can be obtained by asking group leaders to

supply names and addresses of party members; questionnaires may be

subsequently mailed to a sample of party members. Some wilderness areas

(for example, the Okefenokee National Wildlife Refuge Wilderness) require

the names of all members of the party on the permit.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 37

In theory, registration information could be used in the same manner as

permits to derive a sample of wilderness users, especially if registration rates

are known to be high. However, registration rates are much lower in general

than permit compliance rates. Examples of visitor use surveys using registration data are (1) at Cranberry Backcountry in West Virginia, where

registrants were randomly selected, and nonregistrants were systematically

selected on randomly selected days (Echelberger and Moeller 1977); (2) at the

Bob Marshall Wilderness Complex, where visitors were sampled directly at

moderate- to high-use trailheads, and registration cards were sampled at

more remote, low-use trailheads (Lucas 1985).

Convenience sampling does not provide a representative sample of the

population, because the lack of true randomness in sample selection introduces an unquantifiable amount of bias. Convenience samples may be

justified occasionally as a means of obtaining information on, for example,

visitors to a specific internal location (such as a lake basin), or noncompliers

(Lucas and Oltman 1971; Watson 1993). Sampling is performed by patrolling

rangers, or by personnel stationed at entry points to the wilderness. Personnel would then interview all the visitors encountered in that particular

location. The National Park Service, through their Visitor Service Project,

advocates what they call “taking the pulse” of visitor use with intense

convenience samples of visitors.

Other methods of contacting visitors may be required when trailheads are

not established, use is very low or follows unknown patterns, or cost-efficient

alternatives are not readily available. For example, the Corps of Engineers

Visitor contact strategies for surveys must identify the sampling design to

be used, the timing of visitor contact, and the location of contact.
38 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

attempted to contact a sample of dispersed hunters by placing response cards

on vehicle windows on selected sample days; respondents were asked to

deposit completed forms in a designated roadside box. Unfortunately, this

approach provided a response rate of only 25 percent. The Forest Service,

working at Upland Island Wilderness in Texas with very dispersed and

unpredictable entry and exit patterns, contacted apparent recreation visitors by placing mailback cards on vehicle windows; response rates were

almost equally low (Watson and others 1992). In contrast, roadside traffic

surveys were used to contact visitors in a Forest Service wilderness in

Indiana, characterized by an abundance of easy access points from along

adjacent roads; visitors were contacted at places where all visitors to the area

had to pass (Watson and others 1993). Although visitor contact was highly

successful, approximately 50 percent of all vehicles stopped were not wilderness-visit-related traffic. Further consideration of alternative sampling

designs are required.

The timing of visitor contact is important. Visitors may be contacted when

either entering or leaving the area. Information obtained from visitors after

their trips is generally more useful; in addition, visitors may be more open to

questions when leaving the area. The most cost-effective method, when possible,

is to contact visitors arriving and departing during a selected time period.

The location of visitor contact must be carefully selected in order to avoid

undesirable intrusion into the wilderness experience of visitors. Surveys

conducted at trailheads are considered most acceptable. Visitors have occasionally been contacted at campsites and along trails in the wilderness, but

these locations are generally considered intrusive.

2. Obtaining information. Information is solicited from visitors by

means of interviews or questionnaires. Interviews should be kept short,

limiting content to easy-to-answer, factual questions. Whether the visitor is

either just setting out, or leaving for home, there will be low tolerance for

complicated and difficult-to-understand questions, and long, time-intensive

interviews.

The second option for collecting detailed visit and visitor characteristic

data is the mailback questionnaire. Typical response rates to questionnaires

4 to 16 pages long range between 77 percent and 85 percent (Dillman 1978).

However, this level of response usually entails diligent followup; followup

procedures include (1) provision of a postage-paid envelope with the questionnaire, (2) mailing out a reminder postcard, (3) mailing a complete second

questionnaire and return envelope 3 weeks after the first mailout, and (4) a

final mailing of a third questionnaire and return envelope after 7 weeks.

Visitor Use Characteristics.—Any type of visitor information can be

obtained.

Visitor Burden.—Moderate. The extent of visitor burden is determined by

the location and timing of visitor contacts, and the time required for each

visitor to respond to the questions on the survey.

Most visitors appear to value the chance to provide input on wilderness

issues, because these issues are important to them. This suggests that visitor

burden will be a problem (1) where visitors are contacted within the

wilderness (many visitors enjoy this contact, but some do not), or (2) if

interviews are too long, and visitors are anxious to either enter the wilderness or get home. Visitors seldom complain about mailback surveys, even

those that require as much as 30 minutes to complete.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 39

Management Costs.—High. Statistically valid visitor surveys are expensive. Personnel costs include transportation and time required to monitor

different trailheads; administration of the survey may require additional

field personnel. When names and addresses need to be collected in the field,

there are no great savings associated with mailback surveys. When names

can be obtained from a list of permits, however, costs are dramatically

reduced because no field contacts are needed. Costs of mailbacks include the

cost of questionnaire preparation, printing and mailing, and follow-up costs

(postage-paid envelopes, reminder postcards, and follow-up questionnaires).

Personnel time is needed to code and enter data and to analyze the results.

Convenience samples can be substantially less expensive. Data can be

collected as a part of field employees’ normal jobs, so little additional cost is

incurred. However, the quality and utility of information is substantially less

than that obtained from a valid sample.

Additional costs may be incurred by the time and effort it takes to obtain

OMB approval. Federally sponsored information collection procedures requiring individual responses must receive clearance by OMB. The approval

process requires a lead time of about 3 months from the time of submission

to approval; a substantial amount of paperwork is involved. However, the

review and justification required to obtain this clearance assures a highquality survey plan. OMB clearance is critical when important management

decisions are to be based on collected information. The clear approval and

support of the agency, the Department, and OMB will avoid later problems

concerning questions of authority and legality.

Accuracy.—Variable. The level of accuracy is largely dependent on the

sampling procedure. Statistically sound, unbiased sampling techniques

produce the most accurate information. Convenience samples do not provide

a representative sample of the population because the amount of associated

bias is unknown; the quality of the data obtained from convenience samples

is therefore low.

Comments.—Surveys are the most frequently used method of obtaining

detailed information on visitor characteristics, visitor attitudes, and visitor

preferences. The use of surveys is increasing with the current emphasis on

“knowing your customer” and maximizing “customer satisfaction.” The

survey has been used almost exclusively by researchers; however, it is a

practical technique for managers needing to collect information about

recreational use.

Indirect Estimation ________________________________________________

Methods — Indirect estimation techniques involve the prediction of some

desired visitor use characteristic from one or more easy-to-measure variables. These surrogate measures are the predictor variables. The relationship between the predictor(s) and the use measure is quantified by linear

regression. The relative “success” of the predictor variables in predicting the

use characteristic is evaluated by the R2

 value calculated for the regression,

or the width of the confidence interval for the estimate of the “new” predicted

value. The higher the R2

, the more successful the regression model will be in

explaining the variation in the use characteristic. Once this relationship is

quantified, it is only necessary to monitor the predictor variable(s) to obtain
40 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

an estimate of the desired use characteristic. Examples of such predictive

relationships are:

1. The estimation of dispersed recreation day use in Glacier National Park

from weather factors, campground occupancy rates, and the total number of

vehicles entering the Park; variation explained by the predictive model was

75 percent (McCool and others 1990).

2. The estimation of the number of people using the Kissimmee River

Basin, Florida, from lake water levels, daily maximum temperature, and

daily rainfall; variation explained by the predictive model was 69 percent

(Gibbs 1973).

3. The estimation of the number of visitors per day to a given lake basin

from systematic car counts obtained at the trailhead parking lot; variation

explained by the predictive model was 94 percent (Watson and Cronn 1999).

4. The estimation of dispersed recreation use from vehicle traffic recorder

counts placed along major access roads (Erickson and Liu 1982; James 1967;

James and Ripley 1963).

5. The estimation of fishing visitor-days from vehicle traffic counts obtained at both ends of a parking lot (James and others 1971).

An affiliated method of some promise is “double-sampling.” This involves

the simultaneous measurement of a given use variable and a suitable

predictor variable on a predetermined number of randomly selected sample

periods during the use season. Common predictor variables used in doublesampling designs are traffic counts or rates of water consumption at developed sites. Other potential predictor variables include the number of cars

parked at the trailhead or the number of trailhead brochures or maps taken

by wilderness visitors. Double-sampling is closely related to “cordon” sampling (Erickson and Liu 1982, Roggenbuck and Watson 1981, Saunders

1982); cordon sampling is a method of estimating annual recreation use by

interviewing recreational users at roadblocks situated along wilderness area

access roads.

How the predictor variables are measured obviously depends on the types

of variables chosen. For example, several studies estimated dispersed recreation use as a function of vehicle traffic recorder counts (Erickson and Liu

1982; James 1967; James and Ripley 1963). In these studies, use characteristics were determined by survey sampling of traffic along major access

roads; these surveys were coupled with vehicular counts obtained by inductive loop or pneumatic tube counters.

The predictor variables selected must be carefully evaluated, both for their

initial suitability as a predictor variable, and for their continued suitability

over seasons. For example, measures of trail deterioration, such as trail

width and condition, will be adequate predictors of trail use only if trail use

is classified simply on the basis of light versus heavy use; these predictors will

be inadequate if more rigorous predictions of trail use are required (More

1980). Furthermore, the predictive power of certain predictor variables may

be affected by both the activity being evaluated and the location of the study.

For example, the precision of various categories of predicted visitor use in the

Eldorado National Forest was described with 95 percent confidence intervals; precision ranged from ± 15.8 percent for fishing activity over the entire

forest, to ± 130.6 percent for swimming and sunbathing at one site (James

and Henley 1968).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 41

Some indirect relationships may be useful for long periods of time if use

patterns do not appear to change noticeably. For example, the predictive

relationships established between visitor use and traffic counts may be valid

for 3 to 5 years (Saunders 1982). However, periodic checks should be

scheduled to ensure the continued validity of the predictive relationship.

Visitor Use Characteristics.—Potentially, indirect measurements could be

used to predict many types of wilderness use characteristics. However,

certain use characteristics may not be modeled adequately by a suitable

predictor variable; this must be ascertained in preliminary, or pilot, studies.

To date, the use characteristics most commonly evaluated have been total

amount of visits, and time involved in a particular activity. Inter-party

encounter rates have been successfully predicted from a combination of

mechanical counts, visitor counts, and systematic counts of parked vehicles

(Watson and others 1999). The relative success of predicting other visit and

visitor characteristics is untested.

Visitor Burden.—Variable, but should decline to zero. During initial data

collection for establishing the predictive relationship, visitor burden will be

determined by the number and type of use statistics to be predicted, and the

method of obtaining visitor information (on-site interviews, observation,

mailed questionnaires, and so forth).

Once the predictive relationship is established, visitor burden should go to

zero, except for periodic checks required to ensure the continued validity of

the predictive relationship.

Management Costs.—Initially high, but should decline to low levels.

Considerable effort must be expended in developing the predictive relationship between the use characteristic of interest and some appropriate predictor. Accurate information must be obtained for both the use characteristic

and the selected predictive variables. Pilot studies are imperative to determine whether there is in fact a relationship between the given use characteristic and the proposed predictor variables, and whether the proposed relationship is sufficiently strong to be of any use as a means of prediction.

Initial costs would include the purchase cost of equipment required to

monitor the predictor variable and personnel costs associated with collecting

initial data. However, these costs may be incurred only over the short-term,

generally for a single year or use season. The resulting predictive relationship may be able to be used for several years with some confidence before

reevaluation of the predictive relationship is needed. Large initial expenses

may be avoided by cooperation with other agencies (borrowing or timesharing of equipment and personnel).

Accuracy.—Variable. Accuracy depends on the type of predictor variable,

and the strength of the relationship between the predictor and the use

characteristic being estimated. Tarbet and others (1982) emphasized the

need for formalized sample selection and improved quality control for this

type of estimation method.

Aerial Surveys ____________________________________________________

Aerial photography has been considered as a potential method of counting

wilderness visitors since the 1960’s. At that time, remote sensing techniques

to measure outdoor recreation use were not feasible, as desired resolution
42 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

would have required flights at altitudes of 500 feet or less (Schnell and Taft

1972). Even with modern improvements in instrumentation and technology,

an estimated maximum of 1,000-foot altitude flights (or a scale of 1:2,000) are

required to obtain the desired amount of image resolution (Aldritch 1979).

Low-altitude flights are incompatible with wilderness values. Satellite

imagery (obtained at a scale of 1:120,000) may be appropriate for monitoring

recreation areas. There are few data which test the relative discrimination

of aerial photographs at different scales and varying degrees of cover. Aerial

photography has been demonstrated to be a reasonable method of measuring

use on some rivers (Becker and others 1980).

Visitor Use Characteristics.—Visitor counts, spatial use patterns, activity

type.

Visitor Burden.—High. Visitors are not contacted directly, but low-altitude

flights are extremely intrusive, and incompatible with wilderness values.

Management Costs.—High. Costs include survey aircraft flight time, pilot

and personnel wages, camera equipment, film purchase and developing, film

viewing and data analysis.

Accuracy.—Undetermined for most wilderness situations.

Comments.—Aerial surveys are probably inappropriate for most wilderness situations, but may be a reasonable method of measuring use on some

rivers (Becker and others 1980).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 43

Chapter 3: Sampling Methods

Sampling is the systematic strategy by which data are to be collected.

Sampling is essential in some form for all use estimation systems because

proper sampling techniques ensure that the data are representative of the

larger population from which they are drawn. Representative sampling

assures the investigator that the resulting statistics calculated from those

data are reliable estimates of the population values.

There are two general categories of sampling procedures. The first is

convenience or judgment sampling; the data are selected according to the

discretion and subjective knowledge of the investigator. Drawbacks to this

method are discussed in detail below. Probability or statistical sampling

techniques are preferable to convenience sampling because they are based on

the statistical principle of randomization.

We discuss a number of statistical sampling designs appropriate for use in

monitoring wilderness users and use characteristics. Guidelines for selecting the size of the sample are also detailed. General references for sampling

methods and sample size determination include Ackoff (1953), Cochran

(1967), Deming (1960), Scheaffer and others (1986), and Steel and Torrie

(1980).

Convenience or Judgment Sampling _________________________________

Methods based on “professional judgment,” “best guesses,” or “common

sense” are the most frequently used so-called “sampling” techniques. A

recent survey of wilderness managers (covering 423 out of a total of 440

wilderness areas) reported that 63 percent relied on “best guesses” to

estimate visitor use; 61 percent relied on “professional judgment” to formulate regulations (McClaran and Cole 1993). In some cases, on the basis of

previous knowledge and experience, the investigator may consider that

certain well-defined groups are somehow “representative” of the population

as a whole. In other cases, time and logistics may seem to prevent or preclude

the use of statistical sampling methods.

 In reality, convenience or judgment samples are an extremely poor

alternative to statistical sampling procedures. The use of human judgment

invariably results in biased sample selection; judgment is unavoidably

influenced by untested assumptions of how the various properties of the

users or visit characteristics, or both, should be related. Furthermore, it is

impossible to determine the size of the bias from sampling methods of this

kind. The samples obtained from judgment surveys are therefore not representative of the population as a whole. Examples are wilderness users that are

convenient or easy to survey, vocal supporters or critics of special interest

groups at public meetings, users surveyed at easily accessed trailheads. The
44 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

characteristics of the individuals sampled will invariably differ from those of

users who travel into more remote or less-accessible areas, or who do not

belong to a special-interest group. Because standard errors cannot be calculated for such samples, statistical testing procedures and analyses cannot be

used.

Statistical Sampling Designs ________________________________________

Why Use Statistical Sampling?

Although the research ideal would seem to entail the complete census of all

possible members of a population, in fact statistical sampling actually results

in substantial accuracy for far less time and cost. Reasons are as follows:

 1. Elimination of bias in data collection. Bias inevitably results from

reliance upon personal judgment and wishful thinking, and will result in a

sample that is distorted or otherwise unrepresentative of the population

under study. Appropriate sampling is based on randomization techniques,

which ensure protection against unknown bias.

 2. Probability theory can be used to measure the precision of sample

results. Because it is impossible to know the “real” population values, sample

statistics should be selected that estimate underlying population parameters and quantify the certainty of such estimates.

 3. Speed. In general, patterns of wilderness visitation do not allow 100

percent monitoring. A complete census might require an entire season or

even years to complete; certain significant segments of the population may

be completely unavailable for censusing. Regardless, extremely large surveys require substantially longer time periods for data processing; additional

costs will be incurred by overtime needed to process extra information and

finding and eliminating mistakes. Much of the same information could be

obtained through sampling in just a few days or weeks.

 4. Fewer personnel are required to do the work. Smaller numbers of

personnel make for better and more streamlined selection, training, and

crew coordination. Furthermore, even if sufficient money and resources

could be allocated for the transportation, supplies, and labor required by a

large project, government offices are often constrained by personnel ceilings

that restrict the number of people that can be assigned to a single project.

 5. Accuracy and quality of data. Sample information will be more accurate,

first, because crews can be more carefully selected and trained, and second,

because personnel are required to spend relatively less time on the job, thus

reducing fatigue and boredom.

 6. Flexibility. Increased speed of sampling means that a canvass can be

conducted and completed at any time; thus, the logistics of the canvass can

be modified relatively quickly to fit the convenience of the study.

 7. Reduced visitor burden. Minimizing visitor burden must be a primary

consideration in any visitor use study. Good sampling designs reduce visitor

burden by maximizing the information content for the fewest number of

visitor contacts.

What is a Good Sampling Design?

Because populations are characterized by variability, a good sample design

is characterized as efficient if the sampling variation is as small as possible.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 45

The standard error of the mean is a measure of the precision of the sample

estimate (that is, how far an average sample mean deviates from the

population mean). Thus, a given sampling design is more efficient than

another if it results in

(1) a smaller standard error with the same sample size;

(2) the same standard error with a smaller sample size.

Simple random sampling is free of bias because every member of the

population has the same chance of occurring in the sample. However, simple

random sampling does not make use of additional information about the

population structure; for example, that hikers are more likely to have a

college education than other wilderness users, or that wilderness users from

one part of the country are more likely to travel further distances to a

wilderness area than those from other parts of the country. The statistical

efficiency of a simple random sampling design can be increased only by

increasing the sample size. Therefore, in many circumstances it may be more

efficient (as well as less costly and time intensive) to use more complex

sampling designs that utilize additional information about the sample.

Sample Size Determination _________________________________________

When planning a wilderness use study, the essential steps to be performed

before the sampling design is specified are definition of the sampling unit,

and determination of the appropriate sample size.

Defining the Sampling Unit

The first step in sample design is definition of the sampling unit. The

collection of sampling units makes up a subset of the population which is to

be sampled; it follows that there must be a clear and explicit definition of the

population of interest in the statement of objectives. The population is all

people, groups, conditions, levels, and so forth, that the investigator wishes

to learn about, whether or not these are available; examples are all wilderness users who buy a certain product, all wilderness users entering a given

wilderness area, all university students, or all commercial outfitters using a

specific wilderness area.

The population is physically defined by the “list” or “frame.” As defined by

Deming (1960), the frame is a set of physical materials that enumerates the

population and allows it to be sampled. The frame must show a definite

location, address, boundary, or set of rules to define the sampling units to be

drawn by the random sampling process. Examples of suitable frames are

maps, directories, membership lists of hunting or outdoors associations,

telephone directories, lists of state license plates, voter lists, permit numbers, and census statistics. Alternatively, there may be no concrete sampling

frame; in these cases a frame may consist of clearly defined rules for creating

and defining the sampling unit. In still other cases it may be impossible to

obtain a representative sample.

Even with a well-designed selection procedure, a poor response rate to a set

of interviews or questionnaire items may invalidate the results of the study.

Suggestions for improving response rates when these techniques are used

are given in part II. However, the problem of nonresponse should be

anticipated in the early design stage and contingency plans made for

handling nonrespondents.
46 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Example: The manager of a wilderness area wishes to determine the

extent of wilderness use during various times of the season. There are several

possible scenarios that dictate the sampling frame chosen:

 1. The wilderness area has a strictly enforced permit system; very few

wilderness users enter undetected. Suppose permits numbered 3782 through

10532 were issued for a given year. The manager wishes to mail a detailed

questionnaire to 50 randomly selected wilderness users. The frame, or

listing, of the population to be sampled is the total number of issued permits,

or permit numbers 3782 through 10532.

 2. The wilderness area is “open”; that is, there is virtually no regulation of

visitor entry and exit. A potential frame for a given wilderness area is the list

of all households within a 100-mile radius. All households within this area

are numbered, and all those households randomly selected by the sampling

process are enumerated. Some of the sampling units within the sample will

be blank; that is, there are no wilderness users in a given household. Blanks

will be a problem if wilderness users (the feature of interest) are relatively

rare in the population. Considerable time and money may be required to

canvass the sample, only to find few or no representatives of the group of

interest.

 3. The wilderness area is “open”, and there is no practical list of potential

wilderness users that could be used to draw up a sampling frame. Instead,

the manager opts for a set of rules defining the frame. The manager defines

a temporal frame consisting of all the days in the entire season; a random

selection of days will provide a random collection of wilderness visitors.

Sample Size

The most frequently asked question when designing a wilderness use study

is “How large a sample?” Unfortunately, there are no simple answers. In fact,

without an estimate of the variability of the response or outcome of interest,

no answer at all can be given. Estimates of the variability must be obtained

from preliminary data obtained either from a pilot study or from data

obtained during previous years.

Most often managers want estimates of the total number of users or an

average of some characteristic of wilderness visitors. These are but two

examples of parameters of interest that will be determined for some sample

of wilderness visitors. If the sampling is in accordance with some statistical

design, then a measure of uncertainty called the estimated standard error for

the estimate will also be developed. This standard error, denoted SE, may be

thought of as the average amount the estimate from (conceptually) repeated

samples will deviate from the underlying population value. Estimates with

small standard errors are more precise than estimates with large standard

errors.

Armed with an estimate of the standard error, a confidence interval may

be constructed using rules of probability. In general, twice the SE added and

subtracted to the estimate form lower and upper confidence bounds that

bracket the unknown population parameter with probability of about 95

percent. This means that there is about one chance in 20 (5 percent) that the

unknown population parameter lies outside such an interval or that the

interval is incorrect. But we are pretty certain, 95 percent (or 19 times in 20),

that the unknown population parameter lies within the confidence interval.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 47

If a higher level of confidence than 95 percent is desired, the “2” is replaced

by 2.57 for 99 percent. For lower confidence, say 90 percent, the 2 is replaced

by 1.645. Therefore, for a 99 percent confidence interval, 2.57 times the SE

is added and subtracted to the estimate; for a 90 percent confidence interval,

1.645 times SE is added and subtracted.

Formulas in the appendix show how the SE and desired width of the

confidence interval may be used to determine the required sample size for

generating a confidence interval of desired width for a specified level of

confidence for several parameters. Briefly, this is accomplished by setting

the value to be added and subtracted equal to a value and solving for the

sample size, which is an integral part of the SE formula. Further details are

given or referenced in the appendix.

Sampling Designs _________________________________________________

Simple Random Sampling

Simple random sampling, or random sampling without replacement, is the

selection of items from the population such that each item has an equal

probability of being selected. That is, the selection of the sample is entirely

due to chance; it does not mean that selection of a sample is haphazard,

unplanned, or based on guesswork.

The random selection of items is performed by means of a random number

table. A random number table is a sequence of numbers generated by

(conceptually) repeatedly drawing numbers from 0 through 9 from a hat,

replacing each number before the next draw, such that each digit 0 through

9 has an equal probability of occurring in each position in the sequence.

Therefore, we have no reason to expect that any one number will appear more

often than any other number, nor that any sequence of numbers should occur

more often than another sequence, except by chance. Table 3 contains 2,000

computer-generated random digits arranged for convenience in 10 columns

and 40 rows of 5-digit groups.

How to Obtain a Random Sample

Suppose we want a random sample of size n from a population of size N. We

will draw n consecutive numbers from the random number table in table 3,

ignoring any number greater than N, and any number drawn for the second

time (if we are sampling without replacement). If the population is less than

100, we are required to draw a sample of n two-digit numbers; if n is equal

to or larger than 100 and less than or equal to 999, we will be required to draw

a sample of n consecutive three-digit numbers, and so on. The start point may

be anywhere in the table, but a more satisfactory method is to poke at any

spot in the table with a pencil, read the four digits closest to the pencil point,

and use those to locate a start point. Digits read in any direction are

random—left to right, top to bottom, and so forth.

Procedure for Random Sampling

 1. Obtain a list or “frame” for a population of size N; number each item in

the frame.

 2. Decide on the appropriate sample size n to be drawn from the population.

 3. Pick n random numbers from the random number table, excluding those

that are greater than N. If the end of the table is reached, simply “wrap” up

to the top.
48 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

 4. Obtain the observations for the items whose identification number

corresponds to the selected random numbers.

Example: Suppose we need to select a sample of size n = 10 from a

population of size N = 30.

 1. In the random number table (table 3), the pencil falls on the digits 32039

in row 29 and column 9.

Table 3—Random number table.

Column

Row 1 2 3 4 5 6 7 8 9 10

1 10486 24171 46732 28740 26899 19318 44151 05478 65089 13978

2 73679 78358 79152 99760 84501 58832 44612 98740 19052 36084

3 63865 21629 21229 09131 27787 15262 65766 44905 28331 07628

4 49726 40330 44578 39100 14112 30815 21024 47700 20198 32921

5 54523 34394 91794 42527 31970 94092 08841 01786 04623 70491

6 01822 33331 94062 18259 15477 99842 49073 61869 57548 36566

7 97111 41959 87141 28730 19725 63425 42713 79053 89896 88309

8 26649 22013 57096 15949 38399 96190 86375 60585 84033 92924

9 29713 91004 21915 47233 19757 23067 47654 84324 53456 64015

10 75572 94458 30359 96818 12370 98566 82734 74119 57274 21327

11 51353 82896 34206 44715 46721 52506 52375 17401 75584 05222

12 42146 99692 65221 48951 34071 71623 67643 81184 27069 52048

13 59492 61189 23032 22544 38697 98425 71524 57779 84992 11737

14 49613 85175 55232 21373 54868 03444 37782 46427 22917 63802

15 87528 99124 85858 24274 94713 62191 43189 52137 96329 63053

16 38404 34306 23636 61542 68318 43052 44517 57935 41493 21232

17 42298 87135 56083 23148 12226 87360 66392 01842 47682 05849

18 53635 03919 10864 52861 97661 37910 81404 64731 34166 12428

19 41576 20335 40541 09596 24638 47172 38594 50446 38071 41489

20 32611 61789 62034 52161 83326 71415 71683 14277 94489 86411

21 51569 86030 57005 78733 38783 32056 93193 71194 64960 13532

22 92326 24128 14447 27220 70432 00403 55787 89970 45706 90644

23 24430 51212 71687 17866 72434 37132 37025 54517 61746 95219

24 16956 93082 85099 94246 96284 92649 78831 48646 28247 08542

25 35743 50061 36735 93985 91804 49702 87864 95530 35266 76978

26 45371 94239 58168 55388 77872 64363 78120 58078 87229 96888

27 22031 71445 27735 41272 49040 36759 11921 81538 03294 53928

28 58625 14121 72519 36231 99379 17692 70647 34479 59956 23509

29 18256 46418 81212 48594 19727 32483 61344 79533 32039 13373

30 67460 37690 09210 23301 99668 78223 40589 79996 63419 04596

31 95316 35722 32124 47004 40391 25743 11719 23695 73648 22306

32 99806 85844 78984 01557 59797 32480 26817 20216 81800 42301

33 97548 17286 51371 97245 45991 47590 99571 02891 03712 14906

34 88279 52919 09766 91898 90506 65424 10383 41660 53965 62208

35 80223 73728 83290 77247 07426 58769 59858 48176 58750 80039

36 57685 44187 34178 88661 19728 97953 02030 29292 60970 50840

37 47053 79853 83152 69627 69031 37207 63480 20292 73725 48762

38 12516 13362 77021 97117 80076 24403 29688 04008 13554 93159

39 87686 90153 54670 49189 86081 65526 54774 97169 19535 81816

40 24452 00090 42790 70979 96357 50047 25974 60145 39649 10062
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 49

 2. Go to row 32, column 3 (ignore the last digit) as the start point.

 3. Record 10 consecutive pairs of digits less than or equal to 30 by moving

right from the start point. The first eight “usable” numbers are 15, 24, 26, 02,

16, 04, 23, 01. At this point, the line ends; proceed by dropping down to the

next line. The remaining two numbers are 19 and 14.

Advantages of Random Sampling

 1. It is fair—every item in the population has an equal chance of being

selected and measured.

 2. It protects against bias or misrepresentation of the population.

 3. It allows easy data analysis and error calculation.

 4. It requires minimal prior knowledge of the population; that is, no

further information is required as to how the population is structured.

Disadvantages of Random Sampling

 1. It is less statistically efficient than other sampling methods.

 2. It does not make use of additional knowledge of how the population is

structured.

 3. It may be difficult or extremely expensive to implement because all

potential sample items must be able to be inventoried or listed.

Systematic Sampling

Systematic sampling is an approximation of random sampling. The sample

is obtained by randomly selecting the first item of a sample; the remaining

items are selected by systematic selection of each item at some predetermined interval. Examples of systematic sampling schemes in wilderness use

estimation are the selective censussing of every tenth wilderness user, every

fifth car passing a checkpoint, or every fourth group of visitors encountered

during a day of ranger patrol.

Procedure for Systematic Sampling

 1. Given a population of size N, determine the appropriate sample size n.

 2. Calculate the sampling interval k between selected items; k is calculated

as the ratio N/n. This ratio is then rounded off to the nearest whole number.

 3. Using the random number table, randomly select some number i

between 1 and k.

 4. Sample the items identified by the following sequence of numbers:

i, i + k, i + k + k, i + k + k + k, ...., and so forth

or

i, i + k, i + 2k, i + 3k, ...., and so forth

Advantages of Systematic Sampling

 1. Systematic sampling may reduce variability (it may be more efficient than

random sampling), especially if there are patterns or time-order in the data.

 2. It is simple to perform (because only one random number is required).

 3. Sampling effort is guaranteed to be distributed evenly over the population.

Disadvantages of Systematic Sampling

 1. There is only a limited number of different possible samples; since every

kth item is sampled after a random start, there are only k distinct samples.
50 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

This is in contrast to the almost limitless number of different possible

random samples.

 2. Estimates may be severely biased if there are any patterns in the data.

For example, if the sampling units were days over the entire summer season,

and if the 1 in k sampling interval happened to coincide with multiples of 24

hours or 7 days, the same time period would be sampled each day or week.

 3. There is no reliable method of estimating the standard error of the

sample mean.

Example: Suppose we wish to select 25 permits from a total of 8,743 permit

applications. The sampling interval is then 8,743/25 = 349.7 or 350. If the

permit cards were arranged in numerical order, we would select a random

number between 001 and 350 as the first element of the sample. Suppose this

random number was 074; the permits for the sample would be found by

successively adding 350 to successive numbers in the series; in other words,

we would select permits numbered 74, 424, 774, ..., 8474.

Frequently, permits are stored haphazardly in drawers or boxes, and are

not in numerical order. In these cases, much time and labor would be

required to either sort or renumber permits to allow randomization. However, we can use an alternative sampling method which utilizes a given

height of the permit stack as a selection criterion rather than an assigned

numerical interval. For example, suppose the 8,743 permits are in a stack or

drawer 75 inches in depth. Choose a random number i from the range 001 to

350. Count to the ith permit from the front of the stack. From that permit,

select 25 permits at 3-inch intervals.

Computations for Systematic Samples

If the analyst is confident that the systematic sampling produced a sample

free of bias due to patterns in the ordering of data, the sample can be

considered equivalent to a simple random sample for analysis.

Multiple Systematic Sampling

Samples obtained from a systematic sampling procedure may be severely

biased if there is any form of cyclic variation in the data and the interval

between consecutive sampling units equals the period of the variation. Some

protection against this form of bias can be obtained by partitioning the

sample into m groups, and changing the random start number for each group.

If the desired sample size is n, then each group will be of size ng = n/m. For

example, suppose the total sample size desired is 30. Therefore, a possible

sampling scheme would involve selecting a sample divided into m = 5 groups,

of size ng = 30/5 = 6 each. A new random start number is then selected for each

of the m groups.

Computations for Multiple Systematic Samples

Example: For the East Hickory Creek trail data (table 4), we wish to

estimate the mean number of users over the summer season. We have a

sequence of 112 consecutive days, and require a sample of size n = 20. The

sampling interval is thus 112/20 = 5.6; that is, we are required to sample one

day in every 5. To select the random starting position, choose a number

between 1 and 5 from the random number table. Record this number, add 5

to obtain the second number, and so on. For example, suppose the random
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 51

start number chosen is 2. The days to be sampled are then 2, 2 + 5 = 7, 7 + 5

= 12, 12 + 5 = 17, and so on. The resulting systematic sample is as follows:

No. No. No. No.

Day users Day users Day users Day users

2 46 27 13 52 18 77 13

7 13 32 6 57 41 82 7

12 11 37 47 62 10 87 14

17 13 42 9 67 8 92 27

22 41 47 9 72 43 97 11

The sample mean for the number of users is 20.0, and the estimated standard

error, or SE, is 2.98.

Table 4—Estimated daily user and group counts for East Hickory Creek Trail during a 16-week summer season in the Cohutta

Wilderness.

Time Wk Day Usr Gp Time Day Wk Usr Gp Time Wk Day Usr Gp

 1 1 1 57 26 39 6 4 28 5 77 11 7 13 7

 2 1 2 46 23 40 6 5 14 9 78 12 1 75 30

 3 1 3 11 7 41 6 6 9 5 79 12 2 33 19

 4 1 4 19 8 42 6 7 9 5 80 12 3 21 9

 5 1 5 21 11 43 7 1 33 16 81 12 4 34 9

 6 1 6 13 6 44 7 2 57 29 82 12 5 7 5

 7 1 7 13 9 45 7 3 10 5 83 12 6 9 4

 8 2 1 58 31 46 7 4 8 3 84 12 7 8 7

9 2 2 57 27 47 7 5 9 9 85 13 1 28 19

10 2 3 10 5 48 7 6 19 10 86 13 2 38 21

11 2 4 13 7 49 7 7 13 7 87 13 3 14 9

12 2 5 11 6 50 8 1 69 28 88 13 4 9 3

13 2 6 4 4 51 8 2 58 24 89 13 5 20 7

14 2 7 10 6 52 8 3 18 8 90 13 6 18 7

15 3 1 34 17 53 8 4 13 6 91 13 7 14 7

16 3 2 65 26 54 8 5 7 5 92 14 1 27 17

17 3 3 13 6 55 8 6 5 2 93 14 2 48 24

18 3 4 5 4 56 8 7 5 2 94 14 3 3 1

19 3 5 15 10 57 9 1 41 25 95 14 4 26 7

20 3 6 31 9 58 9 2 57 28 96 14 5 8 5

21 3 7 21 6 59 9 3 7 6 97 14 6 11 6

22 4 1 41 25 60 9 4 15 6 98 14 7 10 8

23 4 2 41 21 61 9 5 14 9 99 15 1 78 29

24 4 3 36 7 62 9 6 10 4 100 15 2 34 19

25 4 4 11 5 63 9 7 7 6 101 15 3 7 4

26 4 5 5 5 64 10 1 83 34 102 15 4 18 5

27 4 6 13 6 65 10 2 47 26 103 15 5 12 7

28 4 7 12 3 66 10 3 8 5 104 15 6 16 5

29 5 1 43 24 67 10 4 8 5 105 15 7 11 4

30 5 2 43 24 68 10 5 9 6 106 16 1 26 16

31 5 3 12 6 69 10 6 12 6 107 16 2 53 24

32 5 4 6 5 70 10 7 15 7 108 16 3 16 4

33 5 5 8 4 71 11 1 27 17 109 16 4 16 6

34 5 6 12 7 72 11 2 43 22 110 16 5 9 5

35 5 7 5 5 73 11 3 15 7 111 16 6 25 8

36 6 1 45 25 74 11 4 7 4 112 16 7 14 5

37 6 2 47 23 75 11 5 17 7

38 6 3 9 7 76 11 6 11 8
52 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

However, a time plot of the data shows that the number of users increases

dramatically on weekends (fig. 4); the data are in fact strongly periodic. As

a result, the estimates for the mean and standard error will be biased. We can

correct this bias to a certain extent by frequently changing the random start

number; in other words, by performing multiple systematic sampling.

We decide to draw m = 4 systematic samples, each of size n = 5. The

sampling interval k is 112/5 = 22.4, or 22. Thus, we need to choose 4 random

numbers between 1 and 22. In this example, the random numbers are 17, 6,

12, and 13. The 4 samples are as follows:

Sample 1 Sample 2 Sample 3 Sample 4

No. No. No. No.

Day users Day users Day users Day users

17 13 6 13 12 11 13 4

39 28 28 12 34 12 35 5

61 14 50 69 56 5 57 41

83 9 72 43 78 75 79 33

105 11 94 3 100 34 101 7

Means 15.0 28.0 27.4 18.0

The mean of the 4 sample means is 22.1. For a sub-sampling approach such

as this, the standard error is estimated directly from the four sample means,

that is:

 

SE = − + − + − + − −= [( . . ) ( . . ) ( . . ) ( . . ) ] /( ) / . 15 0 22 1 28 0 22 1 27 4 22 1 18 0 22 1 4 1 4 3 292 2222

Stratified Sampling

Stratified sampling assumes that an extremely diverse, or heterogeneous

population can be divided into non-overlapping groups; these groups are

referred to as strata. A random sample of items is selected from each stratum.

Figure 4—Time plot of the number of visitors using the East Hickory Creek

trail in the Cohutta Wilderness during a single summer season.

0

20

40

60

80

100

0 14 28 42 56 70 84 98 112

Time (days)

Number of Users
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 53

These samples are then combined to form a single estimate for the population

under consideration. Strata may be very different from one another, but

should be homogeneous within each strata. Examples of strata are types of

users (hikers, horse users, hunters, mountain bikers), amount of trail use

(“light,” “moderate,” “heavy”), gender (male, female), user education levels,

and trailhead elevation (high, low).

Procedure for Stratified Sampling

 1. Identify the sampling unit.

 2. Decide on the total sample size N (number of visitors to be surveyed).

 3. Define the strata.

 4. Determine sample size ni for each stratum (see below).

 5. Draw random sample of ni items from each stratum.

 6. Take complete data for each randomly selected item from each stratum.

Choosing Stratum Sample Size

There are three procedures for selecting the appropriate sample size for

each stratum: proportional, disproportional, and optimal allocation.

