Estimating Snag and 

Large Tree Densities and

Distributions on a Landscape

for Wildlife Management

Lisa J. Bate, Edward O. Garton, and Michael J. Wisdom

United States

Department of

Agriculture

Forest Service

Pacific Northwest

Research Station

General Technical

Report

PNW-GTR-425

June 1999
LISA J. BATE is a wildlife biologist, and EDWARD O. GARTON is a professor, Fish 

and Wildlife Resources Department, University of Idaho, Moscow, ID 83844; and

MICHAEL J. WISDOM is a regional wildlife ecologist, U.S. Department of Agriculture,

Forest Service, Pacific Northwest Research Station, Forestry and Range Sciences

Laboratory, 1401 Gekeler Lane, La Grande, OR 97850.

Authors
Bate, Lisa J.; Garton, Edward O.; Wisdom, Michael J. 1999. Estimating snag and 

large tree densities and distributions on a landscape for wildlife management. 

Gen. Tech. Rep. PNW-GTR-425. Portland, OR: U.S. Department of Agriculture, 

Forest Service, Pacific Northwest Research Station. 76 p.

We provide efficient and accurate methods for sampling snags and large trees on a

landscape to conduct compliance and effectiveness monitoring for wildlife in relation to

the habitat standards and guidelines on National Forests. Included online are the necessary spreadsheets, macros, and instructions to conduct all surveys and analyses pertaining to estimation of snag and large tree densities and distributions at the subwatershed scale. The methods focus on optimizing sampling effort by choosing a plot size

appropriate for the specific forest conditions encountered. Two methods are available

for density analysis. Method one requires sampling until a desired precision level is

obtained for a density estimate. Method two is intended for use in areas that have low

snag densities compared to Forest plan targeted densities. After taking a minimum of

60 samples, one may test for a significant difference between the estimated and targeted densities. In addition, data can be used to calculate a distribution index. The value

obtained from the distribution index indicates whether the current distribution of target

snags and large trees across a subwatershed is adequate to meet the habitat needs of

territorial cavity-nesters and other wildlife species. Wildlife use also may be evaluated.

Keywords: Density, distribution, foraging, nesting, monitoring, sampling technique, snag,

large tree, woodpecker, wildlife management, wildlife use. 

Abstract
1 Introduction

4 General Information

4 Files Online

4 Sampling Applications

5 General Snag and Large Tree Sampling Guidelines

5 Landscape Definition and Selection

5 Sampling Objectives

6 Landscape Stratification

8 Methods

8 General Surveying Procedures

9 Establishing Transects

12 Plot Size Selection

14 Snag and Large Tree Survey Techniques

16 Computer Analysis

16 Data Entry

16 Consecutive Plots

17 Formulas

19 Cavity and Foraging Signs

20 Sorting Data Sets

20 Analysis by Segment

22 Analysis by Subsegment

22 Optimal Plot Size

25 Estimating Costs

26 Sample Size Determination

28 Estimating Densities

31 Distribution Analysis

34 Tutorials

34 Example I: Density and Distribution Analysis for 

Single Stratum Landscape

46 Example II: Density and Distribution Analysis for 

Subwatershed with Multiple Strata

61 Acknowledgments

61 English Equivalents

62 References

66 Appendix 1: General Snag and Large Tree Sampling Guidelines

72 Appendix 2: Field Form Explanations

75 Appendix 3: Recommended Plot Sizes for Presampling 

76 Appendix 4: Frequently Used Excel Commands in Computer Analysis

Contents
A wide variety of wildlife depend on snags and large trees for survival and reproduction.

In the Blue Mountains of Oregon and Washington, for example, 62 species of birds 

and mammals use snags or large trees for roosting, denning, feeding, or related life

functions (Thomas and others 1979). Woodpeckers are an especially important group

of species that depends on snags and large trees, and whose role in forested ecosystems is integral to the continued health of such systems. As primary cavity-nesters,

woodpeckers excavate nest and roost sites for themselves and many other species. 

An absence of viable woodpecker populations in fact, means an uncertain future for

secondary cavity-nesters, or nonexcavators. Woodpeckers often are referred to as 

indicator species because it has been assumed that if woodpecker populations are

maintained at viable levels, secondary cavity-nesting populations also will be present 

at viable levels (Thomas and others 1979).

Currently, the nesting and roosting needs of woodpeckers and other cavity-nesters are

assumed to be met by controlling only the density of snags, standing dead trees, on

public lands. This is based on a snag model developed by Thomas and others (1979);

this model assumed a positive, linear relation between woodpecker and snag abundance in the Blue Mountains of Oregon. This relation was confirmed by Mannan and

others (1980) for forests in western Oregon (as stated in Nietro and others 1985). 