1. A proportional sample is chosen so that the number of items selected

from each stratum is proportional to the size of the strata. That is, a fixed

percentage of each strata is sampled.

2. A disproportional sample results when the number of items selected

from each stratum is independent of its size. A disproportional sample

naturally results when the sample size for each stratum is constant.

3. Optimal allocation results in a sample size proportional to both the size

of the sampling units and the variance within each stratum; estimated costs

associated with each sample may also be incorporated into sample size

computations. To estimate sample size with this method, preliminary estimates for both costs and strata standard deviations must be obtained from a

pilot study, or from surveys performed in previous years. Estimates can be

easily obtained if the population can be sampled repeatedly; estimates need

not be highly accurate to give satisfactory results. If the standard deviation

and the cost of sampling are the same for all strata, this method is the same

as proportional allocation.

Advantages of Stratified Sampling

 1. If each stratum is relatively homogeneous and there are large differences between strata, stratified sampling is more statistically efficient than

simple random sampling.

 2. Sample sizes can be chosen separately for each stratum. This is important when different elements of the population must be handled separately

or they present different problems of listing and sampling. The investigator

has more freedom in allocating resources to sampling within each stratum.

Disadvantages of Stratified Sampling

 1. Strata must be well defined so that items may not inadvertently be

classified into more than one group.

 2. There must be accurate information available on the proportion of the

population in each stratum.

 3. There may be considerable costs associated with the preparation of

stratified lists.
54 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Example: There are 50 trailheads (the sampling units) classified by

relative amount of use, defined here as the number of visits per day at a given

trailhead. Four strata of use can be defined: “light use” (≤2 visits/day),

“moderate use” (3-9), “medium use” (10-19), and “heavy use” (≥20). The

manager has resources sufficient to monitor only 17 trailheads.

In this example, Ni represents the number of trailheads in each use

category (i = 4), ni is the number of sample trailheads to be selected from each

use category, and fi = ni/Ni is the sampling fraction for each use category.

Then, the sampling effort required for a proportional and disproportional

stratified random sample is as follows:

Stratum:

number of

visitors Proportional Disproportional

per day Ni ni fi ni fi

2 or less 24 8 0.33 5 0.21

3 to 9 15 5 0.33 5 0.33

10 to 19 8 3 0.33 4 0.50

≥20 3 1 0.33 3 1.00

Total 50 17 17

The manager decides to concentrate sampling effort on the more heavily

used trailheads, while minimizing sampling effort on the less frequently

used trailheads. This decision is justified on several grounds. First, more

heavily used trails are expected to have a larger influence on the overall

estimate of wilderness usage. Second, because potential impact is correlated

with use, monitoring the heavily used trails will provide a more reliable

means of gauging environmental damage. Thus, the manager opts for the

disproportional sampling scheme.

Computations for Stratified Samples

Since stratified sampling selects a simple random sample from each strata, the

initial analysis requires calculation of a sample mean and estimated standard

error of the sample mean for each strata. Strata sizes are then used as weights

in computing weighted averages of the strata means and standard errors.

Cluster Sampling

Many types of populations in wilderness studies are difficult or impossible

to enumerate completely. For example, it is impossible to draw up a list of all

potential wilderness users. However, it may be possible to identify certain

subgroups, or clusters, relatively easily. Cluster sampling involves a simple

random sample of clusters, with the complete census of all items in each

cluster. Clusters are similar, or homogeneous, units, with a high degree of

diversity, or heterogeneity, within each cluster. These characteristics of

cluster sampling contrast to those found in a stratified sample where a

random sample is selected within each stratum, and strata are themselves

diverse with a high degree of within-stratum homogeneity.

Typical clusters are geographical units or areas, social units (such as

households, families), agencies, or temporal units. For example, suppose we

require an evaluation of impact in nondesignated campsite areas in a given

wilderness area. It would take far too much time, resources, and personnel
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 55

to systematically search the entire area. Instead, we might define quartersections as the clusters. Then we would randomly sample clusters in a given

wilderness area, locate and enumerate all campsites occurring in the sampled

clusters. Stopping all cars for interviews with occupants on randomly

selected days would be one example of a temporal cluster, expected maximum

heterogeneity within the day and homogeneity across days.

Procedure for Cluster Sampling

 1. Define the “cluster” to be used as sampling unit.

 2. Number clusters sequentially from 1 to N.

 3. Determine the appropriate number of clusters to be sampled.

 4. Draw a random sample of clusters.

 5. Take complete data from each of the sampled clusters.

The efficiency of cluster sampling may be increased further by stratification, reducing cluster size, and subsampling. See Ackoff (1953) for details.

Advantages of Cluster Sampling

 1. Relatively low field costs, since it requires the enumeration of individuals in selected clusters only.

 2. The characteristics of clusters, as well as those of the population, can be

estimated.

 3. Data can be combined with those obtained in subsequent samples, since

clusters, not individuals, are selected.

Disadvantages of Cluster Sampling

 1. It has lower statistical efficiency than other sampling techniques.

 2. Each member of the population must be uniquely assigned to a cluster;

this may be difficult if the characteristics defining the cluster are ambiguous.

 3. Cluster properties may change so that the cluster sample may not be

usable in later data analysis.

Effects of Sample Design on Use Estimates: A Case Study

 As part of a study estimating visitor impact in the East Hickory Trail in the

Cohutta Wilderness, visitor counts were obtained on a daily basis over the

entire summer season (table 4 and fig. 4). The manager’s immediate objective

was to estimate the daily average number of users. To illustrate the effects

of sampling method on the efficiency of the sample estimate, we analyzed the

same data set using several sampling techniques.

The sampling frame is the total number of days in the season, or N = 112

consecutive days, from the beginning to the end of the summer season.

Assume that a sample size n = 20 will allow estimates of the preferred

population characteristics with the required precision.

 1. Random sampling. We need to select 20 consecutive three-digit

numbers between 1 and 112. Suppose the randomly selected start point

occurred on row 36, column 7. Thus, the first random triplet is 020, or 20. The

next three-digit number, 302, is larger than 112, and is discarded, as are the

next 13 sets of triplets. The next two “usable” random numbers are 031 and

076. The triplet 020 in row 37 columns 7 and 8 is less than 112, but was

selected previously; this second value is discarded. In this example, the

unique set of random numbers obtained was as follows: 020, 031, 076, 040,

081, 015, 090, 097, 006, 054, 084, 052, 107, 033, 044, 001, 101, 046, 049, 073.
56 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Once the entire set of 20 random numbers is obtained, the numbers are

ordered and observations are made on those days. The data are:

No. No. No. No.

Day users Day users Day users Day users

1 57 33 8 52 18 84 8

6 13 40 14 54 7 90 18

15 34 44 57 73 15 97 11

20 31 46 8 76 11 101 7

31 12 49 13 81 34 107 53

The estimated mean number of users is 21.45 (the mathematical average)

and the standard error is 3.79 (from computations described in the appendix).

 2. Systematic sampling. Computations for systematic sampling follow

those for simple random samples. The standard error is 3.44.

 3. Multiple systematic sampling. Computations for multiple systematic sampling are given in Chapter 3: Sampling Methods. The standard error

is 3.292.

 4. Stratified sampling: proportional n. The manager decided to stratify

days on the basis of relative use, as defined by the number of visitors entering

the area. “Light” use occurred on normal business days (Monday through

Friday), whereas weekends (Saturday and Sunday) were characterized by

“heavy” use. There are therefore two strata, weekdays and weekends. In a

112-day season, there were 80 weekdays and 32 weekend days.

For a proportional stratified sampling design, the manager could afford to

take 20 observations, which is about 18 percent of the 112 day season or 18

percent of 32 and 80, which gives 6 and 14 days allocated between the

weekend days and the week days. For convenience, a systematic sample was

used in each stratum after the days in each stratum are numbered separately. The first stratum (“weekday”) consists of 80 days; therefore the

sampling interval is 80/14 = 5.7, or 6, and the start value is selected from the

random numbers between 1 and 6. There are 32 days in the second (“weekend”) stratum. Therefore the sampling interval will be 32/6 = 5.3, rounded to

5, and the start value will be chosen by selecting a random number between

1 and 5.

Suppose the random start values for each stratum are 4 and 1 respectively.

Then the two stratified samples are as follows:

Weekend days Weekdays

Day No. users Day No. users Day No. users

4 57 1 11 43 14

9 43 7 13 49 12

14 57 13 15 55 13

19 83 19 13 61 14

24 33 25 5 67 26

29 78 31 10 73 12

37 13 79 25

Mean 58.5 14.0

SD 19.37 5.43

The combined estimate of the population mean is: (32/112)·(58.5) + (80/

112)·(14.0) = 26.71 with an estimated standard error of 2.25.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 57

 5. Stratified sampling: disproportional n. For a disproportional sample,

the sample sizes for each group will be the same; that is, n1 = n2 = 10. The

sampling interval for the weekend stratum is 32/10 = 3.2, or 3, and the start

value is a random number between 1 and 3. For the weekday stratum, k is

80/10 = 8, and the start value is a random number between 1 and 8. Suppose

the random start values were 1 and 4 for the first and second strata

respectively. Then the sample days and their corresponding data are as

follows:

Weekend days Weekdays

Day No. users Day No. users

1 57 4 13

4 57 12 5

7 41 20 12

10 43 28 14

13 33 36 18

16 58 44 10

19 83 52 7

22 43 60 8

25 28 68 8

29 48 76 16

Mean 49.1 11.1

SD 15.63 4.20

The combined estimate of the population mean is 21.96 with an estimated

standard error of 1.62.

The results for the five types of sampling procedures are summarized as

follows:

Sampling method Estimated population mean Standard error

Random 21.45 3.44

Systematic 20.00 2.98

Multiple systematic 22.10 3.29

Stratified:

proportional 26.71 2.25

Stratified:

disproportional 21.96 1.62

Note that the estimated population means differ for each of the five

sampling methods since they use different samples, but all are reasonably

consistent. Random sampling is least efficient because it has the largest

standard error in comparison with other methods with the same sample size.

Stratified sampling gives the most efficient sample estimates.

Field Sampling Strategies

Sampling strategies must be developed for scheduling the rotation of

“observers” across trailheads, scheduling “observer” effort (observation periods), calibration, compliance estimation, and visitor selection.

Scheduling “Observer” Rotation Across Trailheads

Monitoring every access point is feasible only if the wilderness area has

relatively few access points and funding is not restricted; in this case, a

rotation strategy is not required. However, it is more likely that the number

of available “observers”—mechanical counters, human observers, cameras,

or registration stations—will be insufficient for large-scale monitoring.
58 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Therefore, available resources must be rotated systematically. Rotation

schedules will depend on the number of access points to be surveyed and the

frequency for which use estimates are required.

Rotation strategies are determined primarily by perceived differences in

use occurring in either space or time. We recommend a more-or-less permanent allocation of an “observer” to each high-use trailhead; the overall

accuracy of total use estimates will depend primarily on the accuracy of

estimates obtained for high-use trailheads.

As a general rule of thumb, it is suggested that an “observer” is allocated

to the trailhead with the highest amount of visitor traffic; other “observers”

are rotated systematically across the remaining trailheads, such that the

amount of time allocated to each trailhead is proportional to the use that

trailhead is expected to receive.

Scenario 1. Suppose a manager must monitor use at four trailheads, but

only two mechanical counters are available. One trailhead is believed to

account for about 60 percent of use in that wilderness area; a second trailhead

is believed to account for about 20 percent of the use and the two remaining

trailheads receive an equal amount of the remaining use. Therefore, the

second counter is allocated to the second trailhead for half of the time, and

allocated between the two remaining trailheads in proportion to anticipated use.

Scenario 2. Suppose use estimates are required for an entire wilderness

area over an entire season. It has been determined by preliminary surveys

that use patterns are fairly stable within a particular geographic section of

the wilderness area, but extremely variable over the use season. Therefore,

widespread sampling of the wilderness area is required.

Strategy: Account for use in each section by allocating one counter

for every x access points.

Scenario 3. Suppose more intense sampling of a particular section is

required, but use patterns are sufficiently stable such that monitoring every

other year is sufficient to generate adequate use estimates.

Strategy: (1) Divide wilderness access points into two to four sections, such that each section contains an equal number of access

points or trailheads (say four or five); (2) place counters on all

trailheads within a randomly selected section for 1 year; (3) rotate

counters to a new section each year.

This strategy would reduce costs associated with moving counters;

the obvious disadvantage is that use estimates for a given section can

be obtained only every 2 to 4 years.

Example. Suppose the manager wishes to estimate use for the entire 16-

week summer season; there are four trailheads and two mechanical counters.

One counter is permanently allocated to the high-use trailhead, leaving

three trailheads to be monitored with one counter. The 16-week season is

partitioned into eight 2-week blocks. The counter will be allocated to each

trailhead for two separate time blocks; this leaves two blocks as discretionary

time.

The order in which the counter is assigned to each of the three trailheads

is determined randomly. Suppose the random number sequence for the eight

time blocks is 5 7 8 3 2 6 1 4, and the random sequence for the three trailheads

is 3 4 2. Then the counter will be assigned to trailhead 3 on time blocks 5 and

7, to trailhead 4 on time blocks 8 and 3, and to trailhead 2 for time blocks 2

and 6.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 59

Scheduling Observer Effort

Observation periods are determined by partitioning the visitor season into

defined time blocks, numbering the blocks, then randomly selecting the time

blocks for which observations are to be made. The length of the observation

period is determined by operational convenience; it may be measured in

minutes, hours, days, or weeks. As a general rule of thumb, “observers”

should be placed at each trailhead for at least two observation periods.

Example. A preliminary study of use patterns in a certain wilderness area

suggests that the number of visitors is fairly constant over the season. It was

observed that approximately 20 percent of wilderness users entered the area

on weekdays, another 40 percent of users entered on Saturday mornings, 10

percent on Saturday afternoons, 20 percent on Sunday mornings, and 10

percent on Sunday afternoons. A total of 10 observation periods can be

sampled with the resources available.

The manager decided to partition the sampling day into morning and

afternoon time blocks. Time blocks were further stratified into three operationally defined use categories: low, medium, and high. Observer effort was

allocated in proportion to amount of use. Thus 20 percent of sampling effort

was allocated to low-use periods (that is, two time blocks occurring on either

a weekday morning or afternoon); 40 percent effort to high-use periods (four

Saturday mornings), and the remaining effort to medium-use time periods

(one Saturday afternoon, two Sunday mornings, and one Sunday afternoon.

The specific time blocks to be monitored were selected by random sampling.

The entire monitoring period required for this sampling plan is approximately 4 weeks.

Calibration

Calibration requires that observations obtained from the primary counting

device (usually a mechanical counter) are paired with observations obtained

by a method of known accuracy (either human observers or cameras). The

number of calibration samples to be taken will depend on the amount of

precision required, the resources available for calibration, and the relative

stability of use over time. The accuracy of calibrations must be spot checked

at intervals and updated as required; if use patterns change substantially

over the season, calibrations made at the beginning of the season will not be

applicable to counts made later in the season.

Camera Calibration.—Use of hidden cameras requires a minimum amount

of personnel involvement. Cameras are installed on the traffic area where the

item to be calibrated (mechanical counter, registration station, and so forth)

is installed. To maximize the efficiency of the method, cameras must be set

up so that traffic will be visible for long distances.

There are two general sampling strategies for camera calibration: fixedinterval monitoring and counter-activated monitoring.

(1) Fixed-interval monitoring. The camera is activated at programmed

time intervals; all traffic during a sample period is photographed. Specific

intervals are selected by random sampling procedures.

(2) Counter-activated monitoring. The camera is attached to a mechanical

counter, and takes photos only when the counter is activated by visitor

traffic. This technique provides a measure of overestimation bias only; it does

not provide information on error occurring because of visitors undetected by

the counter. An alternative may be to have a separate activator for the camera.
60 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

For example, a counter may be activited by an active infrared sensor, while

the camera is activated by a passive infrared sensor, or a very sensitive

seismic sensor.

Calibration by Human Observers.—Calibration with observations taken

by human observers is more labor intensive than use of cameras, but is more

accurate. Observers should be stationed close enough to the item to be

calibrated (counter, registration station, and so forth) so that all traffic is

observed; although observers need not be exactly by the check point, they

should not wander up and down the trail.

Scheduling of agency personnel may have to occur within the confines of the

workweek. However, if significant amounts of use occur outside of normal

working hours, it is essential that these time blocks are covered; volunteer

labor may be one option. Observer fatigue and boredom may be a significant

problem if time blocks are extremely long and few visitors are encountered.

Sampling effort may be apportioned according to operationally defined

amounts of relative use observed per time block. At least two observation

periods should be scheduled for each category.

Compliance Estimates

Compliance is the estimate of the number of visitors who actually register

or obtain permits. Compliance estimation is essentially similar to the

calibration procedures described above; visitor registration is “calibrated” by

supplementary observations so that the number of wilderness users who do

not register can be accounted for, and total visitor counts can be adjusted

accordingly. The number of supplementary observations taken will depend

on the amount of precision required, the resources available for compliance

checks, and the relative stability of visitor use over time. If use patterns

change substantially over the season, registration rates or permit compliance rates estimated at the beginning of the season will not be applicable

later in the season; the accuracy of registration rates must be spot checked

at intervals and updated as required.

Frequently, permit or registration compliance estimates are obtained in

the course of routine wilderness ranger patrol. In the so-called “roaming

observation” technique, rangers check for compliance as visitor groups are

encountered, and tally the proportion of those encountered who are not in

compliance. However, this type of visitor sampling results in highly biased

estimates of visitor use. Bias occurs for a number of reasons: (1) because the

probability of visitor contact depends on when and where the observer

travels, (2) scheduling is not random but deliberately selected to coincide

with periods of heaviest use, and (3) the probability that a visitor group will

be encountered is proportional to the length of time spent in a given area,

observer location in relation to visitor distance traveled, and so on.

Unbiased data can be obtained only by implementing predetermined

statistical sampling strategies. Permit checkpoints are established in accordance with a spatial sampling scheme (see above); sampling of visitors at

each checkpoint may be completely random, systematic (for example, selective censusing of every tenth wilderness visitor, or every fifth car passing a

checkpoint), stratified, or a combination of these.

Determining Total Population Size from Compliance Sampling.—The size

of the total wilderness visitor population is estimated by the direct sampling

procedures used to estimate compliance or registration rates. The method is
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 61

analogous to the Peterson or Lincoln capture-recapture indices used in

wildlife population estimation. It should be used whenever total population

size is to be estimated from ratio data.

The total number of visitors in a given time period is N, the quantity to be

estimated. The total number of permits issued (or registration cards completed) is t. At some period during the visitor season, wilderness rangers

survey n visitors, of which s are found to be in compliance (that is, have

actually obtained a permit or registered). Then the compliance rate is

estimated as the proportion of the surveyed sample, or r = s/n. The total

population is estimated as:

Nˆ n

s

t

t

r = ⋅=

The 95 percent confidence interval is N ± 2 · SE, where SE is approximately

SE =

 

t nn s

s

2

3

⋅ − ( ) .

Example. A total of 300 permits were issued for a given wilderness area.

Subsequently, the wilderness ranger randomly sampled 50 visitors, of which

30 had permits. The compliance rate was therefore r = 30/50 = 0.6, or 60

percent. The total number of visitors entering the area was estimated as N

= 300/0.6 = 500, with a 95 percent confidence interval of approximately 500 ±

 

2 300 50 50 30

30

2

3

() ( )

( )

⋅ − ≅ 500 ± 115, or between 385 and 615 visitors.

Visitor Selection

The sampling strategy for visitor selection requires both an estimate of the

sample size, and a time schedule. Unless the wilderness area has a strictly

enforced permit program, visitors cannot be randomly selected prior to

arrival. If there is no regulation of visitor entry and exit, the investigator

must make a random selection of “contact days”, followed by random

selection of visitors within the contact day. Sampling may be completely

random, systematic (for example, selective censusing of every tenth wilderness visitor, or every fifth car passing a checkpoint), stratified, or a combination of these.

The number of visitors that must be sampled is determined with reference

to the population of interest, the type of response variables to be measured

(categorical, count, continuous), the expected variation of the response

variables, and the specified sampling strategy. Determination of the appropriate sample size requires a preliminary estimate of the variability in the

observations. Preliminary estimates are obtained from a pilot study, or from

data collected in previous years.
62 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 63

Part II: Selecting and

Building a Use

Estimation System
64 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 65

Introduction

There are 10 major use estimation systems described in separate sections

within part II. Each section is divided into two parts consisting of a System

Description and a description of the Operational Procedures. Operational procedures are detailed in a series of steps, with their number varying

according to the particular system of interest. Procedural guidelines are

given for the following elements:

1. Use characteristics that can be measured with the particular system

2. Measurement techniques

3. Equipment purchase

4. Equipment installation

5. Data collection strategies

6. Visitor use calculations

Because each section is intended to be self-contained, there is some overlap

in information between sections. Additional information required for implementing the specifics of data collection, sampling strategies, and data

analysis are discussed in part I.

The 10 use systems are summarized (table 5) in terms of two organizational

categories: information category and data collection techniques. Each

column represents a system, designated by a capital letter (A, B, C, and so

forth), followed by the page number indicating where that system is described. The components of each system are indicated by an X in the

appropriate row representing various required components. The potential

for each system to provide needed information is evaluated through categorization of potential objectives:

 I. Visit counts

 II. Observable visit and visitor characteristics

III. Simple nonobservable characteristics (easily reported information implying minimal visitor burden—for example, length of stay, age)

IV. Complex nonobservable characteristics (more complicated or involved information, implying increased visitor burden—for example, attitudes, opinions)

 V. Summary use statistics

The use of table 6 is illustrated in the following example. Suppose the stated

management objective is to obtain a visit count for a certain time period.

Table 5.I. (“Visit Counts”) shows that all systems A through J provide that

information; thus, choice of a system will be dictated by cost and ease of

implementation. However, suppose information must be obtained on some

nonobservable visit characteristic such as length of stay. Table 5.III. (“Simple

Nonobservable Visit and Visitor Characteristics”) shows that systems A, B,

and D will not provide this information at all; options are restricted to the

remaining seven systems.
66 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Table 5—Summary of 10 user-estimation systems categorized by information category and system elements.

System A. Mechanical counters with visual calibration

System B: Mechanical counters with observer calibration and sample observations

System C: Mechanical counters with observer calibration and sample interviews

System D: Visitor registration system with checks for registration rate

System E: Visitor registration system with registration rate checks and sample interviews

System F: Permit system with compliance checks

System G: Permit system with compliance checks and sample interviews

System H: Permit system with compliance checks and mailback questionnaires

System I: Indirect counts

System J: General visitor surveys

Table 5 (cont.)

I. Visit Counts

(individual counts, group counts)

Use estimation system

ABCDEFGH I J

Data collection techniques p. 68 p. 79 p. 90 p. 101 p. 110 p. 121 p. 128 p. 138 p. 150 p. 158

Mechanical counters X X X .......

Visual calibration (accuracy) X X X .......

Sample observations . X ........

Sample interviews . . X .......

Visitor registration . . . X X .....

Registration rate check . . . X X .....

Sample interviews . . . .X. . . . .

Permits . . . . . XXX . .

Permit compliance checks . . . . . XXX . .

Sample interviews . . . . . .X. . .

Sample mailback surveys . . . . . . .X. .

Indirect counts . . . . . . . .X.

General visitor surveys . . . . . . . . .X

Table 5 (cont.)

II. Observable Visit and Visitor Characteristics

(individual counts, group counts, group size, number of stock, method of travel, gender, approximate age classes,

time of entry or exit, day use vs. overnight use)

Use estimation system

ABCDEFGH I J

Data collection techniques p. 68 p. 79 p. 90 p. 101 p. 110 p. 121 p. 128 p. 138 p. 150 p. 158

Mechanical counters . X X .......

Observer validation (accuracy) . X X .......

Sample observations . X ........

Sample interviews . . X .......

Visitor registration . . . X X

 Registration rate check . . . X X .....

 Sample interviews . . . X X .....

Permits . . . . . XXX . .

Permit compliance checks . . . . . XXX . .

Sample interviews . . . . . .X. . .

Sample mailback surveys . . . . . . .X. .

Indirect counts . . . . . . . .X.

General visitor surveys . . . . . . . . .X
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 67

Table 5 (cont.)

III. Simple Nonobservable Visit and Visitor Characteristics

(length of stay, travel routes, sociodemographics., etc.)

Use estimation system

ABCDEFGH I J

Data collection techniques p. 68 p. 79 p. 90 p. 101 p. 110 p. 121 p. 128 p. 138 p. 150 p. 158

Mechanical counters . . X . . . ....

Observer validation (accuracy) . . X . . . ....

Sample interviews . . X . . . ....

Visitor registration . . . .X. . . . .

Registration rate check . . . .X. . . . .

Sample interviews . . . .X. . . . .

Permits . . . . . XXX . .

Permit compliance checks . . . . . XXX . .

Sample interviews . . . . . .X. . .

Sample mailback surveys . . . . . . .X. .

Indirect counts . . . . . . . .X.

General visitor surveys . . . . . . . . .X

Table 5 (cont.)

IV. Complex Nonobservable Visit and Visitor Characteristics

(visitor attitudes and preferences, perceptions of social and resource conditions, and so forth)

Use estimation system

ABCDEFGH I J

Data collection techniques p. 68 p. 79 p. 90 p. 101 p. 110 p. 121 p. 128 p. 138 p. 150 p. 158

Mechanical counters ..........

Observer validation (accuracy) ..........

Sample interviews ..........

Visitor registration . . . .X. . . . .

Registration rate check . . . .X. . . . .

Sample interviews . . . .X. . . . .

Permits . . . . . . XX . .

Permit compliance checks . . . . . . XX . .

Sample interviews . . . . . .X. . .

Sample mailback surveys . . . . . . .X. .

Indirect counts . . . . . . .X.

General visitor surveys . . . . . . . . .X

Table 5 (cont.)

V. Summary Use Statistics

(recreation visitor-days, visitor-hours, and so forth)

Use estimation system

ABCDEFGH I J

Data collection techniques p. 68 p. 79 p. 90 p. 101 p. 110 p. 121 p. 128 p. 138 p. 150 p. 158

Mechanical counters . . X . . . ....

Observer validation (accuracy) . . X . . . ....

Sample observations . . X . . . ....

1 registration . . . .X. . . . .

Registration rate check . . . .X. . . . .

Sample interviews . . . .X. . . . .

Permits . . . . . XXX . .

Permit compliance checks . . . . . XXX . .

Sample interviews . . . . . .X. . .

Sample mailback surveys . . . . . . .X. .

Indirect counts . . . . . . . .X.

General visitor surveys . . . . . . . . .X
68 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System A: Mechanical Counters

With Visual Calibration

System Description ________________________________________________

This system enables the manager to obtain visit counts (individual or group

visits). Mechanical counters are set up to count trail traffic; the reliability of

counter data is assessed by simultaneous monitoring of trail traffic by either

human observers or cameras. These reliability checks (calibration) are the

key feature of the system. Because data recording and calibration are

performed without contacting visitors, there is little or no visitor burden.

Summary of System A:

Type of observations: Counts

Measures of visitor use: Number of individual visits

Number of group visits

Data collection strategies: Sample plan for counter rotation (if applicable)

 • spatial

 • temporal

Sample plan for visual calibration

Techniques/procedures: Mechanical counters

Calibration by visual observations

 • cameras

 • human observers

Visitor burden: None

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics

The use characteristics estimated with this system are limited to individual or group visit counts. Calibration determines the accuracy of the

counts; it does not provide additional data for estimating total use.

Step 2: Decide on Counter Type

There are three main types of counters currently available: photoelectric

counters, sensor pad counters, and loop-type sensor counters. Counter

selection depends on installation site, vandalism concerns, potential environmental influences on counter accuracy, equipment cost, and maintenance

requirements.

1. Installation Site.—Characteristics of the proposed installation site will

determine the type of counter that is most appropriate. Site characteristics

to be evaluated include the presence or absence of tree cover, soil type, and
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 69

slope. Photoelectric counters must be attached on a vertical surface so that

the sensor and the reflector are opposite each other and located at a distance

of 100 feet or less. If counter components are attached to trees, each tree

should be large enough to prevent excessive swaying. If there are no suitable

trees at the proposed site, posts may be installed if the soil allows digging;

however, posts must be concealed in brush to avoid vandalism. Soil type and

depth are important if sensor pads and loop-type counters are considered, as

these sensors should be buried to be operative. If digging is difficult, or the

proposed monitoring site is located on a steep or unstable surface, or both,

these counters will not be appropriate.

2. Equipment Vandalism.—Vandalism, theft, and tampering with counter

equipment are serious concerns, especially in heavy-use areas near trailheads

or parking areas. Because counter components are above ground, photoelectric counters are the most vulnerable to vandalism. Camouflaging the

equipment may prevent detection. The plastic housing of the TrailMaster

counters makes them the most susceptible to vandalism or animal damage;

the long-term durability of these counters has not been assessed. Sensor

pads are less susceptible to vandalism because they are buried, although the

counter mechanism itself must be located so that the counter display can be

read easily. The counter mechanism must therefore be camouflaged. Looptype counters are completely buried and therefore are relatively free from the

potential of damage. Avoid creating obvious trails to equipment placed off the

trails. Visitors may follow these trails out of curiosity, but this traffic may

increase the likelihood of tampering with equipment or disrupt normal

traffic flow.

3. Environmental Influences on Accuracy.—Environmental factors influencing counter accuracy include habitat structure, weather, and wildlife.

Structural factors include canopy density and substrate. For example,

counts obtained from sensor pads may be overestimated by vibration generated by swaying trees or by other ground vibrations which are not related to

visitor traffic; extremely deep or dense snow may diffuse foot traffic vibrations and bias counts upward. Count underestimates occur with photoelectric counters if the emitted beam misses the reflector, as occurs with

excessive tree sway. Wildlife passing within the detection region of passiveinfrared sensors may register a count. During rain events moisture on

receivers and reflectors may affect count accuracy.

4. Equipment Cost.—Prices vary from approximately $300 to $500 for

photoelectric and sensor pad counters to over $1,200 for loop-type counters.

Expense is increased with the inclusion of various options, such as camera

attachments. It is highly desirable that counters provide time and date

stamping of count readings; this option facilitates calibration. See table 2 for

details of equipment manufacturers, specifications, options, and associated

costs.

5. Maintenance Requirements.—Visitation of each counter station should

be performed regularly; schedules will depend on battery life, data storage

capacity, potential for equipment failure or vandalism, and counter rotation

schedules (determined before the monitoring program is in place; see below).

Data must be downloaded before batteries begin to fail, or before storage

capacity is exceeded. Battery life varies from 60 to 90 days for photoelectric

counters to over 1 year for loop-type counters. Data storage capacity is

usually much less than battery life. For example, memory capacity of loop-type

counters is limited to 40 days of hourly time-stamped data; this type of
70 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

counter would have to be visited at least this often. Memory capacity of

certain photoelectric counters may be count-limited rather than time-limited; for example, standard TrailMaster counters have a storage limit of

approximately 1000 counts. For these counters, the time between data

downloadings would depend on visitor traffic volume. Finally, the time order

and intervals of counter rotation and calibration must be scheduled.

Step 3: Decide on the Number of Counters Needed

The number of counters to acquire will be determined by the number of

access points to be monitored and the equipment budget. Ideally, mechanical

counters should be acquired for every access point. In practice, funding

limitations, the size of the wilderness area to be monitored, and relatively

large numbers of potential access points mean that the number of available

counters will be far fewer than the number required. In this case, counters

must be rotated systematically (see step 5).

Step 4: Choose the Calibration Method

Calibration is the procedure for assessing the reliability of the counting

device by comparing its output to some alternative method of known

accuracy. Calibration is performed by recording the number of individuals or

groups passing the mechanical counter during a specified observation period;

simultaneous counter readouts are obtained for the same period.

The calibration method chosen depends on:

1. The relative amount of labor and resources required for implementation.

2. The type of bias that must be estimated.

Counter output may show either overestimation bias (the counter

registers something it should not count), or underestimation bias (the

counter does not count something it should). The calibration technique

chosen should provide an accurate measure of one or both types of bias if

possible.

The two methods of calibrating counters: with cameras, or with human

observers.

1. Camera Calibration.—Cameras are installed at the traffic area where

the counter is installed; to maximize the efficiency of the method, cameras

should be set up in places where traffic will be visible for long distances. This

method minimizes the amount of personnel involvement and both types of

counter bias.

(a) Fixed-interval monitoring. All traffic during a sample period is

photographed. The camera is activated at programmed time intervals; these

intervals are selected by statistical sampling procedures.

(b) Counter-activated monitoring. The camera is attached to the counter

itself, and takes photos only when the counter is activated by visitor traffic.

This technique provides a measure of overestimation bias only; that is, it does

not provide information on errors occurring because of visitors undetected by

the counter. This strategy enables the investigator to verify group size, traffic

direction, and so forth, for visitors who actually activate the camera; blank

photos and wildlife photos enable estimates of false counts.

2. Observer Calibration.—Calibration by human observers is more labor

intensive than camera calibration, but it is more accurate. Observers should
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 71

be stationed close enough to the counter so that all traffic activating the

counter is observed; although observers need not be right on top of the

counter, they should not wander up and down the trail.

For calibration purposes, the minimum information to be recorded by

observers includes: number of individuals, number of groups, method of

travel, direction of travel, and date and time of entry or exit. Additional

information on visit or visitor characteristics may be obtained if desired; a

sample observer recording sheet is shown in figure 1. However, it must be

emphasized that observation is remote; observers do not stop visitors.

Step 5: Develop a Sampling Plan

Sampling plans must be developed for:

1. Systematic scheduling of counter rotation across trailheads (if the

number of counters does not equal the number of access points), and

2. Calibration (if observers or cameras cannot provide for continuous

calibration).

Step 6: Purchase Equipment

Table 2 gives information on counter manufacturers, equipment specifications and associated costs (1995 prices).

Step 7: Install Equipment

Specifics for site location were discussed in step 2. In general, counters

should be placed some distance away from the trailhead so that only bona fide

wilderness visitors are counted, and casual visitors (those who travel only an

extremely short distance) are excluded. However, if the wilderness boundary

is an extremely long distance from the trailhead, the increase in personnel

time involved in traveling to the counter site for reading and calibrating

counters may make this option untenable. We do not advise locating counters

where the trail is unduly wide (thus allowing visitors to travel two or more

abreast and underestimating counts), or at natural resting places (where

they may mill around and cause multiple counts). Narrow portions of the trail

at locations where traffic flow is more or less continuous offer the best count

locations.

The time required for counter installation will vary according to distance

from the trailhead and counter type. After arriving at the selected site, at

least 1 hour will be required for counter installation. This includes time spent

examining the site, selecting the best place for counter location, installing the

sensor and the counting mechanism, setting counter sensitivity or delay, and

testing counter operation. If a counter is mounted on a tree trunk (as is the

case for photoelectric counters), the counter will likely shift slightly within

the first day or two as a result of tree wounding; the counter should therefore

be checked, and realigned if necessary, on the second day after initial

installation. If cameras are used for calibration, additional time is required

to address privacy concerns (the camera must be located far enough from the

trail so that individuals cannot be identified in the pictures, camera adjusted

to be slightly out of focus, and so forth).

After the equipment has been installed, observe conditions for a short time

to make certain that the counter is functioning correctly and that any

camouflage is not obscuring or tripping the counter continuously. Walk over
72 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

the pad or through the beam several times to check counter sensitivity, and

adjust accordingly.

All equipment should be labeled with agency identification, a statement of

purpose, and the name, address, and telephone number of a designated

contact person. A message explaining that the camera is for detecting use

levels, and that individual identities cannot be determined, may reduce the

risk of vandalism if visitors do locate the equipment.

Step 8: Collect Calibration Data

Calibration information is collected according to a specific sampling strategy (as described in step 5). The specifics of collecting calibration information

will depend on whether cameras or human observers are used.

1. Camera Calibration.—Calibration observations are recorded with either motion picture (8-mm or VHS recorder) or a camera. If the camera is on

a timer, photos, or a series of frames, can be obtained at fixed intervals; the

camera can be attached to a mechanical counter and triggered to shoot by

visitor traffic. Because camera detection could result in theft or vandalism of

equipment; cameras must be positioned far enough from the trail so that

visitors cannot hear the shutter or motor action; camera equipment should

be well camouflaged. When performing routine visits, do not approach

equipment over the same route every time; frequent travel could result in the

development of a recognizable path and subsequent detection of equipment

by unauthorized persons.

Film consumption should be monitored closely; calibration data will be

useless if the camera runs out of film during this phase. After removing

exposed film from the camera, label immediately with the date, time, and

location. Protect exposed film from extreme heat and cold until developed.

Record necessary observations from the developed film; observations

include number of individuals, number of groups, date and time of entry or

exit. The method of recording observations should be standardized to minimize errors in recording. After observations are recorded, destroy negatives

and developed photos to assure visitor privacy.

2. Observer Calibration.—The observer must be stationed somewhere

near the counter where the trail is clearly visible. If trail traffic is low,

observers may perform other tasks in the vicinity of the counter, such as trail

clearance and maintenance, visitor education, or reading; these help pass the

time and reduce observer fatigue and boredom. However, if the observer is

stationed at some distance and by observing traffic through binoculars, it is

not advisable to engage in other types of activity because of the potential for

missing visitors if attention is diverted from the trail. Observers should be

in appropriate uniform and possess necessary communication and safety

equipment.

Observations must be recorded in a standardized format. For each data

sheet the observer should record his or her name, the sampling location, the

date, start time, the initial counter reading, end time, and the final counter

reading for that sample period. During the sample period the observer

records the number of individuals or groups passing the observation station,

the time of the event, and the direction of travel. The observer must be

provided with sufficient data forms for the observation period. Observers

must understand the need to completely fill out the data form; sample

observations will be useless if the data collected by the observer cannot be
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 73

matched with the appropriate counter data. Observation sheets should be

filed in a designated place after the observer returns to the office.

Step 9: Collect Counter Data

Counts logged by the mechanical counter are recorded at intervals determined by the sampling plan. If counters are permanently allocated to a given

location, the frequency of recording will be determined by the calibration

sampling plan. At a minimum, counts should be recorded at least twice per

month to ensure that data are not lost because of equipment malfunction.

The person obtaining count readings should check battery power and

equipment operation, and for any changes in the surrounding area which

may affect count accuracy. For example, fallen branches or trees could block

the electronic beam from the scanner, or result in the rerouting of trail traffic

away from the counter path.

Step 10: Estimate Use

Use data are collected in accordance with the desired sample size and the

sampling strategy. Because mechanical counters are the sole method of data

collection, use characteristics estimated with this system are limited to

individual or group visit counts. Use data may be expressed as a rate (for

example, number of visitors/day), or total (for example, number of visitors for

the season). In general, totals are estimated by multiplying the average daily

rate by the number of days in the time period of interest, corrected for possible

bias in estimated counts. Data collected during the calibration phase may be

used to provide estimates of the sample size required for the actual observation phase of the study.

Example. Visitor traffic in the Alpine Lakes Wilderness was studied in

1991. Measures of use were assessed at the primary trailhead access for

Snow Lake—an easily accessed high-use trail with a high concentration of

day users. The total length of the visitor season was 100 days.

1. Calibration.—The initial calibration period was 15 observation days.

The paired data used to establish the calibration relationship were as

follows:

Day Mechanical counts (X) Visitors observed (Y)

Friday 132 119

Saturday 514 408

Sunday 604 556

Wednesday 107 119

Thursday 74 74

Friday 107 113

Saturday 423 424

Sunday 438 323

Friday 92 78

Saturday 370 380

Sunday 406 356

Wednesday 127 98

Thursday 80 87

Saturday 325 252

Sunday 400 361
74 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The summary statistics for these data are as follows: n = 15, ΣX = 4,199,

ΣX2 = 1,643,937, ΣY = 3,748, ΣY2 = 1,294,490, ΣXY = 1,450,388, X = 280,

 Y = 250. If no mechanical counters were used or if their data is ignored, the

observed data could be used to compute an estimate of total use. The mean

of the 15 observed values is 250 with a standard error of 41, making the 95

percent confidence interval 250 ± 2·41 = (167, 332). If the data is stratified

by weekends and weekdays, the estimated means and confidence intervals

are 382 (320, 445) and 98 (84, 113), respectively. Since there were 72

weekdays and 28 weekend days in the 100 day season, these individual

estimators are combined as weighted averages to make overall estimators of

17,786 (15,755, 19,817). Differences from the overall (unstratified) estimator

above may be due to an over representation of weekend days in the sample.

The mechanical counter data may be used to increase precision by estimating a regression relationship (see appendix): Y = 10.15 + 0.86·X. The standard

error of the regression equation ( MSE ) is 33.31. The R2

 value is high (0.96),

suggesting that a straight line is a good approximation of the relationship

between the two variables. However, examination of the data plot (fig. 5)

shows that there are two distinct subgroups in the data. These subgroups

correspond to the day of the week on which observations were obtained;

weekends had substantially higher counts than weekdays. This suggests

that the sampling plan for the observation phase should incorporate stratification by time periods.

Because the regression slope is less than 1, the actual number of visitors

will be overestimated by the mechanical counter data. A crude estimate of the

Figure 5—Plot of visitor counts derived from a mechanical counter in comparison to those obtained from human

observers (Alpine Lakes Wilderness, 1991).

0 

100 

200 

300 

400 

500 

600 

0 100 200 300 400 500 600 700 

Mechanical Counts

Alpine Lakes Wilderness

Actual Counts
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 75

amount of bias is given by the ratio estimator 

r

Y

X = = 250/280 = 0.89; that

is, 89 percent of counts registered by the mechanical counter could be

attributed to visitor traffic, with the remaining 11 percent due to other

causes. If visitor totals are estimated for relatively long time periods, there

may be a substantial amount of accumulated error in the results. Standard

errors and confidence intervals for ratio estimators are not generally recommended and are beyond the scope of this handbook.

2. Sample Size Estimation.—Because count data are collected by mechanical counters, large sample sizes for counts are relatively easy to obtain.

However, observation data are time-intensive and expensive to collect and

process; logistically feasible sample sizes should reflect reasonable operational costs associated with equipment and personnel.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

calibration phase was 250, with S = 160. There are 100 days in the season (N).

Suppose we want to be 95 percent certain that results will have a precision

of ± 5 percent, or ± 13 visitors/day. The estimated number of sampling days

is 

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( ) = 86. If the precision is adjusted to ± 10 percent

(or ± 25 visitors per day), then n = 62. Both of these are too large or too close

to the entire season of 100 days to be of practical use due to the large

underlying variance. A more reasonable level of precision would be ± 30

percent (or ± 75 visitors per day), which would call for a sample size of n = 15

as in the example above.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:
76 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

 

n p p

L = 42 1 ⋅⋅− 2

2

() ( )

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users,

p = 24/40 = 0.60

 and the standard error is p pn ( ) / ( . )( . ) / . 1 0 60 0 40 40 0 0775 −= = .

The 95 percent confidence interval based on these data is approximately 0.6 ±

2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

 

n = = 16 0 5

0 10

400

2

2

(.)

(. ) .

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

[ / ( )] . NS NS n ii ii ⋅ ⋅⋅ ∑ Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous

(that is, the standard deviations observed for each stratum are similar), whereas

optimal allocation should be chosen if strata differ in the amount of variability.

Example. In this example, data are stratified by two time blocks—weekend

days and weekdays. This stratification strategy separates out time periods

according to relative intensity of use, with the heaviest and most variable use

occurring on weekends, and relatively light and uniform use on weekdays.

For a 100-day season, there are about 72 weekdays and 28 weekend days.

Suppose the available resources (budget, labor, time) dictated that the

maximum number of days that could be sampled was n = 25. The initial value

for the standard deviation for each stratum was estimated from the data

obtained during calibration. Sample sizes for each time block are calculated

as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(N1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(N2 = 72)

aStandard deviation.

bSampling proportion.

c

Sample size.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 77

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

(3) Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms

of: (a) the rate (for example, number of visitors per day), or (b) the total (for

example, number of visitors for the season).

(a) Rate of use. In this example the observation period was 15 days; the

counter registered a total of 4,199 counts, averaging 280 counts per day. The

calibration or regression line is used to “correct” for counter bias by using it

to estimate the “actual” value as follows:

Y = 10.15 + 0.86·(280) = 250 visitors per day.

The 95 percent confidence limits are estimated as:

250 ± 2(33.31)

 

1

15

280 280

1 643 937 4 199 15

2

2 + −

−

( )

(, , ) , / = 250 ± 17, or between 233 and

267 visitors per day.

Accuracy may sometimes be increased if regressions are calculated within

each stratum rather than pooled over the entire observation period. In this

example, over 80 percent of all counts registered occurred on weekends; there

were 3,480 counts for the 8 weekend days monitored (averaging 435 counts

per day) and 719 counts for the 7 weekdays (averaging 103 counts per day).

The resulting regression estimates for each strata are as follows:

Weekend: Y = 1.71 + 0.875·(435) = 382 visitors per day, with 95 percent

confidence limits 382 ± 94, or between 288 and 476 visitors per day.

Weekday: Y = 31.1 + 0.654·(103) = 98 visitors per day, with 95 percent

confidence limits 98 ± 27, or between 72 and 125 visitors per day.

These estimators may be combined to get a “corrected” average daily total by

forming a weighted average of the individual estimates. Since there were 72

weekdays and 28 weekend days during the 100 day season, these two

estimates can be combined with weights of 72/100 and 28/100 to make an

overall estimate of visitors over the entire season. This overall estimator is

(72/100)·98 + (28/100)·382 = 178. A confidence interval for the average daily

use would be formed similarly as a weighted average of the lower and upper

confidence limits of the weekend and weekday usage rates of (132, 224).

In this example the small sample sizes and greater variability within strata

make the confidence interval for the stratified estimator much wider than

the unstratified estimator. The moral is that stratification may not always

result in narrower confidence intervals, but it will give more specific information about individual strata that may be very useful.

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.
78 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

In this example, season length was 100 days. The overall visitor use

estimate is therefore 250 (100) = 25,000 visitors (23,300 to 26,700 visitors).

Using the stratified regression estimators, the total count estimates are

17,800 with a confidence interval of (13,200, 22,400).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 79

System B: Mechanical Counters

With Observer Calibration and

Sample Observations

System Description ________________________________________________

This system provides information on both visit counts and simple observable visit and visitor characteristics. Observable characteristics are those

which can be directly observed and need not be determined by contacting

visitors; these include group size, number of stock, method of travel, gender,

approximate age, time of entry or exit, and whether a user appears to be a day

user or an overnight camper. Mechanical counters are set up to count trail

traffic. Monitoring by either human observers or cameras is used to assess

the reliability of counter data (calibration) and obtain information on

simple observable characteristics. Because there is no visitor contact, there

is no visitor burden.

Summary of System B:

Type of observations: Counts

Observable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Use by categories of user

Data collection strategies: Sample plan for counter rotation (if applicable)

• spatial

• temporal

Sample plan for calibration

Sample plan for observations

Techniques/procedures: Mechanical counters

Visual observations (cameras, human observers)

Visitor burden: None

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics

Direct measures of use include individual or group visit counts; mechanical

counters are used to collect count data, and count accuracy is assessed by

calibration with remote observation of actual traffic. However, additional

visit and visitor characteristics are acquired during the calibration process.

These data are simple observable characteristics which are recorded without

visitor contact; these include group size, number of stock, method of travel,

gender, approximate age, time of entry or exit, and whether a user appears
80 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

to be a day user or an overnight camper. Information on user characteristics

is used to categorize count data.

Step 2: Decide on Counter Type

There are three main types of counter currently available: photoelectric

counters, sensor pad counters, and loop-type sensor counters. Counter

selection depends on installation site, vandalism concerns, potential environmental influences on counter accuracy, equipment cost, and maintenance

requirements.

1. Installation Site.—Characteristics of the proposed installation site will

determine the type of counter that is most appropriate. Site characteristics

to be evaluated include the presence or absence of tree cover, soil type, and

slope. Photoelectric counters must be attached on a vertical surface so that

the sensor and the reflector are opposite each other and located at a distance

of 100 feet or less. If counter components are attached to trees, each tree must

be large enough to prevent excessive swaying. If there are no suitable trees

at the proposed site, posts may be installed if the soil allows digging; however,

posts should be concealed in brush to avoid vandalism. Soil type and depth

are important if sensor pads and loop-type counters are considered, as these

sensors should be buried to be operative. If digging is difficult, or the proposed

monitoring site is located on a steep or unstable surface, or both, these

counters will not be appropriate.

2. Equipment Vandalism.—Vandalism, theft, and tampering with counter

equipment are serious concerns, especially in heavy-use areas near trailheads

or parking areas. Because counter components are above ground, photoelectric counters are the most vulnerable to vandalism. Camouflaging the

equipment may prevent detection. The plastic housing of the TrailMaster

counters makes them the most susceptible to vandalism or animal damage;

the long-term durability of these counters has not been assessed. Sensor pads

are less susceptible to vandalism because they are buried, although the

counter mechanism itself must be located so that the counter display can be

read. The counter mechanism must therefore be camouflaged. Loop-type

counters are completely buried and therefore are relatively free from the

potential of damage. Avoid creating obvious trails to equipment placed off the

trails. Visitors may follow these trails out of curiosity, but this traffic may

increase the likelihood of tampering with equipment or disrupt normal

traffic flow.

3. Environmental Influences on Accuracy.—Environmental factors influencing counter accuracy include habitat structure, weather, and wildlife.

Structural factors include canopy density and substrate. For example, counts

obtained from sensor pads may be overestimated by vibration generated by

swaying trees or by other ground vibrations which are not related to visitor

traffic; extremely deep or dense snow may diffuse foot traffic vibrations and

bias counts upward. Count underestimates occur with photoelectric counters

if the emitted beam misses the reflector, as occurs with excessive tree sway.

Wildlife passing within the detection region of passive-infrared sensors may

register a count. During rain events moisture on receivers and reflectors may

affect count accuracy.

4. Equipment Cost.—Prices vary from approximately $300 to $500 for

photoelectric and sensor pad counters to over $1,200 for loop-type counters.

Expense is increased with the inclusion of various options, such as camera
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 81

attachments. It is highly desirable that counters provide time and date

stamping of count readings; this option facilitates calibration. See table 2 for

details of equipment manufacturers, specifications, options, and associated

costs.

5. Maintenance Requirements.—Visitation of each counter station should

be performed regularly; schedules will depend on battery life, data storage

capacity, potential for equipment failure or vandalism, and counter rotation

schedules (determined before the monitoring program is in place; see

below). Data must be downloaded before batteries begin to fail, or before

storage capacity is exceeded. Battery life varies from 60 to 90 days for

photoelectric counters to over 1 year for loop-type counters. Data storage

capacity is usually much less than battery life. For example, memory

capacity of loop-type counters is limited to 40 days of hourly time-stamped

data; this type of counter would have to be visited at least this often. Memory

capacity of certain photoelectric counters may be count-limited rather than

time-limited; for example, TrailMaster counters have a storage limit of

approximately 1,000 counts. For these counters, the time between data

downloadings would depend on visitor traffic volume. Finally, counter

rotation or calibration schedules must be considered.

Step 3: Decide on the Number of Counters Needed

The number of counters to acquire will be determined by the number of

access points to be monitored and the equipment budget. Ideally, counters

should be acquired for every access point. In practice, funding limitations,

the size of the wilderness area to be monitored, and relatively large numbers

of potential access points mean that the number of available counters will

be far fewer than the number required. In this case, counters must be

rotated systematically (see step 5).

Step 4: Choose the Calibration Method

The calibration method chosen depends on the relative amount of labor

and resources required for implementation, and the type of bias that must

be estimated.

Counter output may show either overestimation bias (the counter

registers something it should not count), or underestimation bias (the

counter does not count something it should); the calibration technique

chosen should provide an accurate measure of one or both types of bias if

possible.

The two methods of calibrating counters are with cameras, and with

human observers.

1. Camera Calibration.—Strategies of camera setup will be dictated by

the relative

importance to the manager of the competing goals of labor allocation and

minimization of bias.

(a) Fixed-interval monitoring. All traffic during a sample period is

photographed. The camera is activated at programmed time intervals; these

intervals are selected by statistical sampling procedures (part I, chapter 3).

Cameras are installed at the traffic area where the counter is installed; to

maximize the efficiency of the method, cameras should be set up in places

where traffic will be visible for long distances. This method minimizes the

amount of personnel involvement and both types of counter bias.
82 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

(b) Counter-activated monitoring. The camera is attached to the counter

itself, and takes photos only when the counter is activated by visitor traffic.

This technique provides a measure of overestimation bias only; it verifies

group size, traffic direction, and so forth, for visitors which actually activate

the camera, and blank photos and wildlife photos enable estimates of false

counts. This method does not provide information on errors occurring

because of visitors undetected by the counter.

2. Observer Calibration.—Calibration by human observers is more labor

intensive than camera calibration, but it is more accurate. Observers should

be stationed close enough to the counter so that all traffic activating the

counter is observed; although observers need not be right on top of the

counter, they should not wander up and down the trail.

For calibration purposes, the minimum information to be recorded by

observers includes: number of individuals, number of groups, method of

travel, direction of travel, and date and time of entry or exit. Additional

information on observable visit or visitor characteristics (for example, group

size, number of stock, gender, approximate age, time of entry or exit, and

whether a user appears to be a day user or an overnight camper) are recorded

at this time; a sample observer recording sheet is shown in figure 1. Some

information (such as gender and age categories) may not be easily determined from observations. However, it must be emphasized that observation

is remote; observers do not stop visitors.

Step 5: Develop a Sampling Plan

Sampling plans must be developed for:

1. scheduling counter rotation across trailheads on a systematic basis (if

the number of counters does not equal the number of access points).

2. calibration (if observers or cameras cannot provide for continuous

calibration).

Step 6: Purchase Equipment

Table 2 gives information on counter manufacturers, equipment specifications, and associated costs (1995 prices).

Step 7: Install Equipment

Specifics for site location were discussed in step 2. In general, counters

should be placed some distance away from the trailhead so that only bona fide

wilderness visitors are counted, and casual visitors (those who travel only an

extremely short distance) are excluded. However, if the wilderness boundary

is an extremely long distance from the trailhead, the increase in personnel

time involved in traveling to the counter site for reading and calibrating

counters may make this option untenable. We do not advise locating counters

where the trail is unduly wide (thus allowing visitors to travel two or more

abreast and underestimating counts), or at natural resting places (where

they may mill around and cause multiple counts). Narrow portions of the trail

at locations where traffic flow is more or less continuous offer the best count

locations.

The time required for counter installation will vary according to distance

from the trailhead and counter type. After arriving at the selected site, at

least 1 hour will be required for counter installation. This includes time spent
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 83

examining the site, selecting the best place for counter location, installing the

sensor and the counting mechanism, setting counter sensitivity or delay, and

testing counter operation. If a counter is mounted on a tree trunk (as is the

case for photoelectric counters), the counter will likely shift slightly within

the first day or two as a result of tree wounding; the counter should therefore

be checked, and realigned if necessary, on the second day after initial

installation. If cameras are used for calibration, additional time is required

to address privacy concerns (the camera must be located far enough from the

trail so that individuals cannot be identified in the pictures, camera adjusted

to be slightly out of focus, and so forth).

After the equipment has been installed, observe conditions for a short time

to make certain that the counter is functioning correctly and that any

camouflage is not obscuring or tripping the counter continuously. Walk over

the pad or through the beam several times to check counter sensitivity, and

adjust accordingly.

All equipment should be labeled with agency identification, a statement of

purpose, and the name, address, and telephone number of a designated

contact person. A message explaining that the camera is for detecting use

levels, and that individual identities cannot be determined, may reduce the

risk of vandalism if visitors do locate the equipment.

Step 8: Collect Calibration Data

Calibration information is collected according to a specific plan (as described in step 5). The specifics of collecting calibration information will

depend on whether cameras or human observers are used.

1. Camera Calibration.—Calibration observations are recorded with either motion picture (8-mm or VHS recorder) or a camera. If the camera is on

a timer, photos, or a series of frames, can be obtained at fixed intervals; the

camera can be attached to a mechanical counter and triggered to shoot by

visitor traffic. Because camera detection could result in theft or vandalism of

equipment; cameras must be positioned far enough from the trail so that

visitors cannot hear the shutter or motor action; camera equipment should

be well camouflaged. When performing routine visits, do not approach

equipment over the same route every time; frequent travel could result in the

development of a recognizable path and subsequent detection of equipment

by unauthorized persons.

Film consumption should be monitored closely; calibration data will be

useless if the camera runs out of film during this phase. After removing

exposed film from the camera, label immediately with the date, time, and

location. Protect exposed film from extreme heat and cold until developed.

Record necessary observations from the developed film. Observations must

be recorded in a standardized format to minimize errors in recording.

Observations include location, date, number of individuals, number of

groups, date and time of entry or exit. Observers must understand the need

to completely and correctly fill out the data form; sample observations will be

useless if the data collected by the observer cannot be matched with the

appropriate counter data. Observation sheets should be filed in a designated

place. After observations are recorded, destroy negatives and developed

photos to ensure visitor privacy.

2. Observer Calibration.—It is essential that personnel are thoroughly

trained in the data collection procedures. Training ensures that observers
84 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

are already familiar with the research directives and the data collection

process before actual fieldwork begins. As a result, errors involved in the

learning process are reduced, and there will be greater consistency in

identifying the sampling units and recording responses. Training enables

observers to become familiar with various contingency plans, to identify

potential problems in the research directives, and to make decisions if

problems occur.

Preliminary, or pretest, fieldwork should be conducted before the actual

survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or

inadequacies in the procedures can be identified, and the consistency and

accuracy of personnel can be observed and analyzed.

Observers should be screened at intervals and their performance compared

either with each other or at different time points for the same observer;

screening provides a check on performance and identifies sources of error in

the data.

The observer must be stationed somewhere near the counter where the

trail is clearly visible. If trail traffic is low, observers may perform other tasks

in the vicinity of the counter, such as trail clearance and maintenance, visitor

education, or reading; these help pass the time and reduce observer fatigue

and boredom. However, if the observer is stationed at some distance and is

observing traffic through binoculars, it is not advisable to engage in other

types of activity because of the potential for missing visitors if attention is

diverted from the trail. Observers should be in appropriate uniform and

possess necessary communication and safety equipment.

Observations must be recorded in a standardized format. For each data

sheet the observer should record his or her name, the sampling location, the

date, start time, the initial counter reading, end time, and the final counter

reading for that sample period. During the sample period the observer

records the number of individuals or groups, the time visitors pass the

observation station, and the direction of travel. The observer must be

provided with sufficient data forms for the observation period. Observers

must understand the need to completely and correctly fill out the data form;

sample observations will be useless if the data collected by the observer

cannot be matched with the appropriate counter data. Observation sheets

should be filed in a designated place after the observer returns to the office.

Step 9: Collect Count Data

Counts logged by the mechanical counter are recorded at intervals determined by the sampling plan. If counters are permanently allocated to a given

location, the frequency of recording will be determined by the calibration

sampling plan. At a minimum, counts should be recorded at least twice per

month to ensure that data are not lost because of equipment malfunction.

The person obtaining count readings should check battery power and

equipment operation, and for any changes in the surrounding area which

may affect count accuracy. For example, fallen branches or trees could block

the electronic beam from the scanner, or result in the rerouting of trail traffic

away from the counter path.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 85

Step 10: Estimate Use

Use data are collected in accordance with the desired sample size and the

sampling strategy. Because data from mechanical counters are supplemented with direct observations, use can be estimated for observable categories of visitors, in addition to information on individual or group visit counts.

Use data may be expressed as a rate (for example, number of visitors per day),

or total (for example, number of visitors for the season). In general, totals are

estimated by multiplying the “corrected” average daily rate by the number

of days in the time period of interest. If observations can be classified into two

or more observable categories, the number in each category can be expressed

as a proportion or percentage of the total number of users. However, if sample

sizes are very small, proportion data are useless for evaluation purposes.

Data collected during the calibration phase may be used to provide estimates

of the sample size required for the actual observation phase of the study.

Example. Visitor traffic in the Alpine Lakes Wilderness was studied in

1991. Measures of use were assessed at the primary trailhead access for

Snow Lake—an easily accessed, high-use trail with a high concentration of

day users. The total length of the visitor season was 100 days.

1. Calibration.—The initial calibration period was 15 observation days.

The paired data used to establish the calibration relationship were as

follows:

Day Mechanical counts (X) Visitors observed (Y)

Friday 132 119

Saturday 514 408

Sunday 604 556

Wednesday 107 119

Thursday 74 74

Friday 107 113

Saturday 423 424

Sunday 438 323

Friday 92 78

Saturday 370 380

Sunday 406 356

Wednesday 127 98

Thursday 80 87

Saturday 325 252

Sunday 400 361

The summary statistics for these data are as follows: n = 15, ΣX = 4,199,

ΣX2 = 1,643,937, ΣY = 3,748, ΣY2 = 1,294,490, ΣXY = 1,450,388, X = 280, Y = 250.

If no mechanical counters were used or if their data is ignored, the observed

data could be used to compute an estimate of total use. The mean of the 15

observed values is 250 with a standard error of 41, making the 95 percent

confidence interval 250 ± 2·41 = (167, 332). If the data is stratified by weekends

and weekdays, the estimated means and confidence intervals are 382 (320,

445) and 98 (84, 113), respectively. Since there were 72 weekdays and 28

weekend days in the 100 day season, these individual estimators are

combined as weighted averages to make overall estimators of 17,786 (15,755,

19,817). Differences from the overall (unstratified) estimator above may be

due to an over representation of weekend days in the sample.
86 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The mechanical counter data may be used to increase precision by estimating a regression relationship: Y = 10.15 + 0.86·X 

( .) MSE = 33 31 . The R2

value is high (0.96), suggesting that a straight line is a good approximation

of the relationship between the two variables. However, examination of the

data plot (fig. 5) shows that there are two distinct subgroups in the data.

These subgroups correspond to the day of the week on which observations

were obtained; weekends had substantially higher counts than weekdays.

This suggests that the sampling plan for the observation phase should

incorporate stratification by time periods.

Because the regression slope is less than 1, the actual number of visitors

will be overestimated by mechanical counter data. A crude estimate of the

amount of bias is given by the ratio estimator 

r

Y

X = = 250/280 = 0.89; that

is, 89 percent of counts registered by the mechanical counter could be

attributed to visitor traffic, with the remaining 11 percent due to other

causes. If visitor totals are estimated for relatively long time periods, there

may be a substantial amount of accumulated error in the results. Standard

errors and confidence intervals for ratio estimators are not generally recommended and are beyond the scope of this handbook.

2. Sample Size Estimation.—Because count data are collected by mechanical counters, large sample sizes for counts are relatively easy to obtain.

However, observation data are time-intensive and expensive to collect and

process; logistically feasible sample sizes should reflect reasonable operational costs associated with equipment and personnel.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

calibration phase was 250, with S = 160. There are 100 days in the season

(N = 100). Suppose we want to be 95 percent certain that the results will have

a precision of ± 5 percent, or ± 13 visitors/day. The estimated number of
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 87

sampling days is 

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( ) = 86. If the precision is adjusted

to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these are too large

or too close to the entire season of 100 days to be of practical use due to the

large underlying variance. A more reasonable level of precision would be

± 30 percent (or ± 75 visitors per day), which would call for a sample size of

n = 15 as in the example above.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n p p

L = 42 1 ⋅⋅− 2

2

() ( )

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore the proportion of day users, p = 24/40

= 0.60, and the standard error is p pn ( ) 1 0 60 0 40 40 − / ( . )( . ) / = = 0.0775. The

95 percent confidence interval based on these data is approximately 0.6 ±

2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS ii ii [ ] ⋅ ⋅ /∑( ) ⋅ n. Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—

weekend days and weekdays. This stratification strategy separates out time

periods according to relative intensity of use, with the heaviest and most

variable use occurring on weekends, and relatively light and uniform use on

weekdays. For a 100-day season, there are about 72 weekdays and 28

weekend days. Suppose the available resources (budget, labor, time) dictated
88 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

that the maximum number of days that could be sampled was n = 25. The

initial value for the standard deviation for each stratum was estimated from

the data obtained during calibration. Sample sizes for each time block are

calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(N1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(N2 = 72)

aStandard deviation.

bSampling proportion.

cSample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms of:

(a) the rate (for example, number of visitors per day), (b) the total (for

example, number of visitors for the season), or (c) use by category (for

example, method of travel).

(a) Rate of use. In this example the observation period was 15 days; the

counter registered a total of 4,199 counts, averaging 280 counts per day. The

calibration or regression line is used to “correct” for counter bias by using it

to estimate the “actual” value as:

Y = 10.15 + 0.86·(280) = 250 visitors per day.

The 95 percent confidence limits are estimated as:

250 ± 2(33.31) 

 

1

15

280 280

1 643 937 4 199 15

2

2 + ( ) −

( ) ,, , / − = 250 ± 17, or between 233 and

267 visitors per day.

Accuracy may sometimes be increased if regressions are calculated within

each stratum rather than pooled over the entire observation period. In this

example, over 80 percent of all counts registered occurred on weekends; there

were 3,480 counts for the 8 weekend days monitored (averaging 435 counts

per day) and 719 counts for the 7 weekdays (averaging 103 counts per day).

The resulting regression estimates for each strata are:

Weekend: Y = 1.71 + 0.875·(435) = 382 visitors per day, with 95 percent

confidence limits 382 ± 94, or between 288 and 476 visitors per day.

Weekday: Y = 31.1+ 0.654·(103) = 98 visitors per day, with 95 percent

confidence limits 98 ± 27, or between 72 and 125 visitors per day.

These estimators may be combined to get a “corrected” average daily total by

forming a weighted average of the individual estimates. Since there were 72

weekdays and 28 weekend days during the 100 day season, these two

estimates can be combined with weights of 72/100 and 28/100 to make an

overall estimate of visitors over the entire season. This overall estimator is

(72/100)·98 + (28/100)·382 = 178. A confidence interval for the average daily
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 89

use would be formed similarly as a weighted average of the lower and upper

confidence limits of the weekend and weekday usage rates of (132, 224).

In this example the small sample sizes and greater variability within strata

make the confidence interval for the stratified estimator much wider than

the unstratified estimator. The moral is that stratification may not always

result in narrower confidence intervals, but it will give more specific information about individual strata that may be very useful.

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 250(100) = 25,000 visitors (23,300 to 26,700 visitors).

Using the stratified regression estimators, the total count estimates are

17,800 with a confidence interval of (13,200, 22,400).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users

observed in the sample.

Example. Sample observations of method of travel (the observable visit

characteristic of interest) were made for 2,975 wilderness users. Three travel

categories were reported: hikers, horse users, and mountain bikers. Results

with a 95 percent confidence interval (using χ

2

 procedure based on 2 degrees

of freedom) were:

Hikers: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95% confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ± 0.019 =

(0.731 to 0.769);

Horse users: n2 = 595, p2 = 595/2,975 = 0.20,

95% confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ± 0.018 =

(0.18 to 0.22);

Mountain bikers: n3 = 149, p3 = 149/2,975 = 0.05,

95% confidence interval = 0.05 ± 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ± 0.009 =

(0.04 to 0.06).
90 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System C: Mechanical Counters

With Observer Calibration and

Sample Interviews

System Description ________________________________________________

This system provides information on visit counts, observable characteristics, and simple nonobservable characteristics. Whereas observable characteristics can be determined by observation, nonobservable characteristics

must be determined only by direct visitor contact and interviews. Simple

nonobservable characteristics include length of stay, travel routes, and

sociodemographic information. This is the only system based on mechanical

counters that can generate aggregate, or summary-use, statistics. Mechanical counters are set up to count trail traffic. Monitoring by human observers

is used to assess the reliability of counter data (calibration) and obtain

information on both observable and nonobservable characteristics. Because

there is limited visitor contact, visitor burden is low to moderate.

Summary of System C:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Use by categories of user

Summary use statistics

Data collection strategies: Sampling plan for counter rotation (if applicable)

• spatial

• temporal

Sample plan for visual calibration

Sample plan for interviews

Techniques/procedures: Mechanical counters

Visual observations (human observers only)

Interviews

Visitor burden: Moderate

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics to Measure

Mechanical counters are used to collect visitor count data; count accuracy

is assessed by calibration with data obtained from human observers.

Nonobservable visit and visitor characteristics are acquired during the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 91

calibration process; these data are obtained by interviewing a random

selection of visitors. To minimize visitor burden, only simple nonobservable

characteristics are recorded; these include length of stay, group size, wilderness travel patterns, visitor residence, visit frequency, activities, and visitor

perception of problems, resource conditions, and so forth. Use, in terms of

number of visitors, is usually categorized by one or more nonobservable

characteristics.

Step 2: Decide on Counter Type

There are three main types of counter currently available: photoelectric

counters, sensor pad counters, and loop-type sensor counters. Counter

selection depends on installation site characteristics and limitations, vandalism concerns, environmental factors affecting counter accuracy, equipment cost, and maintenance requirements.

1. Installation Site.—Characteristics of the proposed installation site will

determine the type of counter that is most appropriate. Site characteristics

to be evaluated include the presence or absence of tree cover, soil type, and

slope. Photoelectric counters must be attached on a vertical surface so that

the sensor and the reflector are opposite each other and located at a distance

of 100 feet or less. If counter components are attached to trees, each tree must

be large enough to prevent excessive swaying. If there are no suitable trees

at the proposed site, posts may be installed if the soil allows digging; however,

posts should be concealed in brush to avoid vandalism. Soil type and depth

are important if sensor pads and loop-type counters are considered, as these

sensors must be buried to be operative. If digging is difficult, or the proposed

monitoring site is located on a steep and/or unstable surface, these counters

will not be appropriate.

2. Equipment Vandalism.—Vandalism, theft, and tampering with counter

equipment are serious concerns, especially in heavy-use areas near trailheads

or parking areas. Because counter components are above ground, photoelectric counters are the most vulnerable to vandalism. Camouflaging the

equipment may prevent detection. The plastic housing of the TrailMaster

counters makes them the most susceptible to vandalism or animal damage;

the long-term durability of these counters has not been assessed. Sensor pads

are less susceptible to vandalism because they are buried, although the

counter mechanism itself must be located so that the counter display can be

read. The counter mechanism must therefore be camouflaged. Loop-type

counters are completely buried and therefore are relatively free from the

potential of damage. Avoid creating obvious trails to equipment placed off the

trails. Visitors may follow these trails out of curiosity, but this traffic may

increase the likelihood of tampering with equipment or disrupt normal

traffic flow.

3. Environmental Factors.—Environmental factors influencing counter

accuracy include habitat structure, weather, and wildlife. Structural factors

include canopy density and substrate. For example, counts obtained from

sensor pads may be overestimated by vibration generated by swaying trees

or by other ground vibrations which are not related to visitor traffic;

extremely deep or dense snow may diffuse foot traffic vibrations and bias

counts upward. Count underestimates occur with photoelectric counters if

the emitted beam misses the reflector, as occurs with excessive tree sway.

Wildlife passing within the detection region of passive-infrared sensors may
92 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

register a count. During rain events moisture on receivers and reflectors may

affect count accuracy.

4. Equipment Cost.—Prices vary from approximately $300 to $500 for

photoelectric and sensor pad counters to over $1200 for loop-type counters.

Expense is increased with the inclusion of various options, such as camera

attachments. It is highly desirable that counters provide time and date

stamping of count readings; this option facilitates calibration. See table 2 for

details of equipment manufacturers, specifications, options, and associated

costs.

5. Maintenance Requirements.—Visitation of each counter station should

be performed regularly; schedules will depend on battery life, data storage

capacity, potential for equipment failure or vandalism, and counter rotation

schedules (determined before the monitoring program is in place; see below).

Data must be downloaded before batteries begin to fail, or before storage

capacity is exceeded. Battery life varies from 60 to 90 days for photoelectric

counters to over 1 year for loop-type counters. Data storage capacity is

usually much less than battery life. For example, memory capacity of looptype counters is limited to 40 days of hourly time-stamped data; this type of

counter would have to be visited at least this often. Memory capacity of

certain photoelectric counters may be count-limited rather than time-limited; for example, TrailMaster counters have a storage limit of approximately

1000 counts. For these counters, the time between data downloadings would

depend on visitor traffic volume. Finally, counter rotation or calibration

schedules must be considered.

Step 3: Decide on the Number of Counters Needed

The number of counters to acquire will be determined by the number of

access points to be monitored and the equipment budget. Ideally, counters

should be acquired for every access point. In practice, funding limitations,

the size of the wilderness area to be monitored, and relatively large numbers

of potential access points mean that the number of available counters will be

far fewer than the number required. In this case, counters must be rotated

systematically (see step 5).

Step 4: Develop a Sampling Plan

Sampling plans must be developed for:

1. scheduling counter rotation across trailheads on a systematic basis (if

the number of counters does not equal the number of access points).

2. calibration (if continuous calibration by observers cannot be provided).

3. visitor selection for interviews.

Step 5: Purchase Equipment

Table 2 gives information on counter manufacturers, equipment specifications, and associated costs (1995 prices).

Step 6: Install Equipment

Specifics for site location were discussed in step 2. In general, counters

should be placed some distance away from the trailhead so that only bona fide

wilderness visitors are counted, and casual visitors (those who travel only an

extremely short distance) are excluded. However, if the wilderness boundary
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 93

is an extremely long distance from the trailhead, the increase in personnel

time involved in traveling to the counter site for reading and calibrating

counters may make this option untenable. We do not advise locating counters

where the trail is unduly wide (thus allowing visitors to travel two or more

abreast and underestimating counts), or at natural resting places (where

they may mill around and cause multiple counts). Narrow portions of the trail

at locations where traffic flow is more or less continuous offer the best count

locations.

The length of time required for counter installation will vary according to

distance from the trailhead and counter type. After arriving at the selected

site, at least 1 hour will be required for counter installation. This includes

time spent examining the site, selecting the best place for counter location,

installing the sensor and the counting mechanism, setting counter sensitivity or delay, and testing counter operation. If a counter is mounted on a tree

trunk (as is the case for photoelectric counters), the counter will likely shift

slightly within the first day or two as a result of tree wounding; the counter

should therefore be checked, and realigned if necessary, on the second day

after initial installation.

After the equipment has been installed, observe conditions for a short time

to make certain that the counter is functioning correctly and that any

camouflage is not obscuring or tripping the counter continuously. Walk over

the pad or through the beam several times to check counter sensitivity, and

adjust accordingly.

All equipment should be labeled with agency identification, a statement of

purpose, and the name, address, and telephone number of a designated

contact person.

Step 7: Collect Counter Data

Counts logged by the mechanical counter are recorded at intervals determined by the sampling plan. If counters are permanently allocated to a given

location, the frequency of recording will be determined by the calibration

sampling plan. At a minimum, counts should be recorded at least twice per

month to ensure that data are not lost because of equipment malfunction.

The person obtaining count readings should check battery power and

equipment operation, and for any changes in the surrounding area which

may affect count accuracy. For example, fallen branches or trees could block

the electronic beam from the scanner, or cause a sufficient barrier to trail

traffic to reroute traffic away from the counter path.

Step 8: Select and Train the Interview Team

Careful selection and training of the personnel who are involved in

collecting data are essential if the manager or research planner is not

performing the field research. The research planner must ensure that

interviews are conducted and observations collected in the manner required

by the study plan.

1. Personnel Selection.—Both personality and ability must be evaluated

in the selection process. The importance of visitor contact extends beyond the

quality of data obtained; it is an opportunity to present the image of the

managing agency. Select an interviewer who is friendly, reliable, knowledgeable, flexible, and who demonstrates a positive attitude toward the project.

Personnel who are convinced of the value of the work will bring a sense of
94 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

commitment to the job regardless of the amount of pay or hours worked;

negative attitudes toward the overall objectives of the project, the interview

topic, or the public will jeopardize research results. Personnel should be

familiar with the wilderness area and be prepared to handle requests for

information about the wilderness and the surrounding area. Many of the

questions from visitors will not be related to the interview; providing

information is a courtesy which contributes to establishing rapport with the

visitors and increases visitor cooperation. Personnel should be trained in

emergency procedures. When in the field, personnel should be in appropriate

uniform and possess necessary communication and safety equipment.

2. Training.—It is essential that personnel are thoroughly trained in the

data collection procedures. Training ensures that observers are familiar with

the research directives and the interviewing process before actual fieldwork

begins. As a result, errors involved in the learning process are reduced, and

there will be greater consistency in identifying the sampling units (in this

case visitors to be interviewed) and recording responses. Training enables

observers to become familiar with various contingency plans, to identify

potential problems in the research directives, and to make decisions if

problems occur.

Preliminary, or pretest, fieldwork should be conducted before the actual

survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or

inadequacies in the procedures can be identified and eliminated, and the

consistency and accuracy of personnel can be observed and analyzed.

Observers should be screened at intervals and their performance compared

either with each other or at different time points for the same observer;

screening provides a check on performance and identifies sources of error in

the data.

Step 9: Collect Calibration and Interview Data

Counter calibration and interview data are collected simultaneously by

observers. Both calibration and interview information are collected according to a specific plan (as described in step 4). The observer must be provided

with sufficient research material for the observation period; these materials

include question sheets, data forms, field coding keys, writing tools, and

sampling schedules.

Observers must understand the need to completely and correctly fill out the

data form; sample observations will be useless if the data collected by the

observer cannot be matched with the appropriate counter data. Observation

sheets should be filed in a designated place after the observer returns to the

office.

1. Calibration Data.—Calibration observations must be recorded in a

standardized format. For each data sheet, the observer should record his or

her name, the sampling location, the date, start time, the initial counter

reading, end time, and the final counter reading for that sample period.

During the sample period, the observer records the number of individuals or

groups, the time visitors pass the observation station, and the direction of

travel.

2. Interview Data.—The interview protocol consists of four steps: (a)

determining question format, (b) obtaining OMB-clearance, (c) visitor selection, and (d) data collection.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 95

(a) Question format. The questions asked of the visitor will be dictated

on the basis of the study objectives; that is, on the basis of what the manager

wants to know and why. Questions should be easily understood by the visitor,

they should not be too long, and there should not be too many of them. Ask

only the questions necessary to meet the study objectives, and no more. For

example, suppose the manager is interested in evaluating relative impact in

terms of time spent in different areas by various user groups. Interviews can

be limited to determining method of travel, destination, and length of stay of

visitors encountered at each trailhead; the interview will be short.

 Do not add questions merely to fill up space on the interview sheet. If some

inadequacy or ambiguity becomes apparent with the set questions, clarifying

questions may be added, but only if they satisfy the requirements of step 1.

The question designer is rarely a good judge of the clarity of the questions

(Ackoff 1953); preliminary field tests are invaluable for identifying problems

before the actual field surveys begin.

(b) Obtain OMB-clearance. According to federal legislation, clearance

from the Office of Management and Budget (OMB) is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to that Agency’s

Information Systems office in Washington, DC, which then forwards the

application to the Department of Agriculture, and from there to OMB for

final approval. The time from initial submission to final OMB clearance is

usually about 3 months.

(c) Interview selection. Visitors are selected in accordance with the

predetermined sampling plan (step 4). The location of interviews will be

determined by study objectives; visitors may be interviewed upon either

entry or exit, or both. For example, if the emphasis of the study is on the

effects of group size or place of residence on wilderness use, these factors are

unaffected by interview location. However, if the study objectives require

information on patterns of visitor use within the wilderness area (for

example, travel or camping locations, length of stay), visitors should be

interviewed as they leave.

(d) Data collection. When interviewing visitors, personnel should begin

with a standard introduction. Personnel should give their name and agency

affiliation and the reason for the interview. For example, “Hello, I am

Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.

We are trying to learn more about the use of the Rattlesnake Wilderness. It

will help us with management of the area. May I ask you a few questions

about your visit today?” After the interview, thank visitors for their time.

Personnel may be tempted to add additional questions “just out of curiosity”;

this cannot be justified in any circumstances.

Responses should be recorded as they are given; interviewers should not

rely on memory to fill in the interview sheet at a later time. Make sure every

item is complete and legible; data forms must include date, time, location,

and interviewer’s name. When interview responses are coded, the interviewer should be provided with a field coding key to ensure that responses are

entered correctly. Completed data forms should be filed in a safe place.
96 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Step 10: Estimate Use

Use data are collected in accordance with the desired sample size and the

sampling strategy. Because data from mechanical counters are supplemented with direct observations, use can be estimated for observable categories of visitor, in addition to information on individual or group visit counts.

Use data may be expressed as a rate (for example, number of visitors per day),

or total (for example, number of visitors for the season). In general, totals are

estimated by multiplying the “corrected” average daily rate by the number

of days in the time period of interest. If observations can be classified into two

or more observable categories, the number in each category can be expressed

as a proportion or percentage of the total number of users. However, if sample

sizes are very small, proportion data are useless for evaluation purposes.

Data collected during the calibration phase may be used to provide estimates

of the sample size required for the actual observation phase of the study.

Example. Visitor traffic in the Alpine Lakes Wilderness was studied in

1991. Measures of use were assessed at the primary trailhead access for

Snow Lake—an easily accessed, high-use trail with a high concentration of

day users. The total length of the visitor season was 100 days.

1. Calibration.—The initial calibration period was 15 observation days.

The paired data used to establish the calibration relationship were as

follows:

Day Mechanical counts (X) Visitors observed (Y)

Friday 132 119

Saturday 514 408

Sunday 604 556

Wednesday 107 119

Thursday 74 74

Friday 107 113

Saturday 423 424

Sunday 438 323

Friday 92 78

Saturday 370 380

Sunday 406 356

Wednesday 127 98

Thursday 80 87

Saturday 325 252

Sunday 400 361

The summary statistics for these data are as follows: n = 15, ΣX = 4,199,

ΣX2 = 1,643,937, ΣY = 3,748, ΣY2 = 1,294,490, ΣXY = 1,450,388, X = 280, Y = 250.

If no mechanical counters were used or if their data is ignored, the observed

data could be used to compute an estimate of total use. The mean of the 15

observed values is 250 with a standard error of 41, making the 95 percent

confidence interval 250 ± 2·41 = (167, 332). If the data is stratified by

weekends and weekdays, the estimated means and confidence intervals are

382 (320, 445) and 98 (84, 113), respectively. Since there were 72 weekdays

and 28 weekend days in the 100 day season, these individual estimators are

combined as weighted averages to make overall estimators of 17,786 (15,755,

19,817). Differences from the overall (unstratified) estimator above may be

due to an over representation of weekend days in the sample.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 97

The mechanical counter data may be used to increase precision by estimating a regression relationship: Y = 10.15 + 0.86·X 

( .) MSE = 33 31 . The R

value is high (0.96), suggesting that a straight line is a good approximation

of the relationship between the two variables. However, examination of the

data plot (fig. 5) shows that there are two distinct subgroups in the data.

These subgroups correspond to the day of the week on which observations

were obtained; weekends had substantially higher counts than weekdays.

This suggests that the sampling plan for the observation phase should

incorporate stratification by time periods.

Because the regression slope is less than 1, the actual number of visitors

will be overestimated by the mechanical counter data. A crude estimate of the

amount of bias is given by the ratio estimator r = Y / X = 250/280 = 0.89; that

is, 89 percent of counts registered by the mechanical counter could be

attributed to visitor traffic, with the remaining 11 percent due to other

causes. If visitor totals are estimated for relatively long time periods, there

may be a substantial amount of accumulated error in the results. Standard

errors and confidence intervals for ratio estimators are not generally recommended and are beyond the scope of this handbook.

2. Sample Size Estimation.—Because count data are collected by mechanical counters, large sample sizes for counts are relatively easy to obtain.

However, observation data are time-intensive and expensive to collect and

process; logistically feasible sample sizes should reflect reasonable operational costs associated with equipment and personnel.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

calibration phase was 250, with S = 160. There are 100 days in the season

(N = 100). Suppose we want to be 95 percent certain that results will have a

precision of ± 5 percent, or ± 13 visitors/day. The estimated number of
98 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

sampling days is 

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( )

 = 86. If the precision is adjusted

to ± 10 percent (or ± 25), then n = 62. Both of these are too large or too close

to the entire season of 100 days to be of practical use due to the large

underlying variance. A more reasonable level of precision would be ± 30

percent (or ± 75 visitors per day), which would call for a sample size of n = 15

as in the example above.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n p p

L = 42 1 ⋅⋅− 2

2

() ( )

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected

visitors, 24 appeared to be day users. Therefore, the proportion of day users,

p = 24/40 = 0.60, and the standard error is p pn ( ) 1 0 60 0 40 40 − / . ./ = ( )( ) =

0.0775. The 95 percent confidence interval based on these data is approximately 0.6 ± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The

sample size n required for a 95 percent confidence interval with a length of

at most 0.10 (regardless of the resulting value of p) is approximately

 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400. Therefore, it would be necessary to observe 400 visitors

to obtain this amount of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS ii ii [ ] ⋅ ⋅ /∑( ) ⋅n. Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—

weekend days and weekdays. This stratification strategy separates out time

periods according to relative intensity of use, with the heaviest and most

variable use occurring on weekends, and relatively light and uniform use on

weekdays. For a 100-day season, there are about 72 weekdays and 28

weekend days. Suppose the available resources (budget, labor, time) dictated
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 99

that maximum number of days that could be sampled was n = 25. The initial

value for the standard deviation for each stratum was estimated from the

data obtained during calibration. Sample sizes for each time block are

calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(n1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(n2 = 72)

aStandard deviation.

bSampling proportion.

cSample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy, the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms of:

(a) the rate (for example, number of visitors per day), (b) the total (for

example, number of visitors for the season), (c) use by category (for example,

cooking method), or (d) use description (for example, length of stay).

(a) Rate of use. In this example, the observation period was 15 days; the

counter registered a total of 4,199 counts, averaging 280 counts per day. The

calibration or regression line is used to “correct” for counter bias by using it

to estimate the “actual” value as:

Y = 10.15 + 0.86·(280) = 250 visitors per day.

The 95 percent confidence limits are estimated as:

250 ± 2(33.31) 

 

1

15

280 280

1 643 937 4 199 15

2

2 + ( ) −

( ) ,, , / − = 250 ± 17, or between 233 and

267 visitors per day.

Accuracy may sometimes be increased if regressions are calculated within

each stratum, rather than pooled over the entire observation period. In this

example, over 80 percent of all counts registered occurred on weekends; there

were 3,480 counts for the 8 weekend days monitored (averaging 435 counts

per day) and 719 counts for the 7 weekdays (averaging 103 counts per day).

The resulting regression estimates for each strata are:

Weekend: Y = 1.71 + 0.875·(435) = 382 visitors per day, with 95 percent

confidence limits 382 ± 94, or between 288 and 476 visitors per day.

Weekday: Y = 31.1 + 0.654·(103) = 98 visitors per day, with 95 percent

confidence limits 98 ± 27, or between 72 and 125 visitors per day.

These estimators may be combined to get a “corrected” average daily total by

forming a weighted average of the individual estimates. Since there were 72

weekdays and 28 weekend days during the 100 day season, these two

estimates can be combined with weights of 72/100 and 28/100 to make an

overall estimate of visitors over the entire season. This overall estimator is
100 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

(72/100)·98 + (28/100)·382 = 178. A confidence interval for the average daily

use would be formed similarly as a weighted average of the lower and upper

confidence limits of the weekend and weekday usage rates of (132, 224).

In this example, the small sample sizes and greater variability within

strata make the confidence interval for the stratified estimator much wider

than the unstratified estimator. The moral is that stratification may not

always result in narrower confidence intervals, but it will give more specific

information about individual strata that may be very useful.

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 250(100) = 25,000 visitors (23,300 to 26,700 visitors).

Using the stratified regression estimators, the total count estimates are

17,800 with a confidence interval of (13,200, 22,400).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.

Example. Sample interviews recorded three types of cooking methods:

stoves, wood fires, and neither for 2,975 wilderness users. Results with a 95

percent confidence interval (using χ2 procedure based on 2 degrees of

freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95% confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ± 0.019 =

(0.731 to 0.769);

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95% confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ± 0.018 =

(0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95% confidence interval = 0.05 ± 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ± 0.009 =

(0.04 to 0.06).

(d) Use description. One variable that may be obtained by interview is

information on length of stay. Post stratification may also be of interest.

Example. A sample of 38 interviews had an average length of stay of 2.4

nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.84, 2.76).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 101

System D: Visitor Registration

System With Checks For

Registration Rate

System Description ________________________________________________

This system provides information on visit counts, observable visit and

visitor characteristics, and some simple nonobservable visit characteristics.

In general, visitors fill out survey cards before entering the wilderness area,

and use characteristics are obtained from the resulting information. Registration is voluntary; the accuracy of registration data must be determined by

estimating actual registration rates, or compliance. Compliance rates are

determined by sensor-triggered cameras, or by human observers. Visitor

burden is low to moderate, and involves the time required by the visitor to

complete the registration form.

Summary of System D:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Use by categories of user

Data collection strategies: Sampling plan for station rotation (if applicable)

 • spatial

 • temporal

Sampling plan for compliance (cameras,

humans)

Techniques/procedures: Voluntary visitor registration

Compliance checks

• human observers

• cameras

Visitor burden: Low to moderate

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics to Measure

Direct measures of use include individual or group visit counts. Additional

visit characteristics acquired from the registration cards include length of

stay, entry and exit points, method of travel, group size, number of stock, and

place of residence (applicable to the party leader only).
102 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Step 2: Decide on Registration Form

Standard OMB-approved registration forms are available. Alternatively,

customized registration forms can be used; however, OMB clearance must be

obtained for new forms before the study begins. According to federal legislation, OMB clearance is required if federal employees ask more than nine

members of the public the same set of questions. The proposed set of

questions, methodology, and study justification must be submitted to OMB

through the appropriate channels. For the Forest Service, application for

clearance is submitted to Information Systems in Washington, DC, which

forwards the application to the Department of Agriculture, and from there to

OMB for final approval. The time from initial submission to final OMB

clearance is usually about 3 months.

“Diary”-type registration cards can give more complete information on

wilderness experiences of visitors. Visitors complete the initial portion of the

card upon entry; this section requests basic information on the visitors or

group. The second portion requests information on the trip itself, and is filled

out by the visitor during the trip, or upon leaving the wilderness area. To

reduce error, the two sections should be distinguished by separate headings

and by different colors; however, each section should have the same identification number to allow matching after collection.

Step 3: Decide on Number of Registration Stations

Registration stations are relatively inexpensive to construct, install, and

maintain. However, stations must be kept supplied with adequate amounts

of registration forms and pencils at all times. The image of the agency suffers

if visitors are prevented from registering because supplies are lacking.

Therefore, registration stations should not be placed on every trail if

personnel and time are limited and stations cannot be monitored on a regular

basis. It is preferable to have only the number of registration stations that

can be conveniently monitored and supplied.

Coverage of the wilderness area is performed by alternating “in-use”

stations across trailheads. Strategies for rotation schedules are given in step 5.

Step 4: Decide on Method of Estimating Registration Rates

Because registration is voluntary and there are no penalties for noncompliance, the number of visitors who do register may be highly variable. Factors

affecting registration rates include method of travel (hikers register at a

higher rate than horse riders do), group size (at least one member from a large

group is more likely to register than a member of a small group), and the

location of the registration station (registration rates are lower if located at

the trailhead entrance than those located further up the trail). However,

there is an unknown relationship between visitor characteristics and the

likelihood that a given group will register. Therefore, for practical purposes,

registration stations may be regarded as a type of counter; supplementary

observations must be made to estimate registration rates and “calibrate”

registration information in much the same manner as observations were

used to calibrate mechanical counters. Basic options for determining registration rates include use of cameras or human observers.

1. Cameras.—Either a video camera with VHS recorder or a camera may

be used for recording observations. If the camera is on a timer, photos (or a
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 103

series of frames) can be obtained at fixed intervals (fixed-interval monitoring). Alternatively, the camera can be attached to a mechanical counter and

triggered to shoot by visitor traffic (counter-activated monitoring).

(a) Fixed-interval monitoring. This method requires a minimum amount

of personnel involvement. All traffic during a sample period is photographed.

The camera is activated at programmed time intervals; these intervals are

selected by statistical sampling procedures (part I, chapter 3). Cameras are

installed on the traffic area where the registration station is installed. To

maximize the efficiency of the method, cameras must be set up near the

registration station where traffic will be visible for long distances.

(b) Counter-activated monitoring. The camera is attached to a mechanical counter, and takes photos only when the counter is activated by visitor

traffic. This technique provides a measure of overestimation bias only; it does

not provide information on error occurring because of visitors undetected by

the counter.

2. Observers.—Estimating registration rates with observations taken by

human observers is more labor intensive than use of cameras, but it is more

accurate. Observers should be stationed close enough to the registration

station so that all traffic activating the counter is observed; although

observers need not be exactly by the registration station, they should not

wander up and down the trail. However, it must be emphasized that

observation is remote; observers do not stop visitors.

Step 5: Develop a Sampling Plan

Sampling plans must be developed for scheduling:

1. the rotation of registration stations and cameras (if applicable) across

trailheads.

2. observer monitoring (if continuous compliance checks are not possible).

Registration stations are not expensive to construct, install, or maintain.

However, if labor or supplies (such as cameras) are insufficient for all

trailheads, registration stations must be rotated on a systematic basis.

Step 6: Purchase Equipment

 If registration rates are estimated by camera, appropriate equipment

(cameras, film, mechanical counters) must be obtained from the relevant

suppliers (see part I, chapter 2, for details of counter specifications and

manufacturers).

Step 7: Construct the Registration Stations

Registration rates are greatly affected by station design. Visitors are more

likely to stop and register if the station is both attractive and functional.

Registration stations should be designed to provide (1) a place for supplies

(pencils and registration forms), (2) a convenient, solid writing surface for the

visitor to use when completing the registration form, and (3) a place to deposit

completed forms (normally a slot at the front). Registration stations may be

constructed of wood or metal, and should be set on a post at a convenient

height. Instructions must be provided which clearly detail (1) who is to

register (one person or everyone in the group), (2) when to register (upon

entry or exit), and (3) where to deposit the completed registration form.
104 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

A well-designed, easy-to-read, and attractive sign has the dual purpose of

gaining the attention of the visitor and providing relevant information. The

ideal sign is characterized by high-quality artwork depicting different types

of users (hikers and stock users, and male and female users). The accompanying message should provide clear instructions for the visitor, as well as a

brief explanation of management’s intended use of the information provided

(for example, use estimation, planning maintenance activities, and so forth).

Step 8: Install Equipment

Registration stations are installed as required. Optional equipment installation includes camera setup for registration rate estimation.

1. Registration Stations.—Registration rates are affected by station location. Do not establish registration stations at the trailhead or at parking

areas; registration rates are higher and vandalism is reduced if stations are

located at least one-quarter to 1 mile along the trail. However, if possible,

registration stations should be outside the wilderness boundary. The registration station should be clearly visible from a distance; this is particularly

important in stock-use areas, as horse users need to plan ahead for a stop.

The location site must have sufficient room to allow parties leaving the area

to pass a registering party, and allow members of the group the opportunity

to stop and rest while the designated member registers.

In general, horse users register at much lower rates than hikers do; this is

partly the result of the logistic problems associated with managing pack

strings. Some experimentation with station location may be necessary to

achieve acceptable horse-user registration rates. For example, registration

stations may be located at designated or natural stock loading/unloading

areas, where stock users can register before moving the stock out on the trail.

2. Camera Installation (optional).—When cameras are used to estimate

registration rates, they must be properly placed and maintained if the

resulting observations are to be usable. The camera must be positioned so

that group numbers, the presence of stock and camping gear, and so forth,

can be determined; however, because of privacy concerns, individual identities should not be discernible. The camera should be adjusted to be slightly

out of focus. Cameras must be positioned far enough from the trail so that

visitors cannot hear the shutter or motor action (camera detection could

result in theft or vandalism of equipment); camera equipment should be well

camouflaged.

All equipment should be labeled with agency identification, a statement of

purpose, and the name, address and telephone number of a designated

contact person.

Film consumption should be monitored frequently; registration rates

cannot be estimated if the camera runs out of film during this phase. After

removing exposed film from the camera, label immediately with the date,

time, and location. Protect exposed film from extreme heat and cold until

developed.

Counter-activated cameras: If mechanical counters are used to trigger the

camera, extra time and labor are required for installation. Specifics for

counter site location were discussed in detail for System C, step 2. In general,

mechanical counters should be placed some distance away from the trailhead

so that only bona fide wilderness visitors are counted, and casual visitors

(those who travel only an extremely short distance) are excluded. However,
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 105

if the wilderness boundary is an extremely long distance from the trailhead,

the increase in personnel time involved in traveling to the counter site for

reading and calibrating counters may make this option untenable. Do not

locate counters and counter-activated cameras at the registration station

itself; group members tend to mill around while one member is registering,

and this will cause multiple counts. The counter sensor and camera should

be placed a short distance beyond the registration station to ensure that all

visitors pass the registration station.

The time required for counter installation will vary according to distance

from the trailhead and counter type. After arriving at the selected site, at

least 1 hour will be required for counter installation. This includes time spent

examining the site, selecting the best place for counter location, installing the

sensor and the counting mechanism, setting counter sensitivity or delay, and

testing counter operation. If a counter is mounted on a tree trunk (as is the

case for photoelectric counters), the counter will likely shift slightly within

the first day or two as a result of tree wounding; the counter should therefore

be checked, and realigned if necessary, on the second day after initial

installation.

After the equipment has been installed, observe conditions for a short time

to make certain that the counter is functioning correctly and that any

camouflage is not obscuring or tripping the counter continuously. Walk over

the pad or through the beam several times to check counter sensitivity, and

adjust accordingly.

Step 9: Collect Registration Data

Completed registration cards should be collected on a regular basis. The

person collecting the cards should check the station supplies (unused registration cards and pencils), and replenish if necessary. Keep track of the

number of unused cards in order to assess whether the time intervals for

station visits are appropriate; obviously stations will have to be visited more

frequently if the supply of unused cards runs out before each scheduled

supply drop.

Step 10: Obtain Registration Rate Data

To estimate registration rates, the minimum information required includes number of individuals, number of groups, method of travel, and date

and time of entry or exit. Additional information on observable visit or visitor

characteristics (for example, group size, number of stock, gender, approximate age, time of entry or exit, activity, and whether a user appears to be a

day user or an overnight camper) are recorded at this time. A sample data

sheet is shown in figure 1. However, certain classes of information (such as

gender and age categories) may not be easily determined from observations.

1. Cameras.—Record necessary observations from the developed film.

Observations must be recorded in a standardized format to minimize errors

in recording. Observations include location, date, number of individuals,

number of groups, date and time of entry or exit. Observers must understand

the need to completely and correctly fill out the data form; sample observations will be useless if the data collected by the observer cannot be matched

with the appropriate registration data. Observation sheets should be filed in

a designated place. After observations are recorded, destroy negatives and

developed photos to ensure visitor privacy.
106 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

2. Observers.—Observers should be stationed close enough to the registration station so that all traffic passing the station is accounted for; however,

they do not need to observe whether or not visitors actually register.

Although observers need not be beside the registration station, they should

not wander up and down the trail. Observers do not stop visitors.

Observations are recorded on a standardized form (fig. 1). Observations

include observer name, location, date, number of individuals, number of

groups, date and time of entry or exit. Observers must understand the need

to completely and correctly fill out the data form; sample observations will be

useless if the data collected by the observer cannot be matched with the

appropriate registration data. All deposited registration forms are collected

and labeled at the end of the observation period. Observation sheets and

registration cards should be filed in a designated place.

Step 11: Estimate Use

 Use data are collected in accordance with the appropriate sample size and

the sampling strategy. Data obtained from registration cards are supplemented with observations obtained during the registration-rate estimation

phase. Use can be estimated for both observable and nonobservable categories of visitor, and visitor use is calculated as the number of visitors per

category, expressed as a proportion or percentage of the total number of

users.

1. Estimate Registration Rates.—Registration rate is estimated as the

ratio of the number of registered visitors (determined by the total number of

registration forms collected) to the total number of visitors (determined from

observer counts) during the sample observation periods.

Example. A total of 575 visitors registered during the 7-day registrationrate estimation phase. A random sample of n = 50 visitors indicated that 10

did not register. Therefore, the estimated registration rate r was estimated

as 40/50 = 0.8, or 80 percent. The total number of users (N) for a given period

is estimated by the total number of registered visitors (t) divided by the

registration rate:

 Nˆ = t/r = 575/0.8 = 719.

The 95 percent confidence interval for the total is estimated by N ± 2·SE =

719 ±

 

2 575 50 50 40 40 2 3 [ ] ( ) ⋅ − ( ) /( ) = 719 ± 102, or between 617 and 821 visitors.

2. Sample Size Estimation.—Because visitor count data are collected by

counting registration cards, there may be insufficient resources available to

cover the costs and time involved in the collection, input, and processing of

large amounts of data. Sample sizes for categorical data should be specified

first. Sample sizes should be estimated for each use characteristic to be

measured, and the largest (feasible) sample size is chosen. If a stratified

sampling strategy is used, stratum sample size is calculated according to

whether proportional or disproportional representation is required.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 107

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

compliance estimation phase was 250, with S = 160. There are 100 days in

the season (N = 100). Suppose we want to be 95 percent certain that results

will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated

number of sampling days is 

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( ) = 86. If the precision

is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these

are too large or too close to the entire season of 100 days to be of practical use

due to the large underlying variance. A more reasonable level of precision

would be ± 30 percent (or ± 75 visitors per day), which would call for a sample

size of n = 15.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n

p p

L = 42 1 ⋅( ) ⋅ − ( ) 2

2

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users, p = 24/

40 = 0.60, and the standard error is p pn ( ) 1− / = ( . )( . ) / 0 60 0 40 40 = 0.0775.

The 95 percent confidence interval based on these data is approximately 0.6

± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either
108 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS n ii ii [ ] ⋅ ⋅ / . ∑( ) ⋅ Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—weekend

days and weekdays. This stratification strategy separates out time periods

according to relative intensity of use, with the heaviest and most variable use

occurring on weekends, and relatively light and uniform use on weekdays.

For a 100-day season, there are about 72 weekdays and 28 weekend days.

Suppose the available resources (budget, labor, time) dictated that the

maximum number of days that could be sampled was n = 25. The initial value

for the standard deviation for each stratum was estimated from the data

obtained during the registration rate estimation phase. Sample sizes for each

time block are calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(N1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(N2 = 72)

aStandard deviation.

bSampling proportion.

c

Sample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms

of: (a) the rate (for example, number of visitors per day), (b) the total (for

example, number of visitors for the season), (c) use by category (for example,

cooking method), or (d) use description (for example, length of stay).

(a) Rate of use. Suppose the number of registered visitors for a 30 day

time period was 772. A survey of 50 visitors showed that 46 had permits for

a compliance rate of 46/50 = 0.92.The estimated number of users over the 30

day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users

per day. The estimated confidence interval for the 30 day rate is:

 

839 2 772 50 50 46 46 2 3 ±⋅ ⋅ ⋅ − ( )/ = 839 ± 70 = (769, 909)

which converts to a confidence interval for the daily rate of (25.6, 30.3).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 109

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.

Example. On the registration form 2,975 visitors indicated their method

of cooking during their visit: stoves, wood fires, or neither. Results with a 95

percent confidence interval (using χ2 procedure based on 2 degrees of

freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95 percent confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ±

0.019 = (0.731 to 0.769);

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95 percent confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ±

0.018 = (0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95 percent confidence interval = 0.05 ±

 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ±

0.009 = (0.04 to 0.06).

(d) Use description. One variable that may be obtained by registration

forms is length of stay. Post stratification may also be of interest.

Example. A sample of 38 registration forms had an average length of stay

of 2.4 nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
110 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System E: Visitor Registration

System With Registration Rate

Checks and Sample Interviews

System Description ________________________________________________

This system provides information on visit counts, observable visit and

visitor characteristics, nonobservable characteristics, and summary-use

statistics. In general, visitors fill out survey cards before entering the

wilderness area, and use characteristics are obtained from the resulting

information. Supplementary information is obtained by interviewing visitors. Because registration is voluntary, the accuracy of registration data

must be determined by estimating registration rates, or compliance. Compliance rates are determined by human observers during the interview procedure. Visitor burden is low to moderate, and involves the time required by the

visitor to complete the registration form and time required for interviews.

Summary of System E:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Complex nonobservable characteristics

Summary-use statistics

Measures of visitor use: Number of individual visits

Number of group visits

Use by categories of user

Data collection strategies: Sample plan for registration station rotation (if

applicable)

• spatial

• temporal

Sample plan for registration rate estimates

Sample plan for visitor selection

Techniques/procedures: Voluntary registration

Visual observations (human observers)

Interviews

Visitor burden: Moderate

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics to Measure

Direct measures of use include individual or group visit counts. Additional

visit characteristics acquired from the registration cards include length of
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 111

stay, entry and exit points, method of travel, group size, number of stock, and

place of residence (applicable to the party leader only). Nonobservable visit

and visitor characteristics are acquired by interviewing a random selection

of visitors. To minimize visitor burden, only simple nonobservable characteristics are recorded; these include average length of stay, average group size,

wilderness travel patterns, visitor residence, visit frequency, activities, and

visitor perception of problems, resource conditions, and so forth. Use, in

terms of number of visitors, is usually categorized by one or more nonobservable

characteristics.

Step 2: Decide on Registration Form

Standard OMB-approved registration forms are available. Alternatively,

customized registration forms can be used; however, OMB clearance must be

obtained for new forms before the study begins. According to federal legislation, OMB clearance is required if federal employees ask more than nine

members of the public the same set of questions. The proposed set of

questions, methodology, and study justification must be submitted to OMB

through the appropriate channels. For the Forest Service, application for

clearance is submitted to Information Systems in Washington, DC, which

forwards the application to the Department of Agriculture, and from there to

OMB for final approval. The time from initial submission to final OMB

clearance is usually about 3 months.

“Diary”-type registration cards can give more complete information on

wilderness experiences of visitors. Visitors complete the initial portion of the

card upon entry; this section requests basic information on the visitors or

group. The second portion requests information on the trip itself, and is filled

out by the visitor during the trip or upon leaving the wilderness area. To

reduce error, the two sections should be distinguished by separate headings

and by different colors; however, each section should have the same identification number to allow matching after collection.

Step 3: Decide on Number of Registration Stations

Registration stations are relatively inexpensive to construct, install, and

maintain. However, the number of registration stations in use at any one

time will be determined by the availability of resources (time, supplies, labor)

to ensure adequate monitoring. It is preferable to have only the number of

registration stations that can be conveniently monitored and supplied.

Stations must be kept supplied with adequate amounts of registration forms

and pencils at all times. The image of the agency suffers if visitors are

prevented from registering because supplies are lacking. The number of

stations in use will also be dictated by the number of personnel available to

conduct interviews.

Coverage of the wilderness area is performed by alternating, or rotating,

“in-use” stations across trailheads. Strategies for rotation schedules are

given in step 5.

Step 4: Develop Sampling Plan

Sampling plans must be developed for scheduling (1) rotation of registration stations (if applicable) across trailheads, and (2) observer monitoring

and interviews.
112 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

1. Sample Plan for Rotating Registration Stations Across Trailheads.—

Registration stations are not expensive to construct, install, or maintain.

However, if labor or supplies are insufficient for all trailheads, registration

stations must be rotated on a systematic basis. Rotation strategies are

determined primarily by perceived differences in use occurring in either

space or time. We recommend a more-or-less permanent allocation of a

registration station to each high-use trailhead; the overall accuracy of total

use estimates will depend primarily on the accuracy of estimates obtained for

high-use areas.

(a) Spatial allocation. The following is an example of station allocation

determined by patterns in spatial use. Suppose a manager must monitor use

at four trailheads, but only two stations are available. One trailhead is

believed to account for about 60 percent of use in that wilderness area; a

second trailhead is believed to account for about 50 percent of the remaining

use. A feasible plan for station allocation would be to permanently allocate

one station to the high-use trailhead; the other station is rotated systematically across the remaining three trailheads, such that the amount of time

allocated to each trailhead is proportional to the use that trailhead is

expected to receive. That is, the second station is allocated to the second

trailhead for half of the remaining time, and allocated between the two

remaining trailheads in proportion to anticipated use.

(b) Time allocation. Stations should be placed at each trailhead for at

least two observation periods; observation periods are determined by methods of random selection (part I, chapter 3). One option is to partition the

season into 7-day weeks, then randomly select a given week or weeks as the

observation period for a given station. For example, suppose the manager

wishes to estimate use for the entire 16-week summer season; as in the above

example, there are four trailheads and two stations. One station is permanently allocated to the high-use trailhead; there are therefore three remaining trailheads to be monitored with one station. The manager decides to

partition the 16-week season into eight 2-week blocks so that the station will

be allocated to each trailhead for two separate time blocks; this leaves two

blocks as discretionary time. The order in which the station is assigned to

each trailhead is determined randomly (part I, chapter 3). Suppose the

random number sequence for the eight time blocks is 5 7 8 3 2 6 1 4, and the

random sequence for the three trailheads is 3 4 2. Then the station will be

assigned to trailhead 3 on time blocks 5 and 7, to trailhead 4 on time blocks

8 and 3, and trailhead 2 for time blocks 2 and 6.

2. Sample Plan for Interviews.—Both registration rates and nonobservable

visit characteristics are determined by contacting visitors passing a given

registration station. The procedure for estimating registration rates is

similar to the calibration procedures described for systems using mechanical

counters; visitor registration is “calibrated” by supplementary observations

so that the number of wilderness users who do not register can be accounted

for, and total visitor counts can be adjusted accordingly. Interviews are also

used to obtain information on nonobservable visit characteristics. The

number of interviews required will depend on the desired amount of precision

of both registration rate estimates and estimates of use characteristics, the

available resources, and the relative stability of visitor use over time. If use

patterns change substantially over the season, registration rates estimated

at the beginning of the season will not be applicable later in the season; the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 113

accuracy of registration rates must be spot checked at intervals and updated

as required.

Because human observers are used, registration rate checks may have to

be scheduled within the confines of the workweek. However, if significant

amounts of use occur outside of normal working hours, it is essential that

these time blocks are covered; volunteer labor may be one option. Observer

fatigue and boredom may be a significant problem if time blocks are

extremely long and few visitors are encountered. Sampling effort may be

apportioned according to operationally defined amounts of relative use

observed per time block. At least two observation periods should be scheduled

for each category.

Example. Past experience suggests to a wilderness ranger that the

number of visitors to a certain wilderness area is fairly constant over the

season, with approximately 20 percent of wilderness users entering wilderness area on weekdays, another 40 percent of users enter on Saturday

mornings, 10 percent on Saturday afternoons, 20 percent on Sunday mornings, and 10 percent on Sunday afternoons. A total of 10 observation periods

can be sampled with the resources available. Therefore, the ranger decides

to partition the sampling day into morning and afternoon time blocks. Time

blocks are further stratified into three operationally defined use categories:

low use, medium use, and high use. Observer effort is allocated proportional

to amount of use; thus 20 percent of sampling effort is allocated to low-use

periods (that is, two time blocks occurring on either a weekday morning or

afternoon); 40 percent effort to high-use periods (four Saturday mornings),

and the remaining effort to medium-use time periods (one Saturday afternoon, two Sunday mornings, and one Sunday afternoon. At least 4 weeks are

therefore required for this sampling plan; the specific time blocks to be

monitored are selected by random sampling procedures (part I, chapter 3).

Step 5: Construct the Registration Stations

Registration rates are greatly affected by station design. Visitors are more

likely to stop and register if the station is both attractive and functional.

Registration stations should be designed to provide (a) a place for supplies

(pencils and registration forms), (b) a convenient, solid writing surface for the

visitor to use when completing the registration form, and (c) a place to deposit

completed forms (normally a slot at the front). Registration stations may be

constructed of wood or metal, and should be set on a post at a convenient

height. Instructions must be provided which clearly detail (a) who is to

register (one person or everyone in the group), (b) when to register (upon

entry or exit), and (c) where to deposit the completed registration form.

A well-designed, easy-to-read, and attractive sign has the dual purpose of

gaining the attention of the visitor and providing relevant information.

Figure 6 illustrates an improved version of the more traditional “officiallooking” signs commonly in use. The improved sign is characterized by highquality artwork depicting different types of users (hikers and stock users,

and male and female users). The accompanying message should provide clear

instructions for the visitor, as well as a brief explanation of management’s

intended use of the information provided (for example, use estimation,

planning maintenance activities, and so forth).
114 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Step 6: Install Registration Stations

Registration rates are affected by station location. Do not establish registration stations at the trailhead or at parking areas; registration rates are

higher and vandalism is reduced if stations are located at least one-quarter

to 1 mile along the trail. However, if possible, registration stations should be

outside the wilderness boundary. The registration station should be clearly

visible from a distance; this is particularly important in stock-use areas, as

horse users need to plan ahead for a stop. The location site must have

sufficient room to allow parties leaving the area to pass a registering party,

and allow members of the group the opportunity to stop and rest while the

designated member registers.

In general, horse users register at much lower rates than hikers do; this is

partly the result of the logistic problems associated with managing pack

strings. Some experimentation with station location may be necessary to

achieve acceptable horse-user registration rates. For example, registration

stations may be located at designated or natural stock loading/unloading

areas, where stock users can register before moving the stock out on the trail.

Step 7: Select and Train the Interview Team

Careful selection and training of the personnel who are involved in

collecting data are essential if the manager or research planner is not

Figure 6—Example of an attractive

registration sign.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 115

performing the field research. The research planner must ensure that

interviews are conducted and observations collected in the manner required

by the study plan.

1. Personnel Selection.—Both personality and ability must be evaluated

in the selection process. The importance of visitor contact extends beyond the

quality of data obtained; it is an opportunity to present the image of the

managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar

with the wilderness area and be prepared to handle requests for information

about the wilderness and the surrounding area. Many of the questions from

visitors will not be related to the interview; providing information is a

courtesy which contributes to establishing rapport with the visitors and

increases visitor cooperation. Personnel should be in appropriate uniform

and possess necessary communication and safety equipment.

2. Training.—It is essential that personnel are thoroughly trained in the

data collection procedures. Training ensures that observers are already

familiar with the research directives and the interviewing process before

actual fieldwork begins. As a result, errors involved in the learning process

are reduced, and there will be greater consistency in identifying the sampling

units (in this case visitors to be interviewed) and recording responses.

Training enables observers to become familiar with various contingency

plans, to identify potential problems in the research directives, and to make

decisions if problems occur.

Preliminary, or pretest, fieldwork should be conducted before the actual

survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or

inadequacies in the procedures can be identified and eliminated, and the

consistency and accuracy of personnel can be observed and analyzed. Observers should be screened at intervals and their performance compared either

with each other or at different time points for the same observer; screening

provides a check on performance and identifies sources of error in the data.

Step 8: Collect Registration Rate and Interview Data

Information on registration rates and interview data are collected simultaneously by observers. Both types of information are collected according to

a specific plan (as described in step 4). The observer must be provided with

sufficient research material—data forms, writing tools, schedules, and so

forth—for the observation period. Observers must understand the need to

completely and correctly fill out the data forms. Observation sheets should

be filed in a designated place after the observer returns to the office.

1. Registration Rates.—Registration rate observations are obtained during the sample observation period; all traffic entering the wilderness area is

monitored, but only groups designated by the sampling plan are interviewed.

Observations must be recorded in a standardized format (see fig. 1 for a

sample form). For each data sheet, the observer should record their name, the

sampling location, the date, start time, and end time for that sample period.

The minimum information required to estimate registration rates includes

number of individuals, number of groups, method of travel, date and time of

entry or exit, and use category (day user or overnight user). All deposited

registration cards are collected at the end of the sample observation period.
116 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

2. Interview Data.—The interview protocol consists of four steps: (a)

determining question format, (b) obtaining OMB clearance, (c) visitor selection, and (d) data collection.

(a) Question format. The questions asked of the visitor will be dictated

on the basis of the study objectives; that is, on the basis of what the manager

wants to know and why. Questions should be easily understood by the visitor,

they should not be too long, and there should not be too many of them. Ask

only the questions necessary to meet the study objectives, and no more. For

example, suppose the manager is interested in evaluating relative impact in

terms of time spent in different areas by various user groups. Interviews can

be limited to determining method of travel, destination, and length of stay of

visitors encountered at each trailhead; the interview will be short.

Personnel may be tempted to add additional questions “just out of curiosity”; this cannot be justified in any circumstances. Do not add questions

merely to fill up space on the interview sheet. If some inadequacy or

ambiguity becomes apparent with the set questions, questions may be added,

but only if they clarify the meaning and satisfy the requirements of step 1.

The question designer is rarely a good judge of the clarity of the questions

(Ackoff 1953); preliminary field tests are invaluable for identifying problems

before the actual field surveys begin.

(b) Obtain OMB clearance. According to federal legislation, clearance

from the Office of Management and Budget (OMB) is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which then forwards the application to the Department of Agriculture, and from there to OMB for final approval. The time from

initial submission to final OMB clearance is usually about 3 months.

(c) Interview selection. Visitors are selected in accordance with the

predetermined sampling plan (step 4). The location of interviews will be

determined by study objectives; visitors may be interviewed upon either

entry or exit, or both. For example, if the emphasis of the study is on the

effects of group size or place of residence on wilderness use, these factors are

unaffected by interview location. However, if the study objectives require

information on patterns of visitor use within the wilderness area (for

example, travel or camping locations, length of stay), visitors should be

interviewed as they leave.

(d) Data collection. When interviewing visitors, personnel should begin

with a standard introduction. Personnel should give their name and agency

affiliation and the reason for the interview. For example, “Hello, I am

Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.

We are trying to learn more about the use of the Rattlesnake Wilderness. It

will help us with management of the area. May I ask you a few questions

about your visit today?” After the interview, thank visitors for their time.

Responses should be recorded as they are given; interviewers should not

rely on memory to fill in the interview sheet at a later time. Make sure every

item is complete and legible; data forms must include date, time, location,

and interviewer’s name. Completed data forms should be filed in a safe place.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 117

Step 9: Estimate Use

Use data are collected in accordance with the appropriate sample size and

the sampling strategy. Data obtained from registration cards are supplemented with observations obtained during the registration-rate estimation

phase. Use can be estimated for both observable and nonobservable categories of visitor, and visitor use is calculated as the number of visitors per

category, expressed as a proportion or percentage of the total number of users.

1. Estimate Registration Rates.—Registration rate is estimated as the

ratio of the number of registered visitors (determined by the total number of

registration forms collected) to the total number of visitors (determined from

observer counts) during the sample observation periods.

Example. A total of 575 visitors registered during the 7-day registrationrate estimation phase. A random sample of n = 50 visitors indicated that 10

did not register. Therefore, the estimated registration rate r was estimated

as 40/50 = 0.8, or 80 percent. The total number of users (N) for a given period

is estimated by the total number of registered visitors (t) divided by the

registration rate:

 Nˆ = t/r = 575/0.8 = 719.

The 95 percent confidence interval for the total is estimated by N ± 2·SE =

719 ±

 

2 575 50 50 40 40 2 3 [ ] ( ) ⋅ − ( ) /( ) = 719 ± 102, or between 617 and 821 visitors.

2. Sample Size Estimation.—Because visitor count data are collected by

counting registration cards, there may be insufficient resources available to

cover the costs and time involved in the collection, input, and processing of

large amounts of data. Sample sizes for categorical data should be specified

first. Sample sizes should be estimated for each use characteristic to be

measured, and the largest (feasible) sample size is chosen. If a stratified

sampling strategy is used, stratum sample size is calculated according to

whether proportional or disproportional representation is required.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using fpc, the estimated sample size

is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of
118 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

compliance estimation phase was 250, with S = 160. There are 100 days in the

season (N = 100). Suppose we want to be 95 percent certain that results will

have a precision of ± 5 percent, or ± 13 visitors/day. The estimated number of

sampling days is

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( )

= 86. If the precision is adjusted

to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these are too

large or too close to the entire season of 100 days to be of practical use due to

the large underlying variance. A more reasonable level of precision would be

± 30 percent (or ± 75 visitors per day), which would call for a sample size of

n = 15.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n

p p

L = 42 1 ⋅( ) ⋅ − ( ) 2

2

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users, p = 24/

40 = 0.60, and the standard error is p pn ( ) 1− / = ( . )( . ) / 0 60 0 40 40 = 0.0775.

The 95 percent confidence interval based on these data is approximately 0.6

± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS n ii ii [ ] ⋅ ⋅ / . ∑( ) ⋅ Disproportional sampling occurs

when the same size sample is drawn for each stratum (assuming equal costs

to sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 119

Example. In this example, data are stratified by two time blocks—

weekend days and weekdays. This stratification strategy separates out time

periods according to relative intensity of use, with the heaviest and most

variable use occurring on weekends, and relatively light and uniform use on

weekdays. For a 100-day season, there are about 72 weekdays and 28

weekend days. Suppose the available resources (budget, labor, time) dictated

that the maximum number of days that could be sampled was n = 25. The

initial value for the standard deviation for each stratum was estimated from

the data obtained during the registration rate estimation phase. Sample

sizes for each time block are calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(n1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(n2 = 72)

aStandard deviation.

bSampling proportion.

cSample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms

of: (a) the rate (for example, number of visitors per day), (b) the total (for

example, number of visitors for the season), (c) use by category (for example,

cooking method), or (d) use description (for example, length of stay).

(a) Rate of use. Suppose the number of registered visitors for a 30 day

time period was 772. A survey of 50 visitors showed that 46 had permits for

a compliance rate of 46/50 = 0.92.The estimated number of users over the 30

day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users

per day. The estimated confidence interval for the 30 day rate is

 

839 2 772 50 50 46 46 2 3 ±⋅ ⋅ ⋅ − ( )/ = 839 ± 70 = (769, 909)

which converts to a confidence interval for the daily rate of (25.6, 30.3).

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.
120 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Hiking is by far the most common method of wilderness travel.

Example. On the registration form 2,975 visitors indicated their method

of cooking during their visit: stoves, wood fires, or neither. Results with a 95

percent confidence interval (using χ2 procedure based on 2 degrees of

freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95 percent confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ±

0.019 = (0.731 to 0.769);

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95 percent confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ±

0.018 = (0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95 percent confidence interval = 0.05 ± 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ±

0.009 = (0.04 to 0.06).

(d) Use description. One variable that may be obtained by registration

forms is length of stay. Post stratification may also be of interest.

Example. A sample of 38 registration forms had an average length of stay

of 2.4 nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 121

System F: Permit System With

Compliance Checks

System Description ________________________________________________

Permits are mandatory use-authorization forms issued by the agency. The

information obtained is constrained by what is required by the permit form;

this system provides sufficient information to estimate basic visit counts,

visit and visitor characteristic data, and may enable estimates of certain

summary-use statistics. Compliance checks are required for accurate estimation of total use. Because visitors are responsible for obtaining permits,

visitor burden is relatively high.

Summary of System F:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Complex nonobservable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Total number of users

Use by category of user

Summary-use statistics

Data collection strategies: Permit-issue method

Visitor selection sampling for compliance checks

Techniques/procedures: Permits

Compliance checks

Visitor burden: Moderate to high

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics

Use characteristics that can be obtained are restricted by the permit

format. Information obtained from permits can include the number of

individuals or groups, group size, method of travel, anticipated dates of entry

and exit, length of stay, and place of residence. If mailback sections are

included with the permit, the permit holder can document various triprelated observations, such as number of encounters, travel routes and

destinations, actual length of stay, and perceptions of wilderness conditions.

Step 2: Decide on a Permit Form

Standard OMB-approved permits are available for each agency. Alternatively, customized permit formats can be used. However, OMB clearance
122 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

must be obtained before the study begins if permits are to be issued in a

revised format; this includes the addition of questions to standard permit

forms. According to federal legislation, OMB clearance is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which forwards the application to the Department

of Agriculture, and from there to OMB for final approval. The time from

initial submission to final OMB clearance is usually about 3 months.

Clearance is not required if shortened versions of the standard permit with

fewer questions are used.

Step 3: Establish a Permit-Issue Procedure

The procedure for issuing permits will be determined by (1) the reason for

issuing permits, and (2) the source of issue.

1. Reasons for Permit Issue.—Permits are issued to (a) provide a means of

public contact, (b) restrict use or categories of user, and (c) monitor use.

(a) Public contact. If the objective in issuing permits is to create

opportunities for public contact opportunity, visitors will be required to

obtain permits in person at a centralized agency facility, such as a visitor

center or ranger station. Visitor contact with a trained agency representative

is valuable for promoting the professional image of the agency and increasing

visitor knowledge of regulations, appropriate low-impact behaviors, potential hazards, and wilderness conditions. Visitors have the opportunity to

discuss possible routes and destinations within the wilderness area, and to

obtain other information of interest to them.

(b) Use restriction. If the objective in issuing permits is to restrict use,

visitors will be required to obtain permits at a centralized agency facility,

such as a visitor center or ranger station. Alternatively, if adequate computer

facilities are available, permits can be issued from a number of different field

offices by means of a computerized reservation system so that the number of

permits available at any time can be tracked.

(c) Use monitoring. If permits are issued with the objective of collecting

accurate visitor use data, there are no associated restrictions on where or

how permits are issued. Permits may be issued by the agency or self-issued;

numbers may be limited or unlimited.

2. Source of Permit Issue.—Permits are usually issued by agency personnel, but may be self-issued, or distributed through a cooperative arrangement with local vendors.

In the majority of cases, permits are issued from a central location by the

managing agency. Staff at local ranger stations, information centers, or

National Forest offices are responsible for issuing permits. Occasionally,

permits may be reserved; reservations may be made by telephone or mail, or

in other cases must be made in person if “no-shows” are a problem. Reserved

permits may be mailed, or held until picked up by the visitor.

Self-issued permits are usually obtained from some convenient location. If

permits are unlimited, they may be obtained from a station located outside

the agency office or at trailheads, or from alternative locations, such as local
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 123

businesses. However, if permit numbers are limited, they must be obtained

from a central location.

If there are restrictions on certain types of users, permit-issue locations

may be placed so as to accommodate different user groups. For example, if

overnight use of a wilderness area must be rationed but day use is essentially

unrestricted, a limited number of overnight permits are made available at

some central location, whereas self-issued day-use permits are located at

trailheads.

Permits may be issued through cooperative arrangements with local

vendors or businesses. Wilderness permits may be issued by convenience

stores, bait shops, commercial outfitters, travel information centers, or

nearby campgrounds.

Step 4: Decide on Method of Implementing Compliance Checks

Unlike registration systems, which are voluntary, permit systems are

mandatory. Visitors must obtain a permit to enter the wilderness area;

otherwise they are not in compliance with regulations. However, accuracy of

use estimation will be compromised if rates of compliance are unknown.

Permit compliance may be as low as 53 percent with self-issued day-use

permits to as high as 90 percent; compliance varies with type of user group,

and increases with increased levels of enforcement, increased publicity about

permit requirements, and increased visitor awareness of permit requirements.

The procedure for estimating compliance is similar to the calibration

procedures described for systems using mechanical counters. Visitor counts

obtained from a tally of permits are “calibrated” by supplementary observations so that the number of wilderness users who do not obtain permits can

be accounted for, and total visitor counts can be adjusted accordingly.

Interviews are also used to obtain information on nonobservable visit

characteristics. The number of interviews required will depend on the

desired amount of precision of both compliance estimates and estimates of

use characteristics, the available resources, and the relative stability of

visitor use over time. If use patterns change substantially over the season,

compliance rates estimated at the beginning of the season will not be

applicable later in the season; the accuracy of compliance rates must be spot

checked at intervals and updated as required.

Frequently, permit compliance is determined in the course of routine

wilderness ranger patrol. Rangers check for permit compliance as visitor

groups are encountered, and tally the proportion of those encountered who

do not have a permit; this is the so-called “roaming observation” technique.

However, this type of visitor sampling results in extremely biased estimates

of visitor use. Bias occurs because the probability of visitor contact depends

on when and where the observer travels. Scheduling is not random but

deliberately selected to coincide with periods of heaviest use; the probability

that a visitor group will be encountered is proportional to the length of time

spent in a given area, observer location in relation to visitor distance

traveled, and so on.

Unbiased data can be obtained only by implementing statistical sampling

strategies. Permit checkpoints should be established, and visitors sampled

according to a predetermined sampling plan. Sampling may be strictly random,

or stratified by day and systematic within that day. Sample sizes are determined with reference to the population of interest, the expected variation of

the response variables, and the specified sampling plan (part I, chapter 3).
124 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Step 5: Purchase Equipment

If permits are self-issued, permit stations need to be constructed. These

stations should be both attractive and functional. Self-issue permit stations

should be designed to provide (1) a place for supplies (pencils and permit

forms), (2) a convenient, solid writing surface for the visitor to use when

completing the permit, and (3) a place to deposit completed agency copy

(normally a slot at the front). Stations may be constructed of wood or metal,

and should be set on a post at a convenient height. An attractive and easyto-read sign should be posted with instructions detailing (1) why a permit is

required, (2) who is to obtain a permit (one person or everyone in the group),

(3) where to deposit the completed agency copy, and (4) the consequences of

being found in violation.

Step 6: Estimate Use

Use data are collected in accordance with the appropriate sample size and

the sampling strategy. Data obtained from permits are supplemented with

observations obtained during the permit compliance rate estimation phase.

Use can be estimated for both observable and nonobservable categories of

visitor, and visitor use is calculated as the number of visitors per category,

expressed as a proportion or percentage of the total number of users.

1. Estimate Permit Compliance Rates.—Permit compliance rate is estimated as the ratio of the number of permit holders (determined by the total

number of permits collected) to the total number of visitors (determined from

observer counts) during the sample observation periods.

Example. A total of 575 visitors obtained permits during the 7-day permit

compliance rate estimation phase. A random sample of n = 50 visitors

indicated that 10 did not obtain permits. Therefore, the estimated permit

compliance rate r was estimated as 40/50 = 0.8, or 80 percent. The total

number of users (N) for a given period is estimated by the total number of

permit holding visitors (t) divided by the permit compliance rate:

 Nˆ = t/r = 575/0.8 = 719

The 95 percent confidence interval for the total is estimated by N ± 2· SE =

719 ±

 

2 575 50 50 40 40 2 3 [ ] ( ) ⋅ − ( ) /( ) = 719 ± 102, or between 617 and 821 visitors.

2. Sample Size Estimation.—Because visitor count data are collected by

counting permits, there may be insufficient resources available to cover the

costs and time involved in the collection, input, and processing of large

amounts of data. Sample sizes for categorical data should be specified first.

Sample sizes should be estimated for each use characteristic to be measured,

and the largest (feasible) sample size is chosen. If a stratified sampling

strategy is used, stratum sample size is calculated according to whether

proportional or disproportional representation is required.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 125

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

compliance estimation phase was 250, with S = 160. There are 100 days in

the season (N = 100). Suppose we want to be 95 percent certain that results

will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated

number of sampling days is

 

 

≈

( ) + ( )( ) +

100 160

160 13 13 100

16

2

2

2

( ) = 86. If the precision

is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these

are too large or too close to the entire season of 100 days to be of practical use

due to the large underlying variance. A more reasonable level of precision

would be ± 30 percent (or ± 75 visitors per day), which would call for a sample

size of n = 15.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n

p p

L = 42 1 ⋅( ) ⋅ − ( ) 2

2

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users, p = 24/

40 = 0.60, and the standard error is p pn ( ) 1 0 60 0 40 40 − / . ./ = ( )( ) = 0.0775.

The 95 percent confidence interval based on these data is approximately 0.6

± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either
126 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS n ii ii [ ] ⋅ ⋅ / . ∑( ) ⋅ Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—

weekend days and weekdays. This stratification strategy separates out time

periods according to relative intensity of use, with the heaviest and most

variable use occurring on weekends, and relatively light and uniform use on

weekdays. For a 100-day season, there are about 72 weekdays and 28

weekend days. Suppose the available resources (budget, labor, time) dictated

that the maximum number of days that could be sampled was n = 25. The

initial value for the standard deviation for each stratum was estimated from

the data obtained during the permit compliance rate estimation phase.

Sample sizes for each time block are calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(n1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(n2 = 72)

aStandard deviation.

bSampling proportion.

cSample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms

of: (a) the rate (for example, number of visitors per day), (b) the total (for

example, number of visitors for the season), (c) use by category (for example,

cooking method), or (d) use description (for example, length of stay).

(a) Rate of use. Suppose the number of visitors with permits for a 30 day

time period was 772. A survey of 50 visitors showed that 46 had permits for

a compliance rate of 46/50 = 0.92. The estimated number of users over the 30

day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users

per day. The estimated confidence interval for the 30 day rate is 839 ±

 

2 772 50 50 46 46 2 3 ⋅ ⋅⋅ − ( )/ = 839 ± 70 = (769, 909), which converts to a confidence interval for the daily rate of (25.6, 30.3).
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 127

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.

Example. On the permit form 2,975 visitors indicated their method of

cooking during their visit: stoves, wood fires, or neither. Results with a 95

percent confidence interval (using χ2 procedure based on 2 degrees of

freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95 percent confidence interval = 0.75 ±

 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ± 0.019

= (0.731 to 0.769);

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95 percent confidence interval = 0.20 ±

 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ± 0.018

= (0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95 percent confidence interval = 0.05 ±

 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ± 0.009

= (0.04 to 0.06).

(d) Use description. One variable that may be obtained by permits is

length of stay. Post stratification may also be of interest.

Example. A sample of 38 permits had an average length of stay of 2.4

nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).

Day-use horseback rider registration ranges from a low of

0 percent to 89 percent.
128 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System G: Permit System With

Compliance Checks and Sample

Interviews

System Description ________________________________________________

Permits are mandatory use-authorization forms issued by the agency. Use

information obtained is determined by the permit form and by the interview

format; this system provides sufficient information to estimate summaryuse statistics, as well as basic visit counts, visit and visitor characteristic

data. Compliance checks are required for accurate estimation of total use. A

random selection of visitors is interviewed to obtain supplementary information not provided by the permit. Because visitors are responsible for obtaining permits, and because visitors are contacted directly for interviews, visitor

burden is relatively high.

Summary of System G:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Complex nonobservable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Use by categories of user

Summary-use statistics

Data collection strategies: Permit-issue process

Sampling plan for visitor selection

Techniques/procedures: Permits

Compliance checks

Sample interviews

Visitor burden: Moderate to high

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics

Use characteristics that can be obtained are limited only by the permit

format. Information obtained from permits can include the number of

individuals or groups, group size, method of travel, anticipated dates of entry

and exit, length of stay, and place of residence. Mailback sections attached

to the permit enable the permit holder to document various trip-related

observations, such as number of encounters, travel routes and destinations,

actual length of stay, and perceptions of wilderness conditions.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 129

Nonobservable visit and visitor characteristics not on the permit form are

acquired by interviewing a random selection of visitors. The characteristics

include specific length-of-stay information, anticipated wilderness travel

patterns and routes, visit frequency, activities, and visitor perception of

problems and resource conditions, past wilderness experience, knowledge of

regulations and low-impact procedures, preferences for various management strategies, and so forth.

Step 2: Decide on a Permit Form

Standard OMB-approved permits are available for each agency. Alternatively, customized permit formats can be used. However, OMB clearance

must be obtained before the study begins if permits are to be issued in a

revised format; this includes the addition of questions to standard permit

forms. According to federal legislation, OMB clearance is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to that Agency’s

Information Systems office in Washington, DC, which forwards the application to the Department of Agriculture, and from there to OMB for final

approval. The time from initial submission to final OMB clearance is usually

about 3 months. Clearance is not required if shortened versions of the

standard permit with fewer questions are used.

Step 3: Establish a Permit-Issue Procedure

The procedure for issuing permits will be determined by (1) the reason for

issuing permits, and (2) the source of issue.

1. Reasons for Permit Issue.—Permits are issued to (a) provide a means

of public contact, (b) restrict use or categories of user, and (c) monitor use.

(a) Public contact. If the objective in issuing permits is to create

opportunities for public contact opportunity, visitors will be required to

obtain permits in person at a centralized agency facility, such as a visitor

center or ranger station. Visitor contact with a trained agency representative is valuable for promoting the professional image of the agency and

increasing visitor knowledge of regulations, appropriate low-impact behaviors, potential hazards, and wilderness conditions. Visitors have the opportunity to discuss possible routes and destinations within the wilderness

area, and to obtain other information of interest to them.

(b) Use restriction. If the objective in issuing permits is to restrict use,

visitors will be required to obtain permits at a centralized agency facility,

such as a visitor center or ranger station. Alternatively, if adequate computer facilities are available, permits can be issued from a number of

different field offices by means of a computerized reservation system so that

the number of permits available at any time can be tracked.

(c) Use monitoring. If permits are issued with the objective of collecting

accurate visitor use data, there are no associated restrictions on where or

how permits are issued. Permits may be issued by the agency or self-issued;

numbers may be limited or unlimited.
130 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

2. Source of Permit Issue.—Permits are usually issued by agency personnel, but may be self-issued, or distributed through a cooperative arrangement with local vendors.

In the majority of cases, permits are issued from a central location by the

managing agency. Staff at local ranger stations, information centers, or

National Forest offices are responsible for issuing permits. Occasionally,

permits may be reserved; reservations may be made by telephone or mail, or

in other cases must be made in person if “no-shows” are a problem. Reserved

permits may be mailed, or held until picked up by the visitor.

Self-issued permits are usually obtained from some convenient location. If

wilderness use is unrestricted, permit access does not need to be monitored

closely. As a result, permits may be obtained from a station located outside

the agency office or at trailheads, or from alternative locations, such as local

businesses. However, if permit numbers are limited, permits must be

obtained from a central location where permit acquisition can be regulated.

If there are restrictions on certain types of users, permit-issue locations

may be placed so as to accommodate different user groups. For example, if

overnight use of a wilderness area must be rationed but day use is essentially

unrestricted, a limited number of overnight permits are made available at

some central location, whereas self-issued day-use permits are located at

trailheads.

Permits may be issued through cooperative arrangements with local

vendors or businesses. Wilderness permits may be issued by convenience

stores, bait shops, commercial outfitters, travel information centers, or

nearby campgrounds.

Step 4: Develop Sampling Plan

Sample plans must be developed for:

1. Implementing compliance checks, and

2. Selecting visitors for interviews.

1. Compliance Checks.—Unlike registration systems, which are voluntary, permit systems are mandatory. Visitors must obtain a permit to enter

the wilderness area, otherwise they are not in compliance with regulations.

However, accuracy of use estimation will be compromised if rates of compliance are unknown. Permit compliance may be as low as 53 percent with selfissued day-use permits, to as high as 90 percent; compliance varies with type

of user group, and increases with increased levels of enforcement, increased

publicity about permit requirements, and increased visitor awareness of

permit requirements.

The procedure for estimating compliance is similar to the calibration

procedures described for systems using mechanical counters. Visitor counts

obtained from a tally of permits are “calibrated” by supplementary observations so that the number of wilderness users who do not obtain permits can

be accounted for, and total visitor counts can be adjusted accordingly. The

number of compliance checks required will depend on the desired amount of

precision, the available resources, and the relative stability of visitor use over

time. If use patterns change substantially over the season, compliance rates

estimated at the beginning of the season will not be applicable later in the

season; the accuracy of compliance rates must be spot checked at intervals

and updated as required.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 131

Frequently, permit compliance is determined in the course of routine

wilderness ranger patrol. Rangers check for permit compliance as visitor

groups are encountered, and tally the proportion of those encountered who

do not have a permit; this is the so-called “roaming observation” technique.

However, this type of visitor sampling results in extremely biased estimates

of visitor use. Bias occurs because the probability of visitor contact depends

on when and where the observer travels. Scheduling is not random but

deliberately selected to coincide with periods of heaviest use; the probability

that a visitor group will be encountered is proportional to the length of time

spent in a given area, and observer location in relation to visitor distance

traveled.

Unbiased data can be obtained only by implementing statistical sampling

strategies. Permit checkpoints should be established, and visitors sampled

according to a predetermined sampling plan. Sampling may be strictly

random, or stratified by day and systematic within that day. Sample sizes are

determined with reference to the population of interest, the expected variation of the response variables, and the specified sampling plan (part I,

chapter 3).

2. Interviews.—Interviews are conducted by contacting visitors at a checkpoint station outside the wilderness boundary. Interviews are used to obtain

information on non-observable visit characteristics.

The two steps in the formulation of an appropriate sampling plan for visitor

selection are an estimate of the sample size, and a time schedule.

(a) Sample size estimation. Determination of the appropriate sample

size requires a preliminary estimate of the variability in the observations.

Preliminary estimates are obtained from a pilot study, or from data collected

in previous years. A common requirement of many wilderness studies is the

comparison of count or frequency data by category; categories are identified

by specific visit characteristic. To ensure adequate representation, sampling

may have to be stratified by category. See part I, chapter 3, for further details

of sample design.

(b) Time schedule. For the sample to be representative of all visitors

entering the wilderness area, interviews must be scheduled according to a

statistical sampling plan. Unless the wilderness area has a strictly enforced

permit program, visitors cannot be randomly selected for interviewing prior

to arrival. If there is no regulation of visitor entry and exit, the alternative

is the random selection of interview days, followed by random selection of

visitors within the sample day. Sampling may be completely random,

systematic (for example, selective censusing of every tenth wilderness

visitor, or every fifth car passing a checkpoint), stratified, or a combination

of these (part I, chapter 3).

Step 5: Purchase Equipment

If permits are self-issued, permit stations need to be constructed. These

stations should be both attractive and functional. Self-issue permit stations

should be designed to provide (a) a place for supplies (pencils and permit

forms, (b) a convenient, solid writing surface for the visitor to use when

completing the permit, and (c) a place to deposit completed agency copy

(normally a slot at the front). Stations may be constructed of wood or metal,

and should be set on a post at a convenient height. An attractive and easyto-read sign should be posted with instructions detailing (a) why a permit is
132 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

required, (b) who is to obtain a permit (one person or everyone in the group),

(c) where to deposit the completed agency copy, and (d) the consequences of

being found in violation.

Step 6: Select and Train the Interview Team

Careful selection and training of the personnel who are involved in

collecting data are essential if the manager or research planner is not

performing the field research. The research planner must ensure that

interviews are conducted and observations collected in the manner required

by the study plan.

1. Personnel Selection.—Both personality and ability must be evaluated

in the selection process. The importance of visitor contact extends beyond the

quality of data obtained; it is an opportunity to present the image of the

managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar

with the wilderness area and be prepared to handle requests for information

about the wilderness and the surrounding area. Many of the questions from

visitors will not be related to the interview; providing information is a

courtesy which contributes to establishing rapport with the visitors and

increases visitor cooperation. Personnel should be in appropriate uniform

and possess necessary communication and safety equipment.

2. Training.—It is essential that personnel are thoroughly trained in the

data collection procedures. Training ensures that observers are already

familiar with the research directives and the interviewing process before

actual fieldwork begins. As a result, errors involved in the learning process

are reduced, and there will be greater consistency in identifying the sampling

units (in this case visitors to be interviewed) and recording responses.

Training enables observers to become familiar with various contingency

plans, to identify potential problems in the research directives, and to make

decisions if problems occur.

Preliminary, or pretest, fieldwork should be conducted before the actual

survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or

inadequacies in the procedures can be identified and eliminated, and the

consistency and accuracy of personnel can be observed and analyzed. Observers should be screened at intervals, and their performance compared either

with each other or at different time points for the same observer; screening

provides a check on performance and identifies sources of error in the data.

Step 7: Collect Compliance Rate and Interview Data

Information on compliance rates and interview data are collected separately by observers. Both types of information are collected according to a

specific plan (as described in step 4). The observer must be provided with

sufficient research material—data forms, writing tools, schedules, and so

forth,—for the observation period. Observers must understand the need to

completely and correctly fill out the data forms. Observation sheets should

be filed in a designated place after the observer returns to the office.

1. Compliance Rates.—Compliance rate observations are obtained during

the sample observation period (step 4). Observations must be recorded in a
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 133

standardized format (see fig. 1 for a sample form). For each data sheet, the

observer should record their name, the sampling location, the date, start

time, and end time for that sample period. The minimum information

required to estimate compliance rates includes number of individuals,

number of groups, method of travel, date and time of entry or exit, and use

category (day user or overnight user).

2. Interview Data.—The interview protocol consists of four steps: (a) determining question format, (b) obtaining OMB clearance, (c) visitor selection,

and (d) data collection.

(a) Question format. The questions asked of the visitor will be dictated

by the study objectives; that is, on the basis of what the manager wants to

know and why. Questions should be easily understood by the visitor, they

should not be too long, and there should not be too many of them. The major

principle in question development is the necessity to keep visitor burden to a

minimum. Ask only the questions necessary to meet the study objectives, and

no more.

The questions asked of the respondents will depend on what kind of

information is required to meet the study objectives. Questions can be

categorized on the basis of one or more of the following types of information:

• Attitudes: what people say they want or how they feel about something;

• Beliefs: what people think is true or false;

• Behavior: what people do;

• Attributes: what people are (personal or demographic features).

Questions must be clearly identified according to information type, otherwise responses will lead to a different type of information than required by

the study objectives.

The question designer is rarely a good judge of the clarity of the questions

(Ackoff 1953). Preliminary field tests are invaluable for identifying problems,

and should be conducted before the actual field surveys begin. Colleagues,

potential “users” of the data, and, if possible, a small pretest sample of

prospective respondents should fill out the questionnaire; a debriefing

session should follow to identify problems. If some inadequacy or ambiguity

becomes apparent with the set questions, questions may be added, but only

if they clarify the meaning and satisfy the requirements of step 1.

(b) Obtain OMB clearance. According to federal legislation, clearance

from the Office of Management and Budget (OMB) is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which then forwards the application to the Department of Agriculture, and from there to OMB for final approval. The time from

initial submission to final OMB clearance is usually about 3 months.

(c) Visitor selection. Visitors are selected in accordance with the predetermined sampling plan (step 4). The location of interviews will be determined by study objectives; visitors may be interviewed upon either entry or

exit, or both. For example, if the emphasis of the study is on the effects of

group size or place of residence on wilderness use, these factors are unaffected by interview location. However, if the study objectives require information on patterns of visitor use within the wilderness area (for example,
134 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

travel or camping locations, length of stay), visitors should be interviewed as

they leave. Visitors should not be interviewed inside the wilderness boundary (to avoid threats to the visitor experience from management presence).

(d) Data collection. When interviewing visitors, personnel should begin

with a standard introduction. Personnel should give their name and agency

affiliation and the reason for the interview. For example, “Hello, I am

Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.

We are trying to learn more about the use of the Rattlesnake Wilderness. It

will help us with management of the area. May I ask you a few questions

about your visit today?” After the interview, thank visitors for their time.

Personnel may be tempted to add additional questions “just out of curiosity”;

this cannot be justified in any circumstances.

Responses should be recorded as they are given; interviewers should not

rely on memory to fill in the interview sheet at a later time. Make sure every

item is complete and legible; data forms must include date, time, location,

and interviewer’s name. Completed data forms should be filed in a safe place.

Step 8: Estimate Use

 Use data are collected in accordance with the appropriate sample size and

the sampling strategy. Data obtained from permits are supplemented with

observations obtained during the permit compliance rate estimation phase.

Use can be estimated for both observable and nonobservable categories of

visitor, and visitor use is calculated as the number of visitors per category,

expressed as a proportion or percentage of the total number of users.

1. Estimate Permit Compliance Rates.—Permit compliance rate is estimated as the ratio of the number of permit holders (determined by the total

number of permits collected) to the total number of visitors (determined from

observer counts) during the sample observation periods.

Example. A total of 575 visitors obtained permits during the 7-day permit

compliance rate estimation phase. A random sample of n = 50 visitors

indicated that 10 did not obtain permits. Therefore, the estimated permit

compliance rate r was estimated as 40/50 = 0.8, or 80 percent. The total

number of users (N) for a given period is estimated by the total number of

permit holding visitors (t) divided by the permit compliance rate:

 Nˆ = t/r = 575/0.8 = 719.

The 95 percent confidence interval for the total is estimated by N ± 2·SE =

719 ±

 

2 575 50 50 40 40 2 3 [ ] ( ) ⋅ − ( ) /( ) = 719 ± 102, or between 617 and 821 visitors.

2. Sample Size Estimation.—Because visitor count data are collected by

counting permits, there may be insufficient resources available to cover the

costs and time involved in the collection, input, and processing of large

amounts of data. Sample sizes for categorical data should be specified first.

Sample sizes should be estimated for each use characteristic to be measured,

and the largest (feasible) sample size is chosen. If a stratified sampling

strategy is used, stratum sample size is calculated according to whether

proportional or disproportional representation is required.

(a) Count data. The relation used to estimate sample size is:
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 135

 

n

S

L

≅ ⋅ 



 



 4

2

If the sampled population is small, the finite population correction (fpc) is used

to correct for overestimation bias. Using fpc, the estimated sample size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

compliance estimation phase was 250, with S = 160. There are 100 days in

the season (N = 100). Suppose we want to be 95 percent certain that results

will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated

number of sampling days is 

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( ) = 86.

If the precision

is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these

are too large or too close to the entire season of 100 days to be of practical use

due to the large underlying variance. A more reasonable level of precision

would be ± 30 percent (or ± 75 visitors per day), which would call for a sample

size of n = 15.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n

p p

L = 42 1 ⋅( ) ⋅ − ( ) 2

2

which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users, (p) = 24/

40 = 0.60, and the standard error is p pn ( ) 1 0 60 0 40 40 − / . ./ = ( )( ) = 0.0775.

The 95 percent confidence interval based on these data is approximately 0.6

± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.
136 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS n ii ii [ ] ⋅ ⋅ / . ∑( ) ⋅ Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—weekend

days and weekdays. This stratification strategy separates out time periods

according to relative intensity of use, with the heaviest and most variable use

occurring on weekends, and relatively light and uniform use on weekdays.

For a 100-day season, there are about 72 weekdays and 28 weekend days.

Suppose the available resources (budget, labor, time) dictated that the

maximum number of days that could be sampled was n = 25. The initial value

for the standard deviation for each stratum was estimated from the data

obtained during the permit compliance rate estimation phase. Sample sizes

for each time block are calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(n1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(n2 = 72)

aStandard deviation.

bSampling proportion.

c

Sample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system include individual or group visit counts. Data may be expressed in terms of:

(a) the rate (for example, number of visitors per day), (b) the total (for example,

number of visitors for the season), (c) use by category (for example, cooking

method), (d) use description (for example, length of stay), or (e) summary-use

statistics (for example, recreation visitor days).

(a) Rate of use. Suppose the number of visitors with permits for a 30 day

time period was 772. A survey of 50 visitors showed that 46 had permits for

a compliance rate of 46/50 =0.92.The estimated number of users over the

30 day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28

users per day. The estimated confidence interval for the 30 day rate is
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 137

839 ± 

2 772 50 50 46 46 2 3 ⋅ ⋅⋅ − ( )/ = 839 ± 70 = (769, 909), which converts to a

confidence interval for the daily rate of (25.6, 30.3).

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.

Example. On the permit form 2,975 visitors indicated their method of

cooking during their visit: stoves, wood fires, or neither. Results with a 95

percent confidence interval (using χ2 procedure based on 2 degrees of

freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95 percent confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ± 0.019

= (0.731 to 0.769);

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95 percent confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ± 0.018

= (0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95 percent confidence interval = 0.05 ±

 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ± 0.009

= (0.04 to 0.06).

(d) Use description. One variable that may be obtained by permits is

length of stay. Post stratification may also be of interest.

Example. A sample of 38 permits had an average length of stay of 2.4

nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).

(e) Summary-use statistics. The recreation visitor-day is defined as 12

hours of a given recreation activity performed by the associated proportion

of visitors. It is calculated as the product of the number of activity occasions

and the average amount of time spent in that activity, divided by 12.

Example. The number of permits issued for a given season was 6,750, of

which 1,232 were horse users. For horse users, there were 3.1 people per

group, and 5.2 horses per group; the estimated compliance rate was 95

percent. The total number of horse users was 3.1(1,232)/(0.95) = 4,020 people,

and 5.2(1,232)/(0.95) = 6,744 horses. The average duration of a wilderness

trip was 5 days, or 120 hours. Then, the number of recreation visitor-days for

horse users during the season was 4,020(120)/12 = 40,200.
138 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System H: Permit System With

Compliance Checks and

Mailback Questionnaires

System Description ________________________________________________

Permits are mandatory use-authorization forms issued by the agency. Use

information is determined by both the permit form and questionnaire format;

this system provides sufficient information to estimate summary-use statistics, as well as basic visit counts, visit and visitor characteristic data.

Compliance checks are required for accurate estimation of total use. Mailback

questionnaires provide supplementary information on complex nonobservable

visit characteristics. Mail surveys are much less expensive to implement

than face-to-face interviews, and the inherent problem of low response rate

can be surmounted to a great extent by planned followup. Because visitors

are responsible for obtaining permits, and because visitors fill out and return

questionnaires, visitor burden is relatively high.

Summary of System H:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Complex nonobservable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Use by category of user

Summary-use statistics

Data collection strategies: Permits

Sample plan for compliance checks

Sample plan for visitor selection for questionnaires

Techniques/procedures: Permit issue

Compliance checks

Mailback questionnaires

Follow-up mailing

Estimate response rates

Visitor burden: Moderate to high

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics to Measure

Use characteristics that can be obtained are limited only by the permit

format. Information obtained from permits can include the number of
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 139

individuals or groups, group size, method of travel, anticipated dates of entry

and exit, length of stay, and place of residence. Mailback questionnaires

enable the permit holder to document various trip-related observations, such

as number of encounters, travel routes and destinations, actual length of

stay, and perceptions of wilderness conditions, problems and resource

conditions, past wilderness experience, knowledge of regulations and lowimpact procedures, preferences for various management strategies, and so

forth.

Step 2: Decide on a Permit Form

Standard OMB-approved permits are available for each agency. Alternatively, customized permit formats can be used. However, OMB clearance

must be obtained before the study begins if permits are to be issued in a

revised format; this includes the addition of questions to standard permit

forms. According to federal legislation, OMB clearance is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to that Agency’s

Information Systems office in Washington, DC, which forwards the application to the Department of Agriculture, and from there to OMB for final

approval. The time from initial submission to final OMB clearance is usually

about 3 months. Clearance is not required if shortened versions of the

standard permit with fewer questions are used.

Step 3: Establish a Permit-Issue Procedure

The procedure for issuing permits will be determined by (1) the reason for

issuing permits, and (2) the source of issue.

1. Reasons for Permit Issue.—Permits are issued to (a) provide a means of

public contact, (b) restrict use or categories of user, and (c) monitor use.

(a) Public contact. If the objective in issuing permits is to create

opportunities for public contact, visitors will be required to obtain permits in

person at a centralized agency facility, such as a visitor center or ranger

station. Visitor contact with a trained agency representative is valuable for

promoting the professional image of the agency and increasing visitor

knowledge of regulations, appropriate low-impact behaviors, potential hazards, and wilderness conditions. Visitors have the opportunity to discuss

possible routes and destinations within the wilderness area, and to obtain

other information of interest to them.

(b) Use restriction.—If the objective in issuing permits is to restrict use,

visitors will be required to obtain permits at a centralized agency facility,

such as a visitor center or ranger station. Alternatively, if adequate computer

facilities are available, permits can be issued from a number of different field

offices by means of a computerized reservation system so that the number of

permits available at any time can be tracked.

(c) Use monitoring.—If permits are issued with the objective of collecting accurate visitor use data, there are no associated restrictions on where

or how permits are issued. Permits may be issued by the agency or selfissued; numbers may be limited or unlimited.
140 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

2. Source of Permit Issue.—Permits are usually issued by agency personnel, but may be self-issued, or distributed through a cooperative arrangement with local vendors. In the majority of cases, permits are issued from a

central location by the managing agency. Staff at local ranger stations,

information centers, or National Forest offices are responsible for issuing

permits. Occasionally, permits may be reserved; reservations may be made

by telephone or mail, or in other cases must be made in person if “no-shows”

are a problem. Reserved permits may be mailed, or held until picked up by

the visitor.

Self-issued permits are usually obtained from some convenient location. If

permits are unlimited, they may be obtained from a station located outside

the agency office or at trailheads, or from alternative locations, such as local

businesses. However, if permit numbers are limited, they must be obtained

from a central location.

If there are restrictions on certain types of user, permit-issue locations

may be placed so as to accommodate different user groups. For example, if

overnight use of a wilderness area must be rationed but day use is essentially

unrestricted, a limited number of overnight permits is made available at

some central location, whereas self-issued day-use permits are located at

trailheads.

Permits may be issued through cooperative arrangements with local

vendors or businesses. Wilderness permits may be issued by convenience

stores, bait shops, commercial outfitters, travel information centers, or

nearby campgrounds.

Step 4: Develop the Mailback Questionnaire

To be effective, a questionnaire must (1) enable managers to find out what

they want to know, (2) encourage respondents to answer, and (3) minimize

respondent burden.

There are four major steps involved in the design of an effective questionnaire: (1) question development, (2) format, (3) mailing, and (4) followup

(Dillman 1978). When in the development stages of this system, the manager

is strongly encouraged to have the questionnaire and methodology reviewed

by a social scientist from a university or the agency.

1. Question Development.—The questions asked of the visitor will be

dictated by the study objectives; that is, on the basis of what the manager

wants to know and why. Questions should be easily understood by the visitor,

they should not be too long, and there should not be too many of them. The

major principle in question development is the necessity to keep visitor

burden to a minimum. Ask only the questions necessary to meet the study

objectives, and no more.

The questions asked of the respondents will depend on what kind of

information is required to meet the study objectives. Questions can be

categorized on the basis of one or more of the following types of information:

• Attitudes: what people say they want or how they feel about something;

• Beliefs: what people think is true or false;

• Behavior: what people do;

• Attributes: what people are (personal or demographic features).

Questions must be clearly identified according to information type, otherwise responses will lead to a different type of information than that required

by the study objectives.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 141

The question designer is rarely a good judge of the clarity of the questions

(Ackoff 1953). Preliminary field tests are invaluable for identifying problems,

and should be conducted before the actual field surveys begin. Colleagues,

potential “users” of the data, and, if possible, a small pretest sample of

prospective respondents should fill out the questionnaire; a debriefing

session should follow to identify problems. If some inadequacy or ambiguity

becomes apparent with the set questions, questions may be added, but only

if they clarify the meaning and satisfy the requirements of step 1.

2. Format.—There are three factors to be considered in planning questionnaire format: (a) length, (b) question ordering, and (c) design and layout.

(a) Length. Questions should not be too long, and there should not be too

many of them. Questions must be worded so that respondents understand

them as the investigator wants them to; language should be simple and clear,

and there should not be too much information demanded in any one question.

If in doubt, the question should be broken into two or more questions.

The questionnaire should be as short as possible, without compromising

the study objectives, or resulting in incomplete information. A single-page

questionnaire is acceptable, but may be too short to be useful. The maximum

questionnaire length is approximately 12 pages (Dillman 1978).

Personnel may be tempted to add additional questions “just out of

curiosity”; this cannot be justified in any circumstances. Do not add questions

merely to fill up space on the questionnaire sheet.

(b) Question ordering. Questions are presented in order from simple to

complex; this is the so-called “funnel” format. Question order improves data

quality by encouraging respondents to answer because both resistance to

answering and the perceived effort involved are lessened. Once a commitment is made to answer a few questions, there is an increased likelihood that

the survey will be completed.

The questionnaire is introduced with a paragraph outlining the central

topic, the interest and importance of the topic, and its interest and relevance

to the respondent. The first few questions are the most important, as they will

determine whether the questionnaire is completed or thrown in the garbage.

The first few questions get the survey started by setting the pace and manner

of the survey, and encouraging respondents to answer. In general, initial

questions should be (1) relevant and interesting, (2) easy to answer, and (3)

applicable to all potential visitors. The first question should obviously be

related to the topic, and have socially useful implications. The questions

should be easy to answer, taking only a few seconds to understand and

answer. Therefore, long, complex and open-ended questions, and statements

requiring the respondent to express an attitude or opinion, should be

avoided. The questions should have wide applicability. Questions that

involve a category of “does not apply” or “don’t know” suggest to the

respondent that the rest of the questionnaire is equally irrelevant; this is a

major contributor to nonresponse. Simple, easy-to-answer questions include

questions about wilderness travel routes and destinations, activities participated in, group size and composition, number of other users encountered and

where, length of visit, and so on.

Subsequent questions are ordered in descending importance with respect

to the topic; topical questions are asked before questions related to personal

characteristics. Questions should be ordered so that they follow a logical

sequence. More complex questions will require some thought or judgment on
142 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

the part of the respondent; complex questions are formulated to attain

information on visitor perceptions, judgments, opinions, or attitudes. Examples are the relative importance of various aspects of the wilderness trip

in achieving “quality” wilderness experiences, attitudes toward management strategies intended to reduce visitor impact, and the acceptability of

various levels of social or resource condition impacts. Personal or confidential

questions should be placed last; these include extent of past wilderness

experience, knowledge of low-impact procedures, income and education

levels.

(c) Design and layout. Response rates are greatly affected by the details

of questionnaire design and layout. Questionnaires should be attractive,

easy to read, and look easy to do, so that respondents are motivated to

complete them. The overall design must prevent respondents from missing

or overlooking questions or whole sections.

The following design guidelines are from Dillman (1978).

• Booklet format. The questionnaire should be printed as a booklet, with

approximate dimensions of 6" x 8". If each page is typed using 12-point font

on standard 8.5" x 11" paper with 3⁄4" margins, reduction by 79 percent will

fit booklet format. The questionnaire booklet is reproduced on white or offwhite paper using good-quality printing methods; if pages are printed on

both sides, sixteen pound paper is recommended.

• Cover design. Questionnaire covers determine the overall first impression of the study, and significantly influence response rates. The front cover

must include (a) a study title, (b) a graphic illustration, (c) any needed

directions, (d) the name, address and logo of the sponsoring agency, and (e)

the identification number. The title should give an informative and accurate

impression of the study topic, make the questionnaire sound interesting, and

should be neutral (that is, it should not sound threatening or imply bias). The

illustration adds interest; it should be simple and representative of the topic.

The address of the study sponsor is important as backup information in case

respondents lose return envelopes. The name of the researcher is not

included in the address; the legitimacy of the study is endorsed by the

backing of the sponsoring agency, not by some unknown individual. The back

cover consists of a request for additional comments, and a statement of

thanks. The back cover should never include questions; because questions

are ordered, the questions that would appear there are most likely to be found

objectionable by respondents, and the probability of nonresponse is greatly

increased.

The questionnaire is identified with a stamped individual identification

number; this number corresponds to the number assigned to each recipient

on the mailing list. In general, the ID number should be placed in the upper

right-hand corner of the front cover.

• Lettering. Distinguish questions from answers by using lower-case

letters for questions and UPPER-CASE LETTERS FOR POSSIBLE

ANSWERS.

• Make questions fit the page. Questions should not continue onto the

next page. Manipulate spacing (margins, line spacing), or rearrange question

order. However, large blank spaces should be avoided.

• Identification of answer categories. Assign a number for each

answer category; this provides a convenient method of coding answers for

subsequent computer processing. Place numbers to the left of the answer
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 143

category; this minimizes the possibility of the respondent indicating answers

other than the one intended.

• Vertical flow. Arrange answer categories and associated numbers

vertically on the page, not across the page. Vertical flow prevents the

respondent from inadvertently missing questions or sections of the questionnaire, and prevents the respondent from indicating answers other than the

one intended. The considerable spacing involved with this format gives the

impression that the questionnaire is easy to complete; a densely worded

format appears difficult.

• Instructions for answering. Specific instructions must be provided

on (a) how to provide answers (for example, “Circle number of your answer”)

and (b) how to skip screen questions. Screen questions direct a certain subset

of respondents to skip one or more questions, depending on the answer given.

Respondents can be directed by arrows to the appropriate sections of the

questionnaire.

3. Mailing the Questionnaire.—Besides the questionnaire, the two components to the mailout package include: (a) the cover letter, and (b) the

mailback, or return, envelope.

(a) The cover letter. The cover letter introduces the study to the

respondent. The first paragraph explains what the study is about, convinces

the respondent that the study is useful, and motivates the respondent to fill

out the questionnaire and return it. The study will be perceived as useful if

it is seen to meet the needs of a certain group; however, it is essential that no

bias in the researcher’s motives is apparent. The second paragraph is

designed to convince the respondent that the individual’s response is important to the success of the study. The specific individual who is to complete the

questionnaire should be clearly identified at this point. The third paragraph

is a guarantee of confidentiality. The fourth paragraph repeats the social

usefulness of the study, and contains a promise of action; for example, a copy

of the results (if requested by the respondent), an expression of willingness

to answer questions pertaining to the study (provide a telephone number and

address). Finally, the letter concludes with a statement of thanks, a closing

statement, and the sender’s name and title.

The cover letter should not exceed one page and should be printed on

agency letterhead. It should contain the date of mailing, the name, address

and telephone number of the person sending the questionnaire, and agency

affiliation. The signature should be handwritten.

(b) Return envelope. A postage-paid, pre-addressed return envelope

must be included in the questionnaire package; response rates are significantly lower if return envelopes are not provided. Business reply envelopes

should be used to avoid the use (and potential loss) of postage stamps.

4. Followup. Followup mailings are crucial for ensuring adequate response rates; without followup mailings, response rates will be less than half

of those attained by using a comprehensive followup system (Dillman 1978).

The followup procedure consists of three carefully timed mailings after the

original mailout:

(a) One week: A postcard reminder is sent to everyone. It serves as a

thank-you and acknowledgement for respondents, and as a polite reminder

for nonrespondents.

(b) Three weeks: A second package is sent out to nonrespondents. This

package contains a shorter cover letter intended to inform the nonrespondent

that their questionnaire was not received and that the individual’s response
144 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

is important to the success of the project. A replacement questionnaire and

a postage-paid return envelope are included.

(c) Seven weeks: A final mailing, similar to the second mailing, is sent

to nonrespondents. It has been recommended that this mailing should be

sent by certified mail “to emphasize its importance” to the recipient (Dillman

1978); however, the expense is considerable. Although there is some recent

evidence that certified mailings result in a substantial increase in response

rates, at least one study found that additional responses obtained by this

method had no influence on results.

Step 5: Develop Sampling Plan for Survey

When permit access is strictly regulated, permit compliance is usually very

high (over 95 percent). In this case, the entire sample population is known (in

other words, all permit holders for a given time period), and the devising of

a sampling plan is relatively simple; visitors to be surveyed are randomly

selected from the permit numbers on file (see part I, chapter 3). To increase

representation by locality, samples may be stratified by location.

Determination of the appropriate sample size (that is, the total number of

questionnaires to be issued) requires a preliminary estimate of the expected

variability in the response characteristics of interest. Preliminary estimates

are obtained from a pilot study or from data collected in previous years. A

rule-of-thumb estimate for the standard deviation is based on one-quarter of

the likely range (or minimum and maximum values) of the observations (see

part I, chapter 2). If several sample size estimates are available for different

observations, the largest calculated sample size should be used.

Step 6: Purchase Equipment and Supplies

If permits are self-issued, permit stations need to be constructed. These

stations should be both attractive and functional. Self-issue permit stations

should be designed to provide (1) a place for supplies (pencils and permit

forms), (2) a convenient, solid writing surface for the visitor to use when

completing the permit, and (3) a place to deposit completed agency copy

(normally a slot at the front). Stations may be constructed of wood or metal,

and should be set on a post at a convenient height. An attractive and easyto-read sign should be posted with instructions detailing (1) why a permit is

required, (2) who is to obtain a permit (one person or everyone in the group),

(3) where to deposit the completed agency copy, and (d) the consequences of

being found in violation.

Additional costs are associated with the printing and mailing of questionnaires. Both printing and mailing costs are influenced by questionnaire

length, the number of booklets required, stationary type and weight, method

of mail delivery, and the use of repeated mail followups.

Step 7: Obtain Mailback Responses

A well-organized system must be developed to handle questionnaire

returns. Returns must be individually coded so that the identification

number matches that on the original questionnaire; this enables returns to

be documented so that respondents who have completed questionnaires and

those requiring followup mailings can be managed accordingly. As returns

come in, they should be examined for problems which may result in missing

data (such as sticking pages, unclear directions, and so forth). The researcher
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 145

must be prepared to handle undelivered questionnaires, and answer respondent inquiries.

Step 8: Estimate Response Rates, Compliance Rates, and Use

There are four steps in the estimation procedure: (1) estimating permit

compliance rates, (2) estimating questionnaire response rates, (3) estimating

sample sizes, and (4) estimating total use.

Estimates of permit compliance are required to determine the relationship

between the number of visitors who are in compliance with respect to the

total number of visitors actually entering the wilderness area. The total

number of visitors entering a wilderness area is estimated from the relationship between the number of permits issued, (N), and the rate of permit

compliance, (r).

Visitor use data are collected from information provided on the submitted

permit form; the collection, entry, and processing of data are therefore time

intensive and relatively expensive. Consequently, sample sizes should be

specified for each use characteristic to be evaluated categorically. Preliminary estimates of the required statistics (for example, standard deviation)

can be obtained from observations made during the permit compliance

estimation phase.

Use data are collected in accordance with the appropriate sample size and

the sampling strategy. Information obtained from permits should be sufficient for obtaining data on observable and nonobservable categories of

visitor. The number of visitors per category is expressed as a proportion or

percentage of the total number of users. However, if sample sizes are very

small, proportion data are useless for evaluation purposes. Individual and

group visit count data may be expressed as a rate (for example, number of

visitors per day), or total (for example, number of visitors for the season). In

general, totals are estimated by multiplying the “corrected” average daily

rate by the number of days in the time period of interest.

1. Estimate Permit Compliance Rates.—Permit compliance rate is estimated as the ratio of the number of permit holders (determined by the total

number of permits collected) to the total number of visitors (determined from

observer counts) during the sample observation periods.

Example. A total of 575 visitors obtained permits during the 7-day permit

compliance rate estimation phase. A random sample of n = 50 visitors

indicated that 10 did not obtain permits. Therefore, the estimated permit

compliance rate (r) was estimated as 40/50 = 0.8, or 80 percent. The total

number of users (N) for a given period is estimated by the total number of

permit holding visitors (t) divided by the permit compliance rate:

 ˆ

N tr = / = 575/0.8 = 719

 The 95 percent confidence interval for the total is estimated by N ± 2·SE =

719 ±

 

2 575 50 50 40 40 2 3 [ ] ( ) ⋅ − ( ) /( ) = 719 ± 102, or between 617 and 821 visitors.

2. Response Rates.—There are several methods of calculating questionnaire response rates, (R). The first method is the ratio of questionnaires

returned to those sent out, or
146 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

 

R number returned

number sent out

= × 100

However, if there is a certain proportion of ineligible respondents, or

potential respondents who could not be contacted, the formula must be

modified as follows:

 

R number returned

number sent out non eligible non reachable

= ×

( ) – ( - + - )

 100

(Dillman 1978).

Example. Questionnaires were sent to 200 visitors randomly selected

from permits issued for a given season. A total of 156 questionnaires were

returned. Ten contacts were ineligible and 14 could not be contacted (questionnaires were not forwarded or returned). The response rate is:

 

R = − +×

156

200 10 14 ( )

 100 = 88.6%

3. Sample Size Estimation.—Because visitor count data are collected by

counting permits, there may be insufficient resources available to cover the

costs and time involved in the collection, input, and processing of large

amounts of data. Sample sizes for categorical data should be specified first.

Sample sizes should be estimated for each use characteristic to be measured,

and the largest (feasible) sample size is chosen. If a stratified sampling

strategy is used, stratum sample size is calculated according to whether

proportional or disproportional representation is required.

(a) Count data. The relation used to estimate sample size is:

 

n

S

L

≅ ⋅ 



 



 4

2

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. The average number of visitors observed per day during the

compliance estimation phase was 250, with S = 160. There are 100 days in

the season (N = 100). Suppose we want to be 95 percent certain that results

will have a precision of ± 5 percent, or ± 13 visitors/day. The estimated
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 147

number of sampling days is

 

≈

+

+

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( ) = 86. If the precision

is adjusted to ± 10 percent (or ± 25 visitors per day), then n = 62. Both of these

are too large or too close to the entire season of 100 days to be of practical use

due to the large underlying variance. A more reasonable level of precision

would be ± 30 percent (or ± 75 visitors per day) which would call for a sample

size of n = 15.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n

p p

L = 42 1 ⋅( ) ⋅ − ( ) 2

2

 which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users, p = 24/

40 = 0.60, and the standard error is p pn ( ) 1 0 60 0 40 40 − / . ./ = ( )( ) = 0.0775.

The 95 percent confidence interval based on these data is approximately 0.6

± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS n ii ii [ ] ⋅ ⋅ / . ∑( ) ⋅ Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—

weekend days and weekdays. This stratification strategy separates out time

periods according to relative intensity of use, with the heaviest and most

variable use occurring on weekends, and relatively light and uniform use on

weekdays. For a 100-day season, there are about 72 weekdays and 28

weekend days. Suppose the available resources (budget, labor, time) dictated

that the maximum number of days that could be sampled was n = 25. The

initial value for the standard deviation for each stratum was estimated from
148 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

the data obtained during the permit compliance rate estimation phase.

Sample sizes for each time block are calculated as follows:

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(n1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(n2 = 72)

aStandard deviation.

bSampling proportion.

cSample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms

of: (a) the rate (for example, number of visitors per day), (b) the total (for example,

number of visitors for the season), (c) use by category (for example, cooking

method), (d) use description (for example, length of stay), or (e) summary-use

statistics (for example, recreation visitor days).

(a) Rate of use. Suppose the number of visitors with permits for a 30 day

time period was 772. A survey of 50 visitors showed that 46 had permits for

a compliance rate of 46/50 = 0.92.The estimated number of users over the 30

day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users

per day. The estimated confidence interval for the 30 day rate is 839 ±

 

2 772 50 50 46 46 2 3 ⋅ ⋅⋅ − ( )/ = 839 ± 70 = (769, 909), which converts to a

confidence interval for the daily rate of (25.6, 30.3).

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.

Example. On the permit form 2,975 visitors indicated their method of

cooking during their visit: stoves, wood fires, or neither. Results with a 95

percent confidence interval (using χ2 procedure based on 2 degrees of

freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95 percent confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ± 0.019

= (0.731 to 0.769);
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 149

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95 percent confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ± 0.018

= (0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95 percent confidence interval = 0.05 ± 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ± 0.009

= (0.04 to 0.06).

(d) Use description. One variable that may be obtained by permits is

length of stay. Post stratification may also be of interest.

Example. A sample of 38 permits had an average length of stay of 2.4

nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).

(e) Summary-use statistics. The recreation visitor-day is defined as 12

hours of a given recreation activity performed by the associated proportion

of visitors. It is calculated as the product of the number of activity occasions

and the average amount of time spent in that activity, divided by 12.

Example. The number of permits issued for a given season was 6,750, of

which 1,232 were horse users. For horse users, there were 3.1 people per

group, and 5.2 horses per group; the estimated compliance rate was 95

percent. The total number of horse users was 3.1(1,232)/(0.95) = 4,020 people,

and 5.2(1,232)/(0.95) = 6,744 horses. The average duration of a wilderness

trip was 5 days, or 120 hours. Then, the number of recreation visitor-days for

horse users during the season was 4,020(120)/12 = 40,200.

In 1980, permit systems were in use in 69 wilderness

areas. Of these areas, 17 limited use and 52 did not.
150 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System I: Indirect Counts

System Description ________________________________________________

With this system, various measures of use are estimated from one or more

surrogate measures of use, referred to as predictor variables. Predictors are

easier to obtain than measures of direct use, and entail less burden on

wilderness visitors. The relationship between the predictor(s) and the use

measure is quantified; once this relationship is established, it is only

necessary to monitor the predictor to obtain an estimate of the given use

characteristic. Indirect measurements can be used to predict counts and

summary-use characteristics. Relationships may be valid over several seasons; however, periodic checks should be scheduled to ensure the continued

validity of the predictive relationship. Visitor burden should decline once the

predictive relationship is established.

Summary of System I:

Type of observations: Counts

Observable use characteristics

Simple nonobservable characteristics

 (sometimes)

Measures of visitor use: Number of individual visits

Number of group visits

Summary-use statistics

Data collection strategies: Sampling plan for counter rotation (if applicable)

• spatial

•temporal

Calibration

Techniques/procedures: Mechanical counters

Visual observations (cameras, human observers)

Miscellaneous data collection (weather data,

 trailhead maps, and so forth)

Visitor burden: Variable, declining.

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics

To date, the use characteristics most commonly evaluated by indirect

methods have been visitor counts, time involved in a given activity, and interparty encounter rates. The success of this method for predicting other types

of use characteristics is untested; estimates of nonobservable use characteristics may not be reliable.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 151

Step 2: Select the Appropriate Predictor Variable

Choice of the appropriate predictor variable is determined by several

factors: ease of measurement, predictive power, and stability (that is,

the predictive relationship should be valid for relatively long periods). The

predictor variable may be another (and easier) method of obtaining visitor

counts, such as vehicle axle counts, the number of visitor maps taken from

trailhead stations, or the campground occupancy rates. Alternatively, predictor variables may be environmental or weather factors, such as lake-water

levels, daily maximum temperature, and daily rainfall.

The predictive power of the straight-line model is estimated by the

coefficient of determination, or R2

. This is interpreted as the proportion of

observed variation in Y that can be explained by the straight-line model: the

higher the value of R2

, the better the regression model is in explaining

variation in Y. If R2

 is small, the investigator will need to search for an

alternative predictor variable or variables. Pilot studies must be conducted

to evaluate the initial suitability of potential predictor variables, and whether

the relationship between the proposed predictor variable and the use characteristic of interest is sufficiently strong to be of any use as a means of

prediction.

The stability of the model is evaluated by periodic checks over one season,

or over several years. Some predictor variables may be useful for relatively

long periods, but only if use patterns do not change significantly over time.

Step 3: Select a Direct Counting Method

Visitor counts are determined by observing visitors passing a given point

at selected times. Human observers are preferable; however, cameras may be

used if calibration procedures are strictly followed (see below). Interviews

may be used to obtain information on simple nonobservable visit characteristics. To obtain information on complex nonobservable visit characteristics,

mailback questionnaires may be sent to randomly selected visitors.

Step 4: Develop a Sampling Plan for Direct Counting

The procedure for indirect methods is similar to the calibration procedures

described for systems using mechanical counters. The value of the predictor

variable is “calibrated” by direct counts, or observations, of visitors obtained

simultaneously with measures of the indirect variable so the predictive

power of the predictor variable can be assessed for its adequacy. Once the

adequacy of the predictor is established, visitor counts can be estimated from

the predictive relationship.

The amount of effort and resources expended during this phase will depend

on the required precision of use characteristic estimates, the available

resources, and the relative stability of visitor use over time. If use patterns

change substantially over the season, the predictive relationship estimated

at the beginning of the season will not be applicable later in the season; the

accuracy of the relationship must be spot checked at intervals, and updated

as required.

Use of human observers is labor intensive and expensive, but provides

highly accurate results and greater flexibility in data acquisition. Observers

may be stationed at fixed locations, such as trailheads or campsites, or

alternatively may travel assigned trail segments. For “calibration” purposes,
152 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

the minimum information to be recorded by observers includes number of

individuals, number of groups, method of travel, direction of travel, and date

and time of entry or exit. Additional information on visit or visitor characteristics may be obtained if required by the study objectives. A sample observer

recording sheet is shown in figure 1.

Sampling plans must be developed for:

1. Scheduling rotation of observers (or counters) across trailheads.

2. Calibration of mechanical counters (if applicable).

3. Visitor selection for interviews (if applicable).

Step 5: Install Equipment for Indirect Counts (If Applicable)

If cameras or mechanical traffic counters are used for measuring the values

of the predictor variable, care must be taken in equipment installation,

maintenance, and calibration. Follow manufacturer’s directions for installation, carefully test and retest the accuracy of the counter, and frequently test

battery power and sensor function.

In general, counters should be placed some distance away from the

trailhead so that only bona fide wilderness visitors are counted, and casual

visitors (those who travel only an extremely short distance) are excluded.

However, if the wilderness boundary is an extremely long distance from the

trailhead, the increase in personnel time involved in traveling to the counter

site for reading and calibrating counters may make this option untenable. We

do not advise locating counters where the trail is unduly wide (thus allowing

visitors to travel two or more abreast, and underestimating counts), or at

natural resting places (where they may mill around and cause multiple

counts). Narrow portions of the trail at locations where traffic flow is more

or less continuous offer the best count locations.

The time required for counter installation will vary according to distance

from the trailhead and counter type. After arriving at the selected site, at

least one hour will be required for counter installation. This includes time

spent examining the site, selecting the best place for counter location,

installation of the sensor and the counting mechanism, setting counter

sensitivity or delay, and testing counter operation. If a counter is mounted on

a tree trunk (as is the case for photoelectric counters), the counter will likely

shift slightly within the first day or two as a result of tree wounding; the

counter should therefore be checked, and realigned if necessary, on the

second day after initial installation. If cameras are used, additional time is

required to address privacy concerns (the camera must be located far enough

from the trail so that individuals cannot be identified in the pictures, camera

adjusted to be slightly out of focus, and so forth).

After the equipment has been installed, observe conditions for a short time

to make certain that equipment is functioning correctly, and adjust accordingly. All equipment should be labeled with agency identification, a statement of purpose, and the name, address, and telephone number of a

designated contact person. A message explaining that the camera is for

detecting use levels, and that individual identities cannot be determined,

may reduce the risk of vandalism if visitors locate the equipment.

Step 6: Collect Direct Count Data

Direct count data are generally collected by human observers. Although

labor intensive and expensive, use of human observers provides accurate
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 153

results, and enables greater flexibility in data acquisition. Direct count data

may be obtained by observers without stopping visitors, or by observers who

stop and interview randomly selected visitors.

1. Observer Data.—It is essential that personnel are thoroughly trained in

the data collection procedures. Training ensures that observers are already

familiar with the research directives and the data collection process before

actual fieldwork begins. As a result, errors involved in the learning process

are reduced, and there will be greater consistency in identifying the sampling

units and recording responses. Training enables observers to become familiar with various contingency plans, to identify potential problems in the

research directives, and to make decisions if problems occur.

Preliminary, or pretest, fieldwork should be conducted before the actual

survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or

inadequacies in the procedures can be identified, and the consistency and

accuracy of personnel can be observed and analyzed.

Observers should be screened at intervals and their performance compared

either with each other or at different time points for the same observer;

screening provides a check on performance and identifies sources of error in

the data.

Observers may be stationed at fixed locations, such as trailheads or

campsites, or alternatively may travel assigned trail segments. If trail traffic

is low, observers may perform other tasks in the vicinity of the counter, such

as trail clearance and maintenance, visitor education, or reading; these help

pass the time and reduce observer fatigue and boredom. However, if the

observer is stationed at some distance and is observing traffic through

binoculars, it is not advisable to engage in other types of activity because of

the potential for missing visitors if attention is diverted from the trail.

Observers should be in appropriate uniform and possess necessary communication and safety equipment.

Observations must be recorded in a standardized format. The minimum

information to be recorded by observers includes number of individuals,

number of groups, method of travel, direction of travel, and date and time of

entry or exit. Additional information on visit or visitor characteristics may be

obtained if required by the study objectives. For each data sheet the observer

should record their name, the sampling location, the date, start time, the

initial counter reading, end time, and the final counter reading for that

sample period. During the sample period the observer records the number of

individuals or groups, and the time visitors pass the observation station. The

observer must be provided with sufficient data forms for the observation

period. Observers must understand the need to completely and correctly fill

out the data form; sample observations will be useless if the data collected by

the observer cannot be matched with the appropriate counter data. Observation sheets should be filed in a designated place after the observer returns to

the office.

2. Interview Data.—The interview protocol consists of five steps: (a) determining question format, (b) obtaining OMB clearance, (c) selecting and

training the interview team, (d) visitor selection, and (e) data collection.

(a) Question format. The questions asked of the visitor will be dictated

on the basis of the study objectives; that is, on the basis of what the manager

wants to know and why. Questions should be easily understood by the visitor,
154 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

they should not be too long, and there should not be too many of them. Ask

only the questions necessary to meet the study objectives, and no more. The

interview should be as short as possible to minimize visitor burden.

Personnel may be tempted to add additional questions “just out of

curiosity”; this cannot be justified in any circumstances. Do not add questions

merely to fill up space on the interview sheet. If some inadequacy or

ambiguity becomes apparent with the set questions, questions may be added,

but only if they clarify the meaning and satisfy the requirements of step 1.

The question designer is rarely a good judge of the clarity of the questions

(Ackoff 1953); preliminary field tests are invaluable for identifying problems

before the actual field surveys begin.

(b) Obtain OMB clearance. According to federal legislation, clearance

from the Office of Management and Budget (OMB) is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to that Agency’s

Information Systems office in Washington, DC, which then forwards the

application to the Department of Agriculture, and from there to OMB for

final approval. The time from initial submission to final OMB clearance is

usually about 3 months.

(c) Select and train the interview team. Careful selection and training

of the personnel who are involved in collecting data are essential if the

manager or research planner is not performing the field research. The

research planner must ensure that interviews are conducted and observations collected in the manner required by the study plan.

• Personnel selection. Both personality and ability must be evaluated in

the selection process. The importance of visitor contact extends beyond the

quality of data obtained; it is an opportunity to present the image of the

managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar

with the wilderness area and prepared to handle requests for information

about the wilderness and the surrounding area. Many of the questions from

visitors will not be related to the interview; providing information is a

courtesy which contributes to establishing rapport with the visitors and

increases visitor cooperation. Personnel should be in appropriate uniform

and possess necessary communication and safety equipment.

•Training. It is essential that personnel are thoroughly trained in the data

collection procedures. Training ensures that observers are already familiar

with the research directives and the interviewing process before actual

fieldwork begins. As a result, errors involved in the learning process are

reduced, and there will be greater consistency in identifying the sampling

units (in this case visitors to be interviewed) and recording responses.

Training enables observers to become familiar with various contingency

plans, to identify potential problems in the research directives, and to make

decisions if problems occur.

Preliminary, or pretest, fieldwork should be conducted before the actual

survey begins. These rehearsals ensure that personnel understand procedures, and serve as a test for the efficiency of the methods; problems or

inadequacies in the procedures can be identified and eliminated, and the

consistency and accuracy of personnel can be observed and analyzed. Observers should be screened at intervals and their performance compared either
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 155

with each other or at different time points for the same observer; screening

provides a check on performance and identifies sources of error in the data.

(d) Visitor selection. Visitors are selected in accordance with the predetermined sampling plan (step 4). The location of interviews will be determined by study objectives; visitors may be interviewed upon either entry or

exit, or both. For example, if the emphasis of the study is on the effects of

group size or place of residence on wilderness use, these factors are unaffected by interview location. However, if the study objectives require information on patterns of visitor use within the wilderness area (for example,

travel or camping locations, length of stay), visitors should be interviewed as

they leave.

(e) Data collection. When interviewing visitors, personnel should begin

with a standard introduction. Personnel should give their name and agency

affiliation and the reason for the interview. For example, “Hello, I am

Marilyn Holgate. I work for the Missoula District of the Lolo National Forest.

We are trying to learn more about the use of the Rattlesnake Wilderness. It

will help us with management of the area. May I ask you a few questions

about your visit today?” After the interview, thank visitors for their time.

Responses should be recorded as they are given; interviewers should not

rely on memory to fill in the interview sheet at a later time. Make sure every

item is complete and legible; data forms must include date, time, location,

and interviewer’s name. Completed data forms should be filed in a safe place

in a central location.

Step 7: Collect Predictor Variable Data

Methods of data collection will depend on the type of predictor variable.

Count data may be logged by mechanical counters or obtained by visual

observations (either cameras or human observers). Alternative types of

predictor variables, such as environmental factors, are collected by the most

appropriate means (see below). Predictor data must be collected either

simultaneously or for the same sampling period as direct count data.

1. Counter Data.—Counts logged by the mechanical counter are recorded

at intervals determined by the appropriate sampling plan. If counters are

permanently allocated to a given location, the frequency of recording will be

determined by the calibration sampling plan. At a minimum, counts should

be recorded at least twice per month to ensure that data are not lost because

of equipment malfunction. The person obtaining count readings should check

battery power and equipment operation, and for any changes in the surrounding area which may affect count accuracy.

2. Cameras.—Record necessary observations from the developed film.

Observations must be recorded in a standardized format to minimize errors

in recording. Observations include location, date, number of individuals,

number of groups, date and time of entry or exit. Observers must understand

the need to completely and correctly fill out the data form; sample observations will be useless if the data collected by the observer cannot be matched

with the appropriate registration data. Observation sheets should be filed in

a designated place. After observations are recorded, destroy negatives and

developed photos to ensure visitor privacy.

3. Observers.—Observers should be stationed close enough to the registration station so that all traffic passing the station is accounted for; however,

they do not need to observe whether or not visitors actually register.
156 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Although observers need not be beside the registration station, they should

not wander up and down the trail. Observers do not stop visitors.

Observations are recorded on a standardized form (fig. 1). Observations

include observer name, location, date, number of individuals, number of

groups, date and time of entry or exit. Observers must understand the need

to completely and correctly fill out the data form; sample observations will be

useless if the data collected by the observer cannot be matched with the

appropriate registration data. All deposited registration forms are collected

and labeled at the end of the observation period. Observation sheets and

registration cards should be filed in a designated place.

4. Other.—Daily weather data for the location closest to the wilderness

area can be obtained from the National Weather Service. More accurate

information can be obtained from weather-recording equipment established

close to the site. If the quantity of trailhead literature (such as maps) is used

as a predictor, an observer must be detailed to monitor the station supplies

during time periods coinciding with those used for direct counts.

Step 8: Estimate Use

Linear regression is used to estimate the relationship between the predictor variable and the direct measure of visitor use; regression techniques are

described more fully in the appendix. Before calculating the regression

statistics, the data are plotted and examined for anomalies, such as excessive

curvature or scatter, which would invalidate the assumption of a straightline relationship. To predict use from values of the predictor variable,

calculate the regression relationship, Y B BX = +⋅ 0 1 , and the standard error

of the regression equation ( MSE ). The 95 percent confidence interval for

value of visitor count (Y) for a given car count (X) is approximately equal to

 ˆ

Y ± 2 MSE where ˆ

Y is calculated from the regression equation.

An estimate of use for the entire season is obtained by calculating the

average number of users per day, and multiplying this estimate by the total

number of days in the season.

Example. Visitor traffic at Snow Lake Trailhead in the Alpine Lakes

Wilderness was surveyed to establish the relationship between the numbers

of vehicles in the trailhead parking lot X (predictor variable X) and the

number of visitors counted 1⁄2 mile up the trail (Y). The following data are

plotted in figure 7.

Car counts (X): 10 15 18 20 21 23 25 27 32 33 60 92 105 108 132.

Visitor counts (Y): 25 30 50 55 62 65 61 48 75 67 77 150 158 100 200.

The relationship between car counts and visitor counts was:

 ˆ

Y = 26.48 + 1.145·X

with R2

 = 0.86 and MSE = 19.11.

The average number of cars in the trailhead parking lot was 45 per day.

Therefore, the daily number of visitors was estimated to be 26.48 + 1.15(45)

= 78. The 95 percent prediction interval for this estimate is 78 ± 38.22, or

between 40 and 116 visitors per day. Given a season length of 100 days, the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 157

0 

50 

100 

150 

200 

10 18 21 25 32 60 105 132

Car Counts

Snow Lake Data

Visitor Counts

Figure 7—Plot of visitor counts on car counts for

Snow Lake Trailhead.

number of users per season is estimated as 7,800, with a 95 percent confidence

interval of 4,000 to 11,600 users.
158 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

System J: General Visitor

Surveys

System Description ________________________________________________

This system entails the direct acquisition of information from visitors to the

wilderness area by either face-to-face interviews or questionnaires filled out

by the visitors. Use information is determined by the interview or questionnaire format, or both. This system can provide sufficient information to

enable estimates of summary-use statistics, as well as basic visit counts and

visit characteristic data. A random selection of visitors is contacted at

trailheads or other wilderness access points. Although visitors are contacted

directly, contact time is relatively low and visitor burden is moderate.

Summary of System J:

Type of observations: Counts

Observable characteristics

Simple nonobservable characteristics

Complex nonobservable characteristics

Measures of visitor use: Number of individual visits

Number of group visits

Use by category of user

Summary-use statistics

Data collection strategies: Sampling plan for visitor selection

Techniques/procedures: Interviews, questionnaires

Visitor burden: Moderate

Operational Procedures ____________________________________________

Step 1: Decide on Use Characteristics to Measure

Use characteristics that can be obtained are determined by the question

format. Information obtained from interviews or questionnaires can include

basic descriptions of the visit (such as travel route, length of stay, and

activities participated in), and simple visitor characteristics (such as past

wilderness experience, knowledge of low-impact behavior, preference for

alternative management strategies, and so forth). If mailback questionnaires are used, information can be obtained on complex nonobservable

characteristics pertaining to the wilderness area itself, such as visitor

attitudes and visitor preferences for conditions in wilderness.

Step 2: Decide on Survey Method

Visitors are surveyed by either interviews or questionnaires, or both.

Choice of method depends on the length and complexity of the survey, the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 159

resources available to administer the survey (personnel, time, budget, and so

forth), the demographics of the contact population, and the location of contact

(at trailheads, at locations within the wilderness, or at their place of

residence).

1. Interviews.—Directly surveying visitors by interviews is appropriate if

the survey is relatively short, questions are simple (for example, questions

relating to attributes rather than attitudes), and budgetary resources are

limited. Interviews are especially useful if the contact population is characterized by low standards of literacy, or if there is a significant proportion of

non-English-speaking visitors.

The location of interviews will be determined by study objectives; visitors

may be interviewed upon either entry or exit, or both. For example, if the

emphasis of the study is on the effects of group size or place of residence on

wilderness use, these factors are unaffected by interview location. However,

if the study objectives require information on patterns of visitor use within

the wilderness area (for example, travel or camping locations, length of stay),

visitors should be interviewed at exit points. In general, visitors should not

be interviewed within the wilderness area, especially if surveys are long,

because personnel interruptions may be perceived as an unacceptable visitor

burden. However, if onsite responses are required, interviews may be

conducted at campsites without interfering with travel plans or disturbing

the mood of the wilderness experience.

Telephone interviews are an option if only a short time is available to

complete a study. Visitors are contacted at a trailhead and asked to supply

their name, address, and telephone number; they are contacted later by

phone. However, this method is expensive (telephone charges, interviewer

time), and has a lower response rate than other survey methods.

2. Questionnaires.—Indirect surveys by means of questionnaires are

appropriate if the survey is relatively long, questions are more complex, and

budgetary resources are sufficient for implementing questionnaire development and followup procedures (see Step 3: Formulate the Survey).

Step 3: Formulate the Survey

There are three steps in formulating a survey: (1) developing appropriate

and effective questions, (2) constructing question format, and (3) obtaining

OMB clearance. If the survey is administered by questionnaire, additional

design considerations are necessary.

When in the development stages of this system, the manager is strongly

encouraged to have the survey and methodology reviewed by a social scientist

from a university or the agency.

1. Question Development.—To be effective, the survey must (a) enable

managers to find out what they want to know, (b) encourage respondents to

answer, and (c) minimize respondent burden.

The questions are asked of the visitor will be dictated by the study

objectives; that is, on the basis of what the manager wants to know and why.

Questions should be easily understood by the visitor, they should not be too

long, and there should not be too many of them. The major principle in the

development of questions is the necessity to keep visitor burden to a minimum. Ask only the questions necessary to meet the study objectives, and no

more.
160 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The specific questions asked of the respondents will depend on what kind

of information is required to meet the study objectives. Questions can be

categorized on the basis of one or more of the following types of information:

• Attitudes: what people say they want or how they feel about something;

• Beliefs: what people think is true or false;

• Behavior: what people do;

• Attributes: what people are (personal or demographic features).

Questions must be clearly identified according to information type, otherwise responses will lead to a different type of information than that required

by the study objectives.

The question developer is rarely a good judge of the clarity of the questions

(Ackoff 1953). Preliminary field tests are invaluable for identifying problems,

and should be conducted before the actual field surveys begin. Colleagues,

potential “users” of the data, and, if possible, a small pretest sample of

prospective respondents should be surveyed; a debriefing session should

follow to identify problems. If some inadequacy or ambiguity becomes

apparent with the set questions, questions may be added, but only if they

clarify the meaning and satisfy the requirements of step 1.

2. Question Format.—There are two factors to be considered in planning

survey format: (a) survey length, and (b) relative order of questions.

(a) Length. Questions should not be too long, and there should not be too

many of them. Questions must be worded so that respondents understand

them as the investigator wants them to; language should be simple and clear,

and there should not be too much information demanded in any one question.

If in doubt, the question should be broken into two or more questions.

The survey should be as short as possible, without compromising the study

objectives or resulting in incomplete information. Personnel should not ask

additional questions “just out of curiosity”. Do not add questions merely to fill

up space on the questionnaire sheet. A single-page questionnaire is acceptable, but may be too short to be useful. The maximum length for mailout

questionnaires is approximately 12 pages (Dillman 1978); self-issue questionnaires should not take longer than 10 minutes to complete.

(b) Question sequence. Questions are presented in order from simple to

complex; this is the so-called “funnel” format. Question sequence improves

data quality by encouraging respondents to answer because both resistance

to answering and the perceived effort involved are lessened. Once a commitment is made to answer a few questions, there is an increased likelihood that

the survey will be completed.

The survey is introduced with a brief outline of the central topic, the

interest and importance of the topic, and its interest and relevance to the

respondent. The first few questions are the most important, as they will

determine whether the questionnaire is completed or thrown in the garbage.

The first few questions get the survey started by setting the pace and manner

of the survey, and encouraging respondents to answer. In general, initial

questions should be (1) relevant and interesting, (2) easy to answer, and (3)

applicable to all potential visitors. The first question should obviously be

related to the topic, and have socially useful implications. The questions

should be easy to answer, taking only a few seconds to understand and

answer. Therefore, long, complex and open-ended questions, and statements

requiring the respondent to express an attitude or opinion, should be avoided.

The questions should have wide applicability. Questions that involve a
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 161

category of “does not apply” or “don’t know” suggest to the respondent that

the rest of the questionnaire is equally irrelevant; this is a major contributor

to nonresponse. Simple, easy-to-answer questions include questions about

wilderness travel routes and destinations, activities participated in, group

size and composition, number of other users encountered and where, length

of visit, and so on.

Subsequent questions are ordered in descending importance with respect

to the topic; topical questions are asked before questions related to personal

characteristics. Questions should be ordered so that they follow a logical

sequence. More complex questions will require some thought or judgment on

the part of the respondent; complex questions are formulated to attain

information on visitor perceptions, judgments, opinions, or attitudes. Examples are the relative importance of various aspects of the wilderness trip

in achieving “quality” wilderness experiences, attitudes toward management strategies intended to reduce visitor impact, and the acceptability of

various levels of social or resource condition impacts. Personal or confidential

questions should be placed last; these include extent of past wilderness

experience, knowledge of low-impact procedures, income and education

levels.

3. Obtain OMB Clearance.—According to federal legislation, clearance

from the Office of Management and Budget (OMB) is required if federal

employees ask more than nine members of the public the same set of

questions. The proposed set of questions, methodology, and study justification must be submitted to OMB through the appropriate channels. For the

Forest Service, application for clearance is submitted to Information Systems in Washington, DC, which then forwards the application to the Department of Agriculture, and from there to OMB for final approval. The time from

initial submission to final OMB clearance is usually about 3 months.

4. Additional Design Considerations for Questionnaires.—If the survey is

administered in questionnaire format, additional considerations include

design, mailing, and followup procedures (Dillman 1978).

(a) Design and layout. Response rates are greatly affected by the details

of questionnaire design and layout. Questionnaires should be attractive,

easy to read, and look easy to do, so that respondents are motivated to

complete them. The overall design must prevent respondents from missing

or overlooking questions or whole sections.

The following design guidelines are from Dillman (1978).

• Booklet format. The questionnaire should be printed as a booklet,

with approximate dimensions of 6" x 8". If each page is typed using 12-point

font on standard 8.5" x 11" paper with 3⁄4" margins, reduction by 79 percent

will fit booklet format. The questionnaire booklet is reproduced on white or

off-white paper using good-quality printing methods; if pages are printed on

both sides, sixteen pound paper is recommended.

• Cover design. Questionnaire covers determine the overall first

impression of the study, and significantly influence response rates. The front

cover must include (a) a study title, (b) a graphic illustration, (c) any needed

directions, (d) the name, address, and logo of the sponsoring agency, and (e)

the identification number. The title should give an informative and accurate

impression of the study topic, make the questionnaire sound interesting, and

should be neutral (that is, it should not sound threatening or imply bias). The

illustration adds interest; it should be simple and representative of the topic.

The address of the study sponsor is important as backup information in case
162 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

respondents lose return envelopes. The name of the researcher is not

included in the address; the legitimacy of the study is endorsed by the

backing of the sponsoring agency, not by some unknown individual. The back

cover consists of a request for additional comments, and a statement of

thanks. The back cover should never include questions; because questions

are in the aforementioned order, the questions that would appear there are

most likely to be found objectionable by respondents, and the probability of

nonresponse is greatly increased.

The questionnaire is identified with a stamped individual identification

number; this number corresponds to the number assigned to each recipient

on the mailing list. In general, the ID number should be placed in the upper

right-hand corner of the front cover.

• Lettering. Distinguish questions from answer choices by using lowercase letters for questions and UPPER-CASE LETTERS FOR POSSIBLE

ANSWERS.

• Make questions fit the page. Questions should not continue onto

the next page. Manipulate spacing (margins, line spacing), or rearrange

question order. However, large blank spaces should be avoided.

• Identification of answer categories. Assign a number for each

answer category; this provides a convenient method of coding answers for

subsequent computer processing. Place numbers to the left of the answer

category; this minimizes the possibility of the respondent indicating answers

other than the one intended.

• Vertical flow. Arrange answer categories and associated numbers

vertically on the page, not across the page. Vertical flow prevents the

respondent from inadvertently missing questions or sections of the questionnaire, and prevents the respondent indicating answers other than the one

intended. The considerable spacing involved with this format gives the

impression that the questionnaire is easy to complete; a densely worded

format appears difficult.

• Instructions for answering. Specific instructions must be provided

on (a) how to provide answers (for example, “Circle number of your answer”)

and (b) how to skip screen questions. Screen questions direct a certain subset

of respondents to skip one or more questions, depending on the answer given.

Respondents can be directed by arrows to the appropriate sections of the

questionnaire.

(b) Mailing the questionnaire. Besides the questionnaire, the two components to the mailout package include: the cover letter, and the mailback,

or return, envelope.

• The cover letter. The cover letter introduces the study to the respondent. The first paragraph explains what the study is about, convinces the

respondent that the study is useful, and motivates the respondent to fill out

the questionnaire and return it. The study will be perceived as useful if it is

seen to meet the needs of a certain group; however, it is essential that no bias

in the researcher’s motives is apparent. The second paragraph is designed to

convince the respondent that the individual’s response is important to the

success of the study. The specific individual who is to complete the questionnaire should be clearly identified at this point. The third paragraph is a

guarantee of confidentiality. The fourth paragraph repeats the social usefulness of the study, and contains a promise of action; for example, a copy of the

results (if requested by the respondent), an expression of willingness to

answer questions pertaining to the study (provide a telephone number and
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 163

address). Finally, the letter concludes with a statement of thanks, a closing

statement, and the sender’s name and title.

The cover letter should not exceed one page and should be printed on

agency letterhead. It should contain the date of mailing, the name, address

and telephone number of the person sending the questionnaire, and agency

affiliation. The signature should be handwritten.

• Return envelope. A postage-paid, pre-addressed return envelope must

be included in the questionnaire package; response rates are significantly

lower if return envelopes are not provided. Business reply envelopes should

be used to avoid the use (and potential loss) of postage stamps.

(c) Followup. Followup mailings are crucial for ensuring adequate

response rates; without followup mailings, response rates will be less than

half of those attained by using a comprehensive followup system (Dillman

1978). The followup procedure consists of three carefully timed mailings

after the original mailout:

One week: A postcard reminder is sent to everyone. It serves as a thankyou and acknowledgment for respondents, and as a polite reminder for

nonrespondents.

Three weeks: A second package is sent out to nonrespondents. This

package contains a shorter cover letter intended to inform the nonrespondent

that their questionnaire was not received, and that everyone’s response is

important to the success of the project. A replacement questionnaire and a

postage-paid return envelope are also included.

Seven weeks: A final mailing, similar to the second mailing, is sent to

nonrespondents. It has been recommended that this mailing should be sent

by certified mail “to emphasize its importance” to the recipient (Dillman

1978). However, the expense is considerable; although there is some evidence

that certified mailings result in a substantial increase in response rates,

there is at least one study which found that additional responses had no

influence on the results of the study.

Step 4: Select and Train the Interview Team

Careful selection and training of the personnel who are involved in

collecting data are essential if the manager or research planner is not

performing the field research. The research planner must ensure that

interviews are conducted and observations collected in the manner required

by the study plan.

1. Personnel Selection.—Both personality and ability must be evaluated

in the selection process. The importance of visitor contact extends beyond the

quality of data obtained; it is an opportunity to present the image of the

managing agency. Select an interviewer who is friendly, reliable, knowledgeable, and trained in emergency procedures. Personnel should be familiar

with the wilderness area and be prepared to handle requests for information

about the wilderness and the surrounding area. Many of the questions from

visitors will not be related to the interview; providing information is a

courtesy which contributes to establishing rapport with the visitors and

increases visitor cooperation. Personnel should be in appropriate uniform

and possess necessary communication and safety equipment.

2. Training.—It is essential that personnel are thoroughly trained in the

data collection procedures. Training ensures that observers are already

familiar with the research directives and the interviewing process before
164 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

actual fieldwork begins. As a result, errors involved in the learning process

are reduced, and there will be greater consistency in identifying the sampling

units (in this case visitors to be interviewed) and recording responses.

Training enables observers to become familiar with various contingency

plans, to identify potential problems in the research directives, and to make

decisions if problems occur.

Preliminary, or pretest fieldwork should be conducted before the actual

survey begins. Rehearsals ensure that personnel understand procedures,

and serve as a test for the efficiency of the methods; problems or inadequacies

in the procedures can be identified and eliminated, and the consistency and

accuracy of personnel can be observed and analyzed. Observers should be

screened at intervals and their performance compared either with each other

or at different time points for the same observer; screening provides a check

on performance and identifies sources of error in the data.

Step 5: Develop a Sampling Plan

Sampling plans must be developed for:

1. Scheduling rotation of the interview teams across trailheads.

2. Scheduling interview periods.

3. Selecting visitors to be interviewed.

Step 6: Purchase Supplies

Supply costs are associated with the printing of survey forms, and the

printing and mailing of questionnaires. Both printing and mailing costs are

influenced by survey length, the number of surveys required, stationary type

and weight, and, when applicable, the method of mail delivery, and the use

of repeated mail followups.

Step 7: Collect Interview or Questionnaire Data

Survey data are collected by trained personnel in accordance with a specific

plan (as described in step 5). The interview protocol consists of (a) visitor

selection, and (b) data collection. The interviewer must be provided with

sufficient research material—data forms, writing tools, schedules, and so

forth—for the survey period. Interviewers must understand the need to

completely and correctly fill out the data forms. Interview sheets should be

filed in a designated place after the interviewer returns to the office.

(a) Visitor selection. Visitors are selected in accordance with the predetermined sampling plan (step 5). The location of interviews will be determined by study objectives; visitors may be interviewed upon either entry or

exit, or both. For example, if the emphasis of the study is on the effects of

group size or place of residence on wilderness use, these factors are unaffected by interview location. However, if the study objectives require information on patterns of visitor use within the wilderness area (for example,

travel or camping locations, length of stay), visitors should be interviewed as

they leave. Visitors should not be interviewed inside the wilderness boundary (to avoid threats to the visitor experience from management presence).

(b) Data collection. When encountering and interviewing visitors, personnel should begin with a standard introduction. Personnel should give

their name and agency affiliation and the reason for the interview. For
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 165

example, “Hello, I am Marilyn Holgate. I work for the Missoula District of the

Lolo National Forest. We are trying to learn more about the use of the

Rattlesnake Wilderness. It will help us with management of the area. May

I ask you a few questions about your visit today?” After the interview, thank

visitors for their time. Personnel may be tempted to add additional questions

“just out of curiosity”; this cannot be justified in any circumstances.

Responses should be recorded as they are given; interviewers should not

rely on memory to fill in the interview sheet at a later time. Make sure every

item is complete and legible; data forms must include date, time, location,

and interviewer’s name. Completed data forms should be filed in a safe place.

Step 8: Obtain Mailback Responses

A well-organized system must be developed to handle questionnaire

returns. Returns must be individually coded so that the identification

number matches that on the original questionnaire; this enables returns to

be documented so that respondents who have completed questionnaires and

those requiring followup mailings can be managed accordingly. As returns

come in, they should be examined for problems which may result in missing

data (such as sticking pages, unclear directions, and so forth). The researcher

must be prepared to handle undelivered questionnaires, and answer respondent inquiries.

Step 9: Estimate Use

There are three steps in the estimation procedure: (1) estimating survey

response rates, (2) estimating sample sizes, and (3) estimating total use.

Visitor use data are collected from information provided on the survey

forms; the collection, entry, and processing of data are therefore time

intensive and relatively expensive. Consequently, sample sizes should be

specified for each use characteristic to be evaluated categorically. Preliminary estimates of the required statistics (for example, standard deviation)

can be obtained from observations made during a pilot study or similar

studies conducted elsewhere.

Use data are collected in accordance with the appropriate sample size and

the sampling strategy. Estimates of survey response rates are required to

determine the relationship between the number of visitors who are interviewed with respect to the total number of visitors actually entering the

wilderness area. The total number of visitors entering a wilderness area is

estimated from the relationship between the total number of visitors, (N),

and the rate of survey response, (r). Information obtained from survey forms

should be sufficient for obtaining data on observable and nonobservable

categories of visitor. The number of visitors per category is expressed as a

proportion or percentage of the total number of users.

1. Response Rates.—There are several methods of calculating questionnaire response rates, (R). The first method is the ratio of questionnaires

returned to those sent out, or

 

R = × number returned

number sent out 100
166 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

However, if there is a certain proportion of ineligible respondents, or

potential respondents who could not be contacted, the formula must be

modified as follows:

(Dillman 1978).

Example. Questionnaires were sent to 200 visitors randomly selected

from permits issued for a given season. A total of 156 questionnaires were

returned. Ten contacts were ineligible and 14 could not be contacted (questionnaires were not forwarded or returned). The response rate is:

2. Sample Size Estimation.—Sample sizes for categorical data should be

specified first. Sample sizes should be estimated for each use characteristic

to be measured, and the largest (feasible) sample size is chosen. If a stratified

sampling strategy is used, stratum sample size is calculated according to

whether proportional or disproportional representation is required.

(a) Continuous data. The relation used to estimate sample size is:

If the sampled population is small, the finite population correction (fpc) is

used to correct for overestimation bias. Using the fpc, the estimated sample

size is:

where L is the width of the interval around the projected average, and N is

the size of the true population. In this case, N is the number of days in the

season. Precision is estimated by the confidence level (generally 95 percent)

and the desired width of L. For example, the investigator may wish to be 95

percent certain that the results have a precision of ± 5 percent of the total.

Operationally feasible sample sizes are obtained by varying the amount of

precision of the estimate; highly precise estimates may require sample sizes

that are too large for practical purposes.

Example. From past surveys the average amount spent per trip was $250,

with S = $160. Suppose we want to be 95 percent certain that results will have

a precision of ± 5 percent, or ± $13 per trip. If the total number of visits to a

remote trailhead was 100, then the estimated number of visits to sample is

≈ = 86. If the precision is adjusted to ± 10 percent

(or ± 25 per trip), then n = 62. Both of these are too large or too close to the

 

R = − +× =

156

200 10 14

100 88 6

( )

. %

 

R = × number returned

(number sent out) – (non - eligible + non - reachable) 100

 

n

N S

S L N

≅ ⋅

+ ⋅

2

2

2

2 4 2( )

 

100 160

160 13 13 100

16

2

2

2

( )

( ) ( )( ) +

+

 

n

S

L

≅ ⋅ 



 



 4

2
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 167

entire group of 100 visits to be of practical use due to the large underlying

variance. A more reasonable level of precision would be ± 30 percent (or ±

$75 per visit), which would call for a sample size of n = 15.

(b) Proportion data. Sample size (n) will be at a maximum when the

proportion of observations (p) in any given category is 0.5 (or 50 percent). The

sample size required to estimate an interval of width L around the sample

mean will be:

 

n p p

L = 42 1 ⋅⋅− 2

2

() ( )

 which is maximized for p = 0.5 or n = 16(0.5)(0.5)/L2.

Example. Preliminary data showed that for 40 randomly selected visitors,

24 appeared to be day users. Therefore, the proportion of day users, p = 24/

40 = 0.60, and the standard error is p pn ( ) 1 0 60 0 40 40 − / . ./ = ( )( ) = 0.0775.

The 95 percent confidence interval based on these data is approximately 0.6

± 2(0.0775) = 0.6 ± 0.15, for a confidence interval of (0.45, 0.75). The sample size

n required for a 95 percent confidence interval with a length of at most 0.10

(regardless of the resulting value of p) is approximately 

n = 16 0 5

0 10

2

2

(.)

(. ) = 400.

Therefore, it would be necessary to observe 400 visitors to obtain this amount

of precision for the estimate.

(c) Stratified sampling. If the data are stratified according to trailhead

or time block, sample sizes of each stratum must be calculated to ensure

accurate representation of the population. Sample sizes may be either

proportional or disproportional to stratum size (part I, chapter 3). Proportional sampling subdivides the sample population proportional to the size of

each strata or subgroup. Optimal allocation is a type of stratified sampling

where the sample size within each strata is proportional to both the size and

the variability of the sample within each stratum; the proportionality factor

is calculated as 

NS NS n ii ii [ ] ⋅ ⋅ / . ∑( ) ⋅ Disproportional sampling occurs when

the same size sample is drawn for each stratum (assuming equal costs to

sample each strata).

Proportional sampling should be performed if strata are fairly homogeneous (that is, the standard deviations observed for each stratum are

similar), whereas optimal allocation should be chosen if strata differ in the

amount of variability.

Example. In this example, data are stratified by two time blocks—weekend

days and weekdays. This stratification strategy separates out time periods

according to relative intensity of use, with the heaviest and most variable use

occurring on weekends, and relatively light and uniform use on weekdays.

For a 100-day season, there are about 72 weekdays and 28 weekend days.

Suppose the available resources (budget, labor, time) dictated that the

maximum number of days that could be sampled was n = 25. The initial value

for the standard deviation for each stratum was estimated from the data

obtained during the permit compliance rate estimation phase. Sample sizes

for each time block are calculated as follows:
168 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Optimal

Proportional Disproportional allocation

Stratum sa f b nc fn f n

Weekends 88.0 0.25 7 0.43 12 0.64 16

(n1 = 28)

Weekdays 19.2 0.25 18 0.17 12 0.36 9

(n2 = 72)

aStandard deviation.

bSampling proportion.

cSample size.

Because the two strata differ considerably in variability, the preferred

sampling scheme is optimal allocation; with this strategy the investigator

randomly selects 16 weekend days and 9 weekdays for data collection.

3. Use Estimation.—Use characteristics estimated with this system are

limited to individual or group visit counts. Data may be expressed in terms

of: (a) the rate (for example, number of visitors per day), (b) the total (for

example, number of visitors for the season), (c) use by category (for example,

cooking method), (d) use description (for example, length of stay), or (e)

summary-use statistics (for example, recreation visitor days)

(a) Rate of use. Suppose the number of visitors with permits for a 30 day

time period was 772. A survey of 50 visitors showed that 46 had permits for

a compliance rate of 46/50 = 0.92.The estimated number of users over the 30

day period is 772/0.92 = 839, for an estimated daily rate of 839/30 = 28 users

per day. The estimated confidence interval for the 30 day rate is:

 839 ± 

2 772 50 50 46 46 2 3 ⋅ ⋅⋅ − ( )/ = 839 ± 70 = (769, 909)

which converts to a confidence interval for the daily rate of (25.6, 30.3).

(b) Total use. Total visitor use is estimated by multiplying the “corrected” average daily rate by the number of days in the time period of interest,

corrected by the estimated bias in counts. The assumption implicit in this

method is that use remains uniform over the time period of interest; if use

patterns fluctuate considerably over the season, calibration relationships

should be updated as required, and the new relationship used to calculate use

rates for that time interval.

In this example, season length was 100 days. The overall visitor use

estimate is therefore 28(100) = 2,800 visitors (2,560 to 3,030 visitors).

(c) Use by category. Frequently, visitor use is described in terms of

categories, or groups, of users; the number of users in each category is

expressed as a proportion, or percentage, of the total number of users in the

sample.

Example. On the returned survey forms 2,975 visitors indicated their

method of cooking during their visit: stoves, wood fires, or neither. Results

with a 95 percent confidence interval (using χ2

 procedure based on 2 degrees

of freedom) were:

Stove users: n1 = 2,231, p1 = 2,231/2,975 = 0.75,

95 percent confidence interval = 0.75 ± 5 99 0 75 0 25 2 975 . . . /, [ ] ( )( ) = 0.75 ± 0.019

= (0.731 to 0.769);
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 169

Wood fire users: n2 = 595, p2 = 595/2,975 = 0.20,

95 percent confidence interval = 0.20 ± 5 99 0 20 0 80 2 975 . . . /, [ ] ( )( ) = 0.20 ± 0.018

= (0.18 to 0.22);

Neither: n3 = 149, p3 = 149/2,975 = 0.05,

95 percent confidence interval = 0.05 ± 5 99 0 05 0 95 2 975 . . . /, [ ] ( )( ) = 0.05 ± 0.009

= (0.04 to 0.06).

(d) Use description. One variable that may be obtained by surveys is

length of stay. Post stratification may also be of interest.

Example. A sample of 38 surveys reported an average length of stay of 2.4

nights with a standard error of 0.23 nights. This makes the 95 percent

confidence interval 2.4 ± 2·0.23 = 2.4 ± 0.46 = (1.94, 2.86).

(e) Summary-use statistics. The recreation visitor-day is defined as 12

hours of a given recreation activity performed by the associated proportion

of visitors. It is calculated as the product of the number of activity occasions

and the average amount of time spent in that activity, divided by 12.

Example. The number of permits issued for a given season was 6,750, of

which 1,232 were horse users. For horse users, there were 3.1 people per

group, and 5.2 horses per group; the estimated compliance rate was 95

percent. The total number of horse users was 3.1(1,232)/(0.95) = 4,020 people,

and 5.2(1,232)/(0.95) = 6,744 horses. The average duration of a wilderness

trip was 5 days, or 120 hours. Then, the number of recreation visitor-days for

horse users during the season was 4,020(120)/12 = 40,200.

A study of visitors entering the Bob Marshall Wilderness found an average

group size of 4.7; 61 percent of all groups consisted of two to four people.
170 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Groups traveling with recreational packstock are generally larger than

hiking groups.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 171

Appendices
172 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 173

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USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 175

Appendix B: Data and Data

Analysis

Observations are the raw material of any wilderness use study. Because

information gained from wilderness use studies is primarily numerical, and

because the manager is generally interested in populations or groups,

statistical methodology is required for both the characterization and analysis

of wilderness use data. In this section we describe the general types of

observations that are acquired during the research process, provide elementary methods of analyzing such data, and define the statistical meaning of

the various terms used throughout the text. The techniques presented in this

section are found in most introductory statistics texts; we review them here

in the context of monitoring wilderness use.

Variables_________________________________________________________

Variables are attributes measured by the individual observations; they are

not constant from item to item, but show variation. Variables may be either

quantitative or qualitative.

A quantitative variable can be measured and ranked. Observations on

quantitative variables may be categorized further as continuous or discrete.

A continuous variable is one which can take on virtually any possible value

within some range. Examples are distances traveled per day, and times

between wilderness trips. A discrete variable can take on only a distinct

series of values, with no intermediate values between them; they are

therefore integers. Count data are discrete variables; for example, the

number of hikers per day, the number of packstock per string.

A qualitative, or categorical, variable is one which cannot be directly

measured or ordered. Each observation is some property of the item in the

sample; these properties are classified as belonging to one of a finite number

of categories. These categories can be dealt with statistically if they can be

assigned counts or frequencies. In the simplest case, there are only two

categories required for describing all possible responses; such data are

binomial. For example, visitors classified on the basis of gender would be

either male or female. Multinomial data are described by several categories.

Examples are types of users (hikers, horseback riders, canoeists), ethnic

origin, state of residency, and so on.

Populations and Samples___________________________________________

A population consists of all possible values of a variable. When all values

of a population are known, it follows that the population can be characterized

exactly. The various characteristics of the population, such as the population
176 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

mean μ and the population variance σ2, are known as parameters. The

parameter has a fixed numerical value which is usually unknown to the

investigator.

A sample is a subset, or part, of the population. Sample characteristics,

such as the sample mean and the sample variance S2

, are used to estimate

population parameters; a given sample characteristic is known as a statistic.

Our goal is to use characteristics of the sample to make inferences about the

corresponding characteristics of the population; thus, if the inferences are to

be valid, the sample must be representative of that population.

To ensure that a sample is representative of the population of interest, we

must employ principles of randomization. When randomly selected from a

population, each item has an equal probability of being selected. A random

sample is not haphazard, unplanned, or based on guesswork; such methods

of data selection will lead to biased results. Instead, random selection of

sample items is performed by using a random number table—a sequence of

numbers generated by a uniformly distributed random distribution. There

are two benefits to this approach. First, the selection of items is not

influenced by unknown or unsuspected biases on the part of either the

investigator or the circumstances surrounding the selection of the sample.

Second, we can apply the statistical laws of probability to infer the expected

values of an estimate and its sampling variation. A description of random

sampling and how it is performed is given in chapter 3.

Descriptive Statistics: Data Plots ____________________________________

Graphs are a quick and easy method of data analysis. Humans are

primarily visual animals; it is much easier to understand and summarize

large amounts of quantitative information when it is presented as a diagram,

rather than as a list of numbers. Data plots are a highly effective means of

(1) exploring the data set for patterns and relationships, (2) checking the data

for conformity to basic statistical assumptions if further statistical analysis

is to be performed, and (3) presenting quantitative information in as concise

and effective means as possible. In fact, plotting data is the most important

step in the analysis, and should be performed first, before more rigorous

analyses are performed.

Four basic types of data plots are considered here: (1) stem-and-leaf

displays, (2) histograms and bar charts, (3) scatterplots, and (4) time plots.

Stem-and-Leaf Displays

This type of data plot shows the frequency distribution of a single variable.

It is also useful for obtaining ranked data arrays, and for computing the

median of the sample. It is constructed by splitting the value of each

observation into two parts: the stem, which consists of one or two leading

digits, and the leaf, which consists of the remaining digits. Stem values are

listed on the left of the page, and leaf values are listed beside the corresponding stem in the order in which they are encountered.

Example. The user count data for the East Hickory Creek Trail (table 4)

consists of counts between 1 and 83. The stem would be the first digit and

the leaf the second digit; for example, the “User” count 57 (observation

number 1, week 1, day 1) would have a stem of 5 and a leaf of 7. The stemand-leaf display for the East Hickory Creek Trail user data is as follows:
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 177

0| 4556859998975577889779893879

1| 193303103513222409383540255713484108261664

2| 11871807665

3| 41633484

4| 61133571738

5| 7877873

6| 59

7| 58

8| 3

This diagram shows that the distribution of these data is highly skewed to

the right, with a few large values but with the majority of values in the lower

counts. The importance of symmetrical data distributions and corrections for

asymmetrical data are discussed next.

Histograms and Bar Charts

A bar chart is a method of showing the frequency distribution for a single

categorical or classification variable. A bar chart is constructed by first

forming a frequency table, dividing the sample into classification categories.

Bars are then drawn with height proportional to the frequency or relative

frequency of each category. Although pie charts are often used to display

categorical data, bar charts are preferred since comparison of pie slices is not

as straightforward as comparison of bars.

A histogram is another method of showing the frequency distribution for a

single continuous variable. A histogram is constructed by subdividing the

measurement axis into a number of nonoverlapping, consecutive intervals of

equal length. Each observation is contained in one of these intervals; the

number of observations in each interval is the frequency. Above each interval

a rectangle is drawn with the height proportional to the frequency (relative

frequency). The stem-and-leaf display discussed above is a rudimentary

histogram and is easily converted to a frequency table.

Example. Horse users in a certain wilderness area were asked to indicate

the type of community where they were raised. The frequency distribution for

the data are shown below; the resulting bar chart is shown in Figure 8.

Figure 8—Bar chart showing the relative frequency of horse users coming from different

community types.

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Community type

Farming

Country, not farm

Small town

Large town

City

Relative frequency of horse users
178 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Type of community Frequency Relative frequency

Farming 126 0.58

Country, not farm 59 0.27

Small town 8 0.04

Large town 16 0.07

City 7 0.03

Example. The user count data for the East Hickory Creek Trail (table 4)

can be presented as a frequency table (below, constructed from the raw data

or equivalently the stem-and-leaf display above) or as a histogram (fig. 9).

Relative

Class Frequency Frequency

1-9 28 0.25

10-19 42 0.38

20-29 11 0.10

30-39 8 0.07

40-49 11 0.10

50-59 7 0.06

60-69 2 0.02

70-79 2 0.02

>=80 1 0.01

Figure 9—Histogram showing the distribution of the daily number of users for the East

Hickory Creek Trailhead in the Cohutta Wilderness.

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80 90

User Count

Histogram for East Hickory Creek Users

Relative Frequency
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 179

Scatterplots

When two measurements are made on each item, a scatterplot of the paired

measurements can show the patterns in the data, or indicate the amount of

association between the two variables. Scatterplots are useful when the data

set is large, if there is a lot of variation in the data (which may mask

important relationships), and for checking the linearity of the relationship.

Scatterplots are especially critical in calibration problems where the relative

agreement between two measures must be assessed.

Example. The following data were visitor counts obtained by a mechanical

counter and by human observers at the Snow Lake Trailhead, located in the

Alpine Lakes Wilderness, Washington.

Counter: 132 514 604 107 74 107 423 438 92 170 186 127 80.

Observers: 119 308 556 119 74 113 424 270 78 180 61 8 187.

The ideal relationship between the two sets of counts would be a 1:1

correspondence between the two methods. A less desirable, but still workable, situation would be one method showing consistently higher readings

than the other.

The plot of these data (fig. 5) reveal a large amount of scatter about the 1:1

line. In general, data from human observers are more accurate than those

from mechanical counters.

Time Plots

These are similar to scatterplots, except that each observation for the

variable of interest is plotted in time order. This type of plot is extremely

useful for detecting cycles or other kinds of time-dependent patterns in the

data. It is an invaluable tool in monitoring programs, especially when the

objective is to evaluate the effects of some intervention, such as a change in

management policy or initiation of some educational program, on some

visitor characteristic.

Statistical analyses of time-dependent data are mathematically very

complex, and require considerable skill and judgment. (A very simple time

trend analysis is presented in a later section.) However, time plots are simple

to construct and can give a substantial amount of useful information which

may not be immediately apparent for the tabulated data. It should be noted

that a number of statistical methods (including the calculation of descriptives

such as the variance and standard deviation), are not appropriate for timedependent observations, and will give completely misleading results.

Example 1. Figure 4 shows a time plot of number of users monitored on the

East Hickory Creek Trail for the 112 days of the summer season. It is

immediately obvious from visually inspecting this plot that the data are

extremely cyclic. Peak numbers of users occur (not unexpectedly) on weekends, averaging about 50 per weekend day, and declining to an average of

about 10 users on weekdays. Patterns relevant to a number of management

questions (what are trail use patterns? should the trail be managed for peak

or average numbers? how are party averages affected by time in the week?

are large party sizes unusual? etc.) can be readily answered by visual

inspection.

Example 2. Figure 10 shows the number of violations committed by

wilderness visitors before commencement of an education program, and the
180 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

number of violations after the program was in place. In this instance the

program appears to be effective to some extent because the number of

violations has declined. However, violations are occurring at a new steadystate level. Further management could be directed toward determining

whether the educational program is no longer effective for all visitors, or if

only a small subset of offenders needs to be targeted by an alternative

program.

It is extremely important in this kind of monitoring that there are some kind

of baseline or control measurements made before the policy or program change

to determine if the new situation actually has affected the response.

Determination of statistical differences between several series is beyond

the scope of this handbook. Competent statistical assistance should be

obtained.

Descriptive Statistics: Continuous Data _______________________________

There are several types of numerical summary measures which characterize a given data set and communicate some of its more important characteristics. The two most important attributes of a set of numbers are (1) the

location, or central value, and (2) the spread or dispersion around that central

value.

Measures of Central Tendency

The mean.—The most common measure of central tendency for a given set

of numbers is the mean, or arithmetic average. The sample mean is calculated as the sum of all the observations in the set, divided by the sample size:

 

Y YY Y

n

Y

n

n

i

i

n

= + +...+ = =

∑

1 2 1

Figure 10—The number of violations committed by wilderness

visitors before and after the initiation of a wilderness education

program.

0

2

4

6

8

10

12

14

16

18

0 10 20 30 40

Time (weeks)

Number of violations
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 181

Example. In a preliminary study of visitor impact on the Snow Lake Trail,

the numbers of visitor groups were recorded during 8 hours of observation on

each of 11 randomly selected days over the season. The data are as follows:

52, 115, 209, 46, 19, 44, 149, 158, 47, 70, 76.

The sum of these n = 11 observations is 

Yi

i=

∑

1

11

 = 985. The sample mean is:

 

Y

Yi

i = == =

∑

1

11

11

985

11

89 54 .

The median.—In a set of ranked or ordered observations (smallest to

largest), the sample median is the middle value, so that half the numbers are

less than the median value and half are greater. When the data set has an

odd number of values, there is a unique middle value among the ranked

numbers. When the data set has an even number of values the median is

calculated as the average of the two middle values in the ordered data set.

Example. For the Snow Lake Trail data, ordering gives:

19, 44, 46, 47, 52, 70, 76, 115, 149, 158, 209.

The median is therefore 70.

The median is insensitive to extremes in the data, such as very large or very

small data values. For example, if we increased the largest observation to

500, the median would be unaffected. This contrasts with the mean, which

can be markedly affected by even one extreme value.

In general, the mean and median will not be equal to each other. If the

population is skewed, the arithmetic mean will be “pulled” in the direction of

the skew. Thus, if the population is negatively skewed (where the distribution of the observations shows a pronounced tail to the left), the median will

be smaller than the mean; if the population is positively skewed, the mean

will be larger than the median. Thus, in certain cases the median may be

more appropriate than the mean for describing skewed data or outlying

observations.

Quartiles and percentiles.—The median divides the data set into two parts

of equal size. We could obtain finer resolution of our data set by dividing it

into more than two parts. Quartiles are four equal divisions of the data set,

such that the first quartile separates the lower one-quarter, or 25 percent, of

the data from the remaining three-quarters, the second quartile is the

median, and the third quartile partitions the top quarter of the data from the

lower three-quarters. Percentiles divide the data set into 100 equal parts,

such that the 99th percentile separates the highest 1 percent of the data from

the remaining 99 percent, and so on. Percentiles are not recommended unless

the number of observations is very large (>1000).

Measures of Variability

A measure of central tendency gives only partial information for a given

data set; it provides us with a measure of location but does not give any

information about the amount of variability around the location. In wilderness use studies, most investigators are interested in determining the
182 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

magnitude of a certain outcome, or the size of the difference of that outcome

between groups. The precision of the particular sample statistic used is given

by the degree of variability in the measured outcome. Mean values should

never be given without some measure of their variability.

It is important to note that measures of variability based on random

sampling give only the effects of sampling variation on the precision of the

estimated statistics. They cannot correct for errors which are not related to

sampling; for example, biases in study design or incorrect analyses.

Range.—The simplest measure of variability is the range, which is the

difference between the largest and smallest values in a data set:

Range = max (Yi) – min (Yi)

Thus, a small range indicates a small amount of variability, whereas a large

range indicates a large amount of variability. In general, the range is

presented in terms of its minimum and maximum values, and the difference

is not computed.

Because it depends on the two most extreme values in the data set, the

range is overly sensitive to those values; the magnitudes of the intermediate

observations are ignored.

The Sample Variance and Standard Deviation.—The population variance

(denoted by σ2

) is a measure of the amount of variation among the observations in a population. The sample variance S2

 is calculated as the sum of

squared deviations of observations from the mean, divided by n – 1:

 

S

Y Y

n

i

i

n

2

2

1

1 =

−

−

=

∑( )

( )

A more accurate and computationally simpler method of calculating S2 is:

 

S

Y

Y

n

n

i

i

i

n

i

n

2

2 1

2

1

1 =

−





 





−

=

=

∑

∑

First, each observation is squared and the squared values are added together. Second, the sum of all observations is squared and divided by the

sample size n. This value is subtracted from the total of the squared

observations and this difference is divided by (n – 1). The positive square root

of the sample variance is called the sample standard deviation (S); it is one of

the most important descriptive statistics. S can be thought of as a measure

of how far a typical observation deviates from the average.

If the sample comprises more than 5 percent of the population (assuming

sampling is done without replacement), the S2 is too large, on average. To

correct this problem, multiply by the finite population correction factor (fpc),

defined as (N – n)/N.

Example. For the Snow Lake Trail data, the sum of all n = 11 observations

was 

 

Yi

i=

∑ = 1

11

985, and the sum of squared observations was 

 

Yi

i

2

1

11

124 073 =

∑ = , .

Then the sample variance S2

 was calculated as:
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 183

 

S2

2

124 073 985

11

10 = 3 587 0727

−

=

, ( )

, .

Since the season at Snow Lake is roughly 100 days, a sample of 11 days

exceeds the 5 percent rule, so the estimated variance needs to be adjusted

using the fpc. S2

 = 3,587.0727 (100 – 11)/100 = 3,192.495. The square root of

this corrected estimate of the population variance is the sample standard

deviation, 

S = = 3 192 494 56 5 , . ..

The Standard Error .—An investigator rarely studies every member of the

population, but only a small representative sample. The mean calculated

from such a sample consists of observations drawn at random from the

population; therefore, there is nothing distinctive or unusual about this

sample or its mean. If another sample were selected, chance alone almost

always produces a sample consisting of different observations and consequently a different sample mean. Each randomly drawn sample has a mean,

and each sample mean is an estimate of the true (but unobservable)

population mean. If it were possible to calculate the means of all possible

samples of a given size from a population, we would obtain a distribution of

sample means whose values would differ from one another, but would cluster

around the true population value. The standard deviation of the population

of all possible sample means is called the standard error. The standard error

quantifies the variability of the sample means relative to the true population

mean, or the certainty with which we can estimate the true population mean

from the sample. The standard error quantifies the precision with which the

sample mean estimates the true population mean.

 The standard error of the mean (SE) is computed for a simple random

sample as:

 

SE Standard deviation

sample size =

Example. For the Snow Lake data, the estimated standard error of the

mean is:

SE = 56.5/ 11 = 17.03.

Confidence Intervals .—A confidence interval is the range of values for the

mean that can be considered feasible for the population. The width of a

confidence interval depends partly on the standard error (and therefore on

both the standard deviation and the sample size), but also on the amount of

“confidence” we wish to associate with the resulting interval. The investigator selects the degree of confidence to be associated with the confidence

interval. A 95 percent confidence interval is the most common choice,

although smaller or larger confidence intervals can be computed according

to the degree of confidence required. If a 95 percent confidence level is

specified, approximately 95 percent of such intervals will correctly contain

the unknown population mean. This also means that about 1 in 20 such

intervals (5 percent) will not contain the unknown population mean.

A value from Student’s t distribution is multiplied by the estimated

standard error when n is smaller than 30. For sample sizes of 30 or more, the

multiplier is selected from the standard normal (or z) distribution. For most
184 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

practical purposes, 2.0 is an adequate approximation for the multiplier to

construct a 95 percent confidence interval.

Procedure: For a given confidence level, the confidence interval for a

population mean is calculated from the mean Y the sample size n, and the

standard deviation S. Recall that SE = S/ n. Then the 95 percent confidence

interval is approximately:

 

( ) Y SE Y SE −⋅ +⋅ 2 2 ,

Example. For the Snow Lake data, n = 11, Y = 89.54, and S = 56.5. The

degrees of freedom associated with the estimate of S are (11 – 1) = 10. The

approximate 95 percent confidence interval is given by 89.54 ± 34.06 = (55.48

to 123.61).

Descriptive Statistics: Categorical Data _______________________________

Much of the data describing wilderness visit and visitor characteristics are

categorical. That is, each observation in a sample belongs to one of a finite

number of groups or categories. In the simplest case, such data are binomial;

there are only two categories required for describing all possible responses.

For example, a visitor classified on the basis of gender would be either male

or female. Multinomial data are described by several categories; examples

are ethnicity (white, African-American, Hispanic, Native American, etc.),

marital status (single, married, divorced, widowed, separated), state of

residence, and so on. Such data cannot be summarized by the statistics used

for continuous data, such as mean and standard deviation. For example, if

ethnic groups were classified into 10 groups labeled from 1 to 10, an “average”

ethnicity code would be meaningless. Instead, the investigator is interested

in the number of items in each category, expressed as a proportion or

percentage of the total number of observations; measures of central tendency

and spread can be calculated for data expressed in this form. The value of the

total should always be presented when proportion data are used. However,

if the sample size is very small, proportion data will be useless for evaluation

purposes.

Binomial Data

Assumptions for binomial sampling require that observations are independent; that is, each element of the population has an equal probability of being

selected, and selecting any particular observation does not influence the

outcome or selection of any other observation. Furthermore, the overall

proportion of observations having the feature of interest must not change

during the sampling process.

In the simplest case, a given variable can be described in terms of two

possible outcomes; one outcome specifies individuals which have the feature

of interest (“successes”, or YES = 1), and the other outcome specifies

individuals which do not have that feature (“failures”, or NO = 0).

Sample Calculations.—Let p represent the proportion of “successes.” For a

random sample of size n, the average or expected number of “successes” is n·p.

Then, where there are X individuals having the feature of interest:

p = X/n
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 185

In other words, p is a mean of a set of observations that are either 0 or 1. The

standard error for the proportion of “successes”, SEp, is calculated as the

square root of the product of the proportion of “successes” p and the

proportion of “failures” (1 – p), divided by the sample size:

 

SE p p

n p = ( ) 1−

Confidence Intervals.—The 95 percent confidence interval for a proportion

p may be approximated for most practical purposes by:

p ± 2·SEp.

Example. A survey of 100 randomly selected wilderness visitors reported

that 36 visitors used a campstove. Let p denote the proportion of all visitors

who used a stove. Then p = X/n = 36/100 = 0.36 and the estimated standard

error of p is 

p p

n

( ) .( .) 1 0 36 1 0 36

100

− = − , or 0.048.

The approximate 95 percent confidence interval for p is:

 

p p p

n

± − 2 = ± 1 0 36 2 0 36 0 64 100 ( ) . ( . )( . ) /

or (0.266 to 0.454).

The length of the 95 percent confidence interval is 0.188, or about 19

percent. Suppose we wish to increase the precision of this estimate to 10

percent. Then the sample size necessary to obtain a 95 percent confidence

interval with this amount of precision is:

 

n ≈ 



 



 = 4 2 0 36 0 64

0 10

369

2

2

( ) ( . )( . )

(. )

Multinomial Data

Multinomial responses are an extension of the simpler binomial case.

Instead of only two possible outcomes, each observation results in one of k

possible outcomes, where k is a number greater than two. For example,

suppose we determine that there are three types of wilderness users: hiker,

horseback rider, and mountain biker. There are thus k = 3 possible outcomes,

or categories, for each visitor. A multinomial analysis would involve classifying each of n visitors who entered the wilderness area into one of the k = 3

categories.

Sample calculations : There is probability pi that an observation will occur

in category i. For k categories, there will be ni observations in each category,

and the sum of all observations 

 

n n i

i

k

=

=

∑ .

1

Recall that in a two-category (binomial) situation, the expected number of

“successes” and the expected number of “failures” are n·p and (1 – p)n

respectively. Similarly, in a multinomial situation, the expected number of
186 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

observations resulting in category i is n·pi where i = 1, 2, ..., k categories, and

the expected number of “failures” is (1 – pi )n.

Confidence Intervals.—The 95 percent confidence interval cannot be approximated by 2·SE. Instead, the formula used to calculate the confidence

interval for the expected or mean values of each pi is:

 

p SE i ± ⋅ χα, 1 k− i

2

where 

χα,k−1

2 is the 100(1–α)

th percentile of a chi-square (χ2

) distribution, with

(k –1) degrees of freedom, and the standard error calculated for each category

is SEi = 

p p

n

i i ( ) 1− .

Example. A survey of n = 100 wilderness visitors reported three user type

categories: hikers, mountain bikers, and horseback riders. They observed

n1 = 67 hikers, n2 = 25 horseback riders, and n3 = 8 mountain bikers. The

proportions of each type of user were as follows:

Hikers Horse users Mountain bikers

ni 67 25 8

pi p1 = 67/100 p2 = 25/100 p3 = 8/100

= 0.67 = 0.25 = 0.08

To obtain the simultaneous 95 percent confidence intervals for p1, p2, and p3,

we use the tabulated value of χ 3 1 2 0 95

2

– = , . = 5.99. The 95 percent confidence

intervals are given by:

 

p1 0 67 5 99 0 67 0 33

100

:. .

( . )( . ) ± 



 



 = (0.56 to 0.79)

 

p2 0 25 5 99 0 25 0 75

100

:. .

( . )( . ) ± 



 



 = (0.14 to 0.36)

 

p3 0 08 5 99 0 08 0 92

100

:. .

( . )( . ) ± 



 



 = (0.013 to 0.15).

Differences Between Variables ______________________________________

In the previous section we demonstrated the procedures for estimating a

given population parameter by using sample statistics; we evaluated the

precision of that estimate by calculating confidence intervals. However,

many wilderness problem situations involve the detection of differences

between some observed value and some other value, either historical or

maximum allowable use levels, or values derived from previous studies. In

this section we discuss the procedures for testing for differences between two

values.

When evaluating differences between values, in effect we are evaluating

the competing claims of the two values as to which estimate of the value is
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 187

the correct one for the population, or alternatively, how well the two values

agree. Methods for deciding between these competing claims are called

hypothesis testing.

Detailed information on hypothesis testing procedures are given in a

number of statistical texts (for example, Neter and others 1985, Snedecor and

Cochran 1980, Steel and Torrie 1980). For our purposes it is important to note

that there is a close relationship between the use of a confidence interval and

a hypothesis test. We can infer the result of the hypothesis test at a level of

statistical significance associated with the confidence interval. For example,

a value falling outside of the 95 percent confidence interval calculated for the

difference between two sample means indicates that there is a statistically

significant difference between the sample means at the α = 0.05 level. This

is generally interpreted as a decision to reject the null hypothesis of no

difference between sample values. However, presenting differences in terms

of confidence intervals is more informative than expressing the probability

level of statistical test of significance. Generally, the investigator is more

interested in determining the magnitude of the difference rather than a

single arbitrary decision value for statistical significance; confidence intervals produce a range of values for the population value of the difference

(Gardner and Altman 1986).

Determination of sample sizes necessary to detect specified differences is

similar to procedures discussed previously. Those interested in further

details are encouraged to consult either a statistician or a statistical text.

One-Sample Tests

A one-sample test is appropriate if interest centers on detecting departures

of the sample estimate (calculated from the data) from some null, or

reference, values. For example, reference values may be historical use levels

or maximum allowable use levels. The null hypothesis is that there is no

difference between the observed mean and the reference value; that is

(Observed Mean Use Level = Historical Use Level). If the historical mean

value lies outside the confidence interval constructed around the sample

mean, then the equality hypothesis is rejected.

The procedure for comparing a sample proportion p to a reference proportion p0 is similar. For the null hypothesis that p = p0, if p0 falls outside the

confidence interval for p, then the null hypothesis is rejected.

Procedure:

 1. Identify the parameter of interest (for example, the mean, proportion,

etc.) to be estimated, and describe it in the context of the wilderness

“problem” to be evaluated.

 2. Determine the null value; that is, the historic value, the maximum

acceptable value, the regulatory or legislated value, or other reference value

of interest.

 3. Calculate the mean and standard error for the sample data.

 4. Calculate a confidence interval for the parameter of interest (the

population mean or proportion).

 5. If the reference value falls outside the confidence interval, the hypothesis is rejected.

Example. In a certain wilderness area prior to 1985, horses were the only

type of packstock used; the average daily number of horse-user groups up to

that time was 20. However, after 1985, llama use became more prevalent.
188 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The manager wishes to determine whether or not the prevalence of horse use

has changed from “historical” levels. The null hypothesis is that (Current

Horse Use = 20).

Sample data for the number of horse-user groups collected for 10 randomly

selected days over a single season were:

17, 9, 6, 5, 6, 34, 7, 21, 6, 4.

The sample mean X = 11.5, n = 10, SD = 9.67, and the reference mean is 20.

Then the 95 percent confidence interval for the mean is 11.5 ± 2·(9.67/

 10 = (5.38, 17.62). Because the value of 20 falls outside (above) the 95

percent confidence interval for the current horse use, the manager concludes

that the prevalence of horse use measured during this particular season is in

fact lower than historical levels. However, this year may be atypical in some

way; for example, unusually bad weather or economic conditions may have

adversely affected the numbers of horse users. To determine if this observation is actually a trend toward lower horse use in general, the manager will

have to obtain data for several more seasons.

Comparing Two Samples

The investigator may be interested in detecting a difference between the

means of samples from two different populations. Examples include detecting differences between current values for population and “baseline” measurements for the sampled population, or measurements made at a different

location or under different circumstances.

For evaluating the difference between two independent samples, estimates

of the difference between the population means and an estimate of the

standard error for that difference are required. The null hypothesis is that

there is no difference between means. The standard error for X – Y is

estimated by the square root of the sum of the squared standard errors for

each of the two means:

 

SE S

n

S

n X Y− = + 1

2

1

2

2

2

The 95 percent confidence interval for the difference between two means is

approximated by:

 

X Y SEX Y − ±⋅ − 2

The samples are judged to be significantly different if the confidence interval

does not contain 0.

Evaluating the difference between population proportions is similar; the

null hypothesis is that the difference between the population proportions is

zero. The standard error for the difference is estimated by:

 

SE p p

n

p p

n p p 1 2

1 1

1

2 2

2

1 1 − = ( ) − + ( ) −

The 95 percent confidence interval for the difference is approximated by

 

p p SE 1 2 2 p p 1 2 − ±⋅ − .
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 189

Procedure:

 1. Identify the parameter of interest (for example, the mean, proportion,

and so forth), and describe it in the context of the wilderness “problem” to be

evaluated.

 2. Calculate the sample estimates of the mean or proportion for both

groups.

 3. Calculate the difference between sample estimates.

 4. Calculate the standard error for the difference of the sample estimates.

 5. Calculate the confidence interval for the difference between the population means.

Example. At Snow Lake wilderness area, group counts were obtained over

an 8-hour period for each of 12 randomly sampled days in 1990 and 11

randomly sampled days in 1991. These counts produced the following data:

1990: 148, 138, 45, 62, 123, 340, 273, 92, 231, 205, 115, 107.

1991: 52, 115, 209, 46, 19, 44, 149, 158, 47, 70, 76.

The null hypothesis is that there is no difference in mean group size between

years.

For the 1990 sample, n1 = 12, X = 156.58 and S = 88.62; for the 1991 sample,

n2 = 11, Y = 89.55, and S = 59.89. The difference between the sample means

is X – Y =156.58 – 89.55 = 67.03. The estimated standard error for this

difference is:

 

SEp p 1 2

88 62

12

59 89

11

2 2

− = ( ) + . . ( ) = 31.31.

The 95 percent confidence interval for the difference is 67.03 ± 2(31.31) = (4.4,

129.7). The value 0 falls outside the 95 percent confidence interval; therefore,

the data casts doubt on the veracity of the hypothesis of no difference between

1990 and 1991 use levels. In other words, mean group size in 1991 was

significantly smaller than group size in 1990.

Comparing More Than Two Samples

Analysis of Variance.—The analysis of quantitative data obtained from

more than two samples is usually performed by the procedure known as

analysis of variance, or ANOVA. The independent variable whose effect on

the response is to be studied is the factor under study (sometimes referred to

as the treatment), and the different subpopulations, or components, are the

levels of that factor.

Example. The manager of a given wilderness area wishes to determine

the effects of four types of travel methods (hiking, rafting, horseback riding,

mountain biking) on total distance traveled by visitors. The response is total

distance traveled. The factor is travel method. The levels are the types of

travel methods; hiking, rafting, horseback riding, and mountain biking each

constitute a level.

Example. The manager wishes to determine whether the relative location

of registration stations affects the number of visitors actually registering.

Three locations were tested: at the trailhead, at a fixed distance down the

trail (one-quarter mile from the trailhead), at a “natural” stopping place (on
190 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

top of an incline). The response is the number of completed registration cards

as a proportion of the total number of visitors passing the registration

stations. The factor is station location. The levels are the three location

categories.

In these examples the factor is qualitative, and the levels correspond to

different qualitative attributes or categories of the factor. Factors may also

be quantitative; in these cases the levels are described by a numerical

quantity on a scale (for example, age in years, number of years of education).

Analysis of variance determines whether or not there are differences in the

true averages associated with the different levels of the factor. If the null

hypothesis is rejected, this is interpreted to mean at least two of the mean

responses are different. The test statistic is the ratio of factor variance to the

common variance—the F-statistic. The calculated F-value is compared to the

critical F values which are tabulated in the back of many statistical texts. The

appropriate critical F is determined by the number of degrees of freedom

associated with the numerator and denominator of the ratio. As a general

rule of thumb, when F is close to 1, the null hypothesis cannot be rejected (the

average responses are similar for all groups), and if F is much larger than 1

(as determined from the appropriate table of F values), then the null

hypothesis is rejected (at least one mean is different).

The calculations used to obtain the calculated F-statistic are performed by

using formulae similar to those used to calculate the single sample mean X

and sample variance S2. Because these calculations are fairly involved,

standard computer statistical packages are used.

Analysis of variance techniques are outside the scope of this handbook. For

more information, the reader is encouraged to consult Neter and others

(1985), or other statistical texts.

Comparison of Proportions .—A common requirement of many wilderness

studies is the comparison of count or frequency data when observations can

be classified according to two or more different factors. This class of problems

occurs when there are R populations divided into C categories. The table that

displays the observations is called a two-way contingency table. In these cases

we wish to determine whether various categories are statistically independent; that is, if the proportions observed for all categories are similar to

expected values. Under the hypothesis of statistical independence, the row

(or column) classification is not influenced by the column (or row) classification. Under this hypothesis the distribution of the cell frequencies within any

given row (or column) are proportional to the overall column (or row)

frequencies. Examples are comparisons of patterns of use between day hikers

and overnight hikers, or the proportions of wilderness users from an urban

background who ride horses versus those that hike.

The test statistic used to perform this test is the chi-square (χ2

) statistic:

 

χ2

2

= ( ) ∑ Observed Expected

Expected

–

all cells

The observed cell counts are the number of observations in each cell. The

expected cell counts are calculated as: (rth row total)·(cth column total)/n,
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 191

where n is the total number of observations. The χ2 value calculated by this

formula is compared to the critical tabulated value; the appropriate χ2

 is

selected with reference to a given probability α (usually 0.05), and the

appropriate degrees of freedom. The number of degrees of freedom used to

calculate the critical value are (R – 1)·(C – 1) if there are R rows and C

columns. If the calculated χ2

 value is larger than the critical value, the null

hypothesis of independence between row and column classifications is

rejected.

Confidence intervals for individual cells or for differences between cells

may be computed as described previously for multinomial proportion data.

Procedure:

 1. Tabulate the sample count data according to their respective group R

and category C; these are the observed cell counts.

 2. Calculate the row and column totals.

 3. Calculate the expected cell counts.

 4. Determine the appropriate degrees of freedom (R – 1) and (C – 1).

 5. Calculate χ

2

, and compare to the tabulated value of χ

2

 with (R – 1)(C – 1)

degrees of freedom.

 6. Calculate confidence intervals for any or all differences.

Example. A wilderness manager wished to determine whether use patterns of different categories of users changed as a result of a certain specified

management action. The use category was length of stay; categories of use

were specified as “short-term” (under 4 hours), “intermediate” (over 4 hours

but not overnight), and “overnight.” The response was visitor number. A

randomly selected baseline sample of 240 visitors was obtained and classified

before the management action, and 200 randomly selected visitors were

classified after the action. The data are:

Type of use Before action After action Total

Short term 72 80 152

Intermediate 120 70 190

Overnight 48 50 98

Column totals 240 200 N = 440

The expected cell counts are:

Type of use Before action After action Total

Short term 

( )( ) . 152 240

440 = 82 91 

( )( ) . 152 200

440 = 69 09 152

Intermediate 

( )( ) . 190 240

440 = 103 64 

( )( ) . 190 200

440 = 86 36 190

Overnight 

( )( ) . 98 240

440 = 53 45 

( )( ) . 98 200

440 = 44 55 98

Column totals 240 200 440
192 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The calculated χ

2

 statistic is:

 

χ2

22 2 72 82 91

82 91

80 69 09

69 09

120 103 64

103 64 = ( ) − + ( ) − + . ( ) −.

.

.

.

. +

 

+ − + − + ( .) −

.

( .)

.

( .)

.

70 86 36

86 36

48 53 45

53 45

50 44 55

44 55

222

= 1.436 + 1.723 + 2.582 + 3.099 + 0.556 + 0.667= 10.063

with (R – 1)(C – 1) = (3 – 1)(2 – 1) = 2 degrees of freedom. The critical χ2

2, 0.95

= 5.992. Because 10.063 > 5.992, we conclude that there was a difference in

use as a result of the management action.

To pinpoint which of the three types of users were affected by the management action, we can perform either of two tests:

(1) Calculate combined χ2 values for each row, and compare to the critical

χ2

 with (C – 1) = (2 – 1) = 1 degrees of freedom. The critical χ

2

1,0.95 = 3.84. The

difference between “before” and “after” groups within each user type is

significant if χ2

calculated > χ2critical. The χ2

 values for each of the three user

categories were, respectively:

Short term: 1.436 + 1.723 = 3.183 < 3.84.

Intermediate: 2.582 + 3.099 = 5.681 > 3.84.

Overnight: 0.556 + 0.667 = 1.223 < 3.84.

(2) Calculate the approximate 95 percent confidence intervals for the

differences in proportions for each of the user categories (the formula is given

in the section Multinomial Data). The difference between “before” and “after”

groups within each user type is significant if the value 0 lies outside the

interval.

The proportions for each cell are:

Type of use Before action After action Difference

Short term 0.30 0.40 –0.10

Intermediate 0.50 0.35 0.15

Overnight 0.20 0.25 –0.05

The confidence intervals for each difference (by user type) are:

Short term: (–0.19 to –0.01)

Intermediate: (0.06 to 0.24)

Overnight: (–0.13 to 0.03).

Therefore, the intermediate users were strongly affected by the management

action, showing a statistically significant decline in numbers. Short-term

users were marginally affected by the management action, showing a slight

increase. Overnight users were relatively unaffected.

To further isolate differences between observed and expected frequencies,

the individual contributions to the overall chi-square test statistic may be

compared to a critical chi-square value with 1 degree of freedom, 3.843. For

this example the largest cell contribution is 3.099 which is smaller than

3.843. This means there are no individual cells with observed frequencies

that differ significantly from their expected frequencies under the null

hypothesis of independence of the row and column classifications.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 193

Association of Two Variables ________________________________________

This section describes methods of association analysis where the variation

in one variable is used to account for the variation in another variable and to

predict (or forecast) values of that second variable. There are four basic

types of association analyses. Regression specifically uses the value of one

variable to predict the value of the other. Regression techniques are most

frequently used for obtaining indirect measures of hard-to-measure use

characteristics as a function of more easily measured variables; they are

occasionally used in calibration applications. Correlation analysis examines the strength of the linear relationship between two continuous variables. Calibration is the assessment of the relative agreement of two

independent measures of the same use characteristic. In its simplest form,

trend detection looks for relationships as a function of time. Compliance

estimates are a form of “calibration”; supplementary observations are used

to adjust visitor counts for the bias occasioned by visitors failing to comply

with the mandatory permit or voluntary registration systems.

An introduction to the basic concepts of association analyses are given

below. Detailed discussion of these topics is beyond the scope of this manual;

interested readers should consult Neter and others (1985), Steel and Torrie

(1980), or other statistical texts for further information.

Regression

The simplest relationship between two variables X and Y is a straight line.

The data comprising X and Y are a set of pairs (x, y); Y is the dependent

variable (the variable to be explained) and X is the independent (or explanatory) variable. The general relationship between Y and X is given by:

Ye = β0 + β1·X

where Ye is the expected, or mean, value of Y; β0 is the intercept, or value of

Y when X = 0; and β1 is the slope of the relationship, or the change in Y for

a unit change in X. There are specific assumptions regarding the distributions of each variable, the most important of which is that X, being the

independent variable, can be determined with little or no error relative to Y;

this is the fundamental assumption of any linear regression problem.

Therefore, the investigator must be very clear about which variable can in

fact be defined as the independent variable.

The intercept is estimated by:

b Y bX 0 1 =−⋅

The slope is estimated by:

b

X Y

X Y

n

X

X

n

i i

i

i

n

i

i

n

i

n

i

i

i

n

i

n

1

1 1

1

2 1

2

1

=

−





 









 





−





 





= =

=

=

=

∑ ∑

∑

∑

∑
194 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

The percentage variation explained by the regression of Y on X is:

 

R

Y Y

Y Y

i

i

n

i

i

n

2

2

1

2

1

=

( ) −

( ) −

=

=

∑

∑

ˆ

where Y

ˆ

i

 is the estimated value obtained from the fitted regression; that is,

ˆ

Y Y bX X ( ) i i =+ − 1 = b0 + b1·Xi. The value of R2

 is always between 0 and 1. The

square root of R2

 is the correlation coefficient R, which should be given the

same sign as the regression coefficient, b1.

Most modern spreadsheets such as Excel, Lotus, or Quattro provide for

regression analysis. As part of their summary output an analysis of variance

(ANOVA) table is generated, similar to the one produced for comparing

several groups. The sources of variability are: SSTotal = 

Y Y i

i

n

( ) − =

∑ 2

1

 =

SSRegression + SSError where SSError = 

Y Y i i

i

n

( ) − =

∑ ˆ 2

1

and SSRegression =

 

Y Y ˆ

i

i

n

( ) − =

∑ 2

1

. Note that given any two sums of squares the third may be

computed by addition or subtraction. An alternate formula for SSError is

(1 – R2

)SSTotal. The degrees of freedom for SSRegression for a simple linear

model is 1 since there is a single predictor variable. The degrees of freedom

for SSError is (n – 2). Dividing the SSError by the degrees of freedom for error

gives the Mean Square Error, abbreviated MSE (i.e., MSE = SSError/(n –

2)). As before, an F ratio is computed by changing sums of squares into mean

squares and then forming their ratio, i.e., F = (SSRegression/1)/(SSError/

(n – 2)). The hypothesis that β1 = 0 is rejected if the calculated F ratio exceeds

the appropriate table value with 1 and (n – 2) degrees of freedom.

In many analyses of wilderness use, the investigator wishes to predict the

anticipated response for some given value of X. The mean response is

calculated simply by plugging in the given value of X into the regression

equation and calculating Y. The 95 percent confidence interval for this new

observation of Y is:

 

Y MSE

n

X X

X X

new

new

i

i

n ±⋅ + + ( ) −

( ) −























 =

∑

2 1 1

2

2

1

An essential first step in the analysis of regression data is to examine a

scatterplot of the data. The nature of the scatter will show whether there is

in fact a linear relationship between the two variables. If the relationship

between X and Y is positive or increasing from left to right, b1 will be positive,

and if the relationship is negative or decreasing from left to right, b1 will be

negative.
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 195

Multiple regression models consist of two or more independent variables

that are used to predict the dependent variable. See Neter and others (1985),

Steel and Torrie (1980), or other statistical texts for details on computation

and inference.

Example. Visitor traffic at Snow Lake Trailhead in the Alpine Lakes

Wilderness was surveyed to establish the relationship between the numbers

of vehicles in the trailhead parking lot (indicator variable) and the number

of visitors counted 1⁄2 mile up the trail (Y). The data were:

Cars Visitors

10 25

15 30

18 50

20 55

21 62

23 65

25 61

27 48

32 75

33 67

60 77

92 150

105 158

108 100

132 200

The relationship between car counts and visitor counts was:

Y = 26.48 + 1.15 X

with r

2

 = 0.86. That is, the mean number of visitors increases by 1.15 for every

additional car, and 86 percent of the variation in direct visitor counts could

be explained when car counts are considered.

The summary statistics for this relationship are:

 

nX X X

Y Y XY

i

i

n

i

i

n

i

i

n

i i

i

n

i

i

n

== = =

== =

= =

= = =

∑ ∑

∑ ∑ ∑

15 48 07 721 57 663

1 223 134 651 85 139

1

2

1

1

2

1 1

, ., , , ,

,, ,, ,.

Then 

MSE = 134 651 26 48 1 223 1 15 85 139 − −

13

, ( . )( , ) ( . )( , ) = 19.11.

The average number of cars in the trailhead parking lot was 45 per day.

Therefore, the associated number of visitors was estimated to be 26.48 +

1.15(45) = 78. The 95 percent prediction interval for this estimate is:

78 2 19 11 1 1

15

45 48 07

57 633 721 15

2

2 ± ++ −

− (.) ( .), / = 78 ± 39 = (39, 117).

Example of the sample relationship between

number of cars and visitors.

0 

50 

100 

150 

200 

10 18 21 25 32 60 105 132

Car Counts

Snow Lake Data

Visitor Counts
196 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

Correlation

Rather than predict the value of Y from X, we may be interested only in

determining the strength of the linear association between the two variables.

Correlation analysis does not assume a cause-and-effect relationship between X and Y.

The correlation between two variables is expressed as a coefficient (the

correlation coefficient r), rather than an equation. The value of r does not

depend on which variable is designated X and which is Y; neither is it affected

by the units in which X and Y are measured. The correlation coefficient

always takes on a value between –1 and +1. If r is near 0, this is interpreted

as the absence of a linear relationship; it does not necessarily mean that there

is no relationship at all. A “strong” correlation is implied if |r| ≥ 0.8, a

correlation is “weak” if |r| ≤ 0.5, and a correlation is “moderate” if 0.5 < |r|

< 0.8. However, if the association between the two variables is curved, the

calculated r will underestimate the true strength of the relationship; conversely, r will be too high if several observations are different from the rest.

Therefore, it is critical to examine a scatterplot of the data before attempting

to interpret the practical significance of r.

Example. The correlation between car counts and visitor counts is:

r = 0 86 . = 0.93.

Calibration

An important part of all wilderness use studies is the evaluation of the

reliability of different methods of data collection. In general, reliability is

assessed by comparing two methods of measuring a given use characteristic;

calibration is the determination of how well the two measures agree. For

example, it is a common practice to evaluate the effectiveness of mechanized

counters for obtaining visitor traffic counts by comparing readings to data

collected by human observers. In these cases, one method (for example,

human observers) is known to be highly accurate, but is relatively expensive;

the other method may be cheaper and less time intensive to operate, but the

accuracy is unknown or variable. The investigator uses the two different

methods to obtain a simultaneous measure of a given use characteristic (the

observations are therefore paired). If agreement between the two methods is

high, the cheaper method can be substituted with no loss of accuracy.

Alternatively, there may be no agreement between methods, indicating that

no substitution is possible. A third alternative is that the data obtained from

the new method show consistent deviations from the values obtained by the

original method. The bias associated with the new method can be quantified,

and the cheaper method substituted for the old, with the data adjusted by the

appropriate correction factor.

There are several cautions to be observed when collecting and analyzing

calibration data:

1. The purpose of calibration is to assess the differences between paired

observations; this means the observations must be true pairs. For example, if

observations from human observers are to be used to check the accuracy of

a mechanical counter, human observers must take data for the same location

and for the same time periods as the mechanical counters. Suppose the
USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000 197

working day of the human observer is only 8 hours, but the mechanical

counter can run day and night. The counts made by the mechanical counter

outside the working hours of the human observer should not be included in

the analysis.

2. It is not correct to compare two methods by either (a) evaluating the

means and standard errors of each group separately, or (b) calculating the

correlation between methods. Using these analyses to evaluate the relative

merits of two different methods is completely misleading. A calibration

problem has only one randomly selected set of visitors, but two observations

are made for each individual visitor.

Comparing separately calculated means and standard errors implicitly

assumes that there are two randomly sampled populations. The correlation

coefficient is actually a test of how likely it is that the two variables are not

related at all; on the other hand, variables in a calibration problem are

obviously associated by their very nature.

3. Many errors of analysis and interpretation can be avoided by plotting the

data first.

These last two points can be demonstrated by a simple example. Suppose

A and B represent two methods of obtaining visitor count data. Figure 11

shows two situations where (a) there is little agreement between the two

methods, and (b) agreement is good, but method B gives consistently higher

readings than method A. Method A and method B can be summarized by the

same respective means and standard errors in both instances! However,

visual inspection of these data leads us to conclude that in the first case the

two methods do not agree and no substitution is possible; no further analysis

is required. In the second case, methods A and B appear to agree, but

estimates obtained from B would require adjustment by a constant correction factor; further calculations are performed to obtain the correction factor

and the associated precision.

The major assumption underlying all calibration techniques is that the

original relationship calculated for the calibration data remains the same

over the duration of the season. This will not be true in practice. For example,

visual calibration devices such as cameras may be triggered by leaves

blowing across the sensors, which will be more of a problem in autumn. The

Method C

Calibration Example 2

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70

Method A

Calibration Example 1

Method BMethod B

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70

Figure 11—Hypothetical examples of patterns of visitor count data

obtained by two methods. Example 1 shows poor agreement between

methods. Example 2 shows good agreement between methods.

Method B
198 USDA Forest Service Gen Tech. Rep. RMRS-GTR-56. 2000

sensitivity of the trigger device will be affected by battery aging and failure.

To assure accuracy in count data, calibration should be performed at

frequent intervals and, if possible, whenever the power source is changed,

and/or the trigger devices are altered.

The easiest method of calibrating or comparing two counting methods is to

first plot the data. The method considered most accurate is plotted along the

vertical axis and the candidate method is plotted along the horizontal axis.

A regression line may then be fitted to the data. If the slope is not significantly

different from zero, then there is no relationship between the two methods

and the candidate method should be discontinued. If the intercept (bo) is

nonzero, then there is an inherent bias between the two methods.

Consider the scatter plots in Figure 11.Methods A and C are to be evaluated

as more efficient or less costly alternatives to Method B. Figure 11A shows

no relationship between the two figures, and in fact the R2 value is 0.02, much

too close to 0 to indicate a useful relationship. The F ratio is 0.25, much less

than any critical value with 1 and 12 degrees of freedom. Figure 11B on the

other hand shows a fairly strong relationship, and in fact the R2

 value is 0.94

with an F ratio of 189.84. However the intercept is computed as 13.26,

meaning that Method C is underestimating the count obtained by Method B

by about 13 individuals. Because this is a strong relationship, knowing the

count using Method C, we can predict with good accuracy what the Method

B count would be.
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