The model, however, did not account for the foraging needs of woodpeckers and other

cavity-nesters, and more recent studies have shown that foraging structures can differ

from nesting and roosting structures for woodpeckers (Bate 1995, Bull and Holthausen

1993, Dixon 1995). For example, large trees (>20 inches [51 cm] diameter at breast

height [d.b.h]) are also critical for woodpecker populations; large trees develop deep 

furrows that harbor increased arthropod densities (Bull and others 1986, Mariani and

Manuwal 1990). Some species, such as the white-headed woodpecker (Picoides 

albolarvatus), depend on the seeds produced by mature ponderosa pine (Pinus 

ponderosa Dougl. ex Laws.) for autumn foraging (Dixon 1995). In addition, other

species such as the pileated woodpecker (Dryocopus pileatus) select large hollow 

trees for roosting (Bull and others 1992). Finally, retaining large trees across a 

landscape provides a continual source of large snags, even in areas managed 

primarily for timber resources.

Although most resource specialists recognize the need to retain adequate densities of

snags and large trees across a landscape, these structures have declined in abundance

for various reasons (Hann and others 1997). Large trees are targeted for removal 

during timber harvesting. Snags also have been systematically removed from public

lands. Historically, snags have been reduced because of even-age management 

techniques (Titus 1983), fuelwood cutting, and the elimination of snags as a source 

of disease and insect pests (Dickson and others 1983, Ffolliot 1983, Styskel 1983). 

In addition, Hope and McComb (1994) found that snag retention programs on National

Forests are hampered by problems with safety, funds, and inconsistent standards and

guidelines. Consequently, density, size, and condition of snags on National Forests

often fail to meet the snag (Morrison and others 1986) and woodpecker guidelines 

outlined in Forest plans (Bate 1995). 

1

Introduction
1 Deschutes National Forest, Bend and Fort Rock Ranger 

Districts, 1230 NE 3d, Suite A-262, Bend, OR 97701.

2 Willamette National Forest, Blue River Ranger 

District, Blue River, OR 97413.

Cavity-nesting birds are not the only species affected by reduced snag densities.

Commodity values of timber can be reduced by insect damage. Most cavity-nesters 

are insectivores, and have proven instrumental in preventing, or retarding, local insect

outbreaks (Beebe 1974, Otvos 1979). Some species of woodpeckers will aggregate in

areas where insect outbreaks are occurring, thus accelerating the decline of the insect

population (Otvos 1979). In addition, as foraging woodpeckers remove the bark of 

beetle-infested trees by chipping and probing, the microenvironment of the remaining

beetle eggs and larvae is altered. The remaining eggs and larvae may be more 

susceptible to mortality caused by parasites and extreme temperature fluctuations

(Otvos 1979). Thomas and others (1979) provided additional compelling arguments 

and evidence in support of maintaining viable populations of woodpeckers and other

insectivores for their benefits to forest-based economies.

National Forests are required to maintain viable levels of native wildlife populations 

on public lands. This was the objective in 1974 when the Forest and Rangeland

Renewable Resources Planning Act (RPA) became law (Forest and Rangeland

Renewable Resources Planning Act 1974). Then in 1976, the National Forest

Management Act was passed as an amendment to the RPA. This second law 

requires the preparation of forest plans that include periodic evaluation and 

monitoring of management objectives, standards, and guidelines for National Forest

Service lands and its resources (U.S. Laws, National Forest Management Act 1976).

Woodpeckers, an important wildlife resource because of their role as indicator 

species and controlling agents of forest insect pests, are a primary focus of the 

Forest Service’s monitoring efforts. 

To help ensure that viability requirements are met, targeted woodpecker and snag 

densities are set by each National Forest based on land use allocation and the forest

community type. Many National Forests use the findings from the Blue Mountains for

their target guidelines (Thomas and others 1979). For example, at the Deschutes

National Forest, old-growth and riparian areas are managed for 100 percent of the

woodpecker potential maximum population (PMP)(Thomas and others 1979), whereas

in even-aged ponderosa pine harvest units, visual corridors, and deer management

areas, 40 percent of the PMP is the objective (Deschutes National Forest plan 1992).1

In contrast, forests west of the Cascade Range such as the Willamette National Forest

aim to maintain habitat capability at the 40 percent PMP (Nietro and others 1985) level

on all subwatersheds (Willamette National Forest plan 1992).2

There are three types of monitoring in National Forests: implementation, effectiveness,

and validation. Implementation, or compliance, monitoring determines whether a

National Forest complies with the objectives, standards, and guidelines outlined in 

their Forest plan. For example, Were a minimum of 0.9 snags per acre (2.2 snags per

ha) left in a stand after timber harvest? Effectiveness monitoring refers to periodically 

collecting the necessary data to determine whether management actions are producing

the desired effect. For example, Are woodpeckers present at 40 percent of their PMP

(Thomas and others 1979) level when 0.9 snags per acre (2.2 snags per ha) are left? 

2
Validation monitoring collects information to support, or refute, the assumptions of the

guidelines and objectives stated in the Forest plan for a particular species. For example, Does woodpecker abundance respond in a positive, linear fashion to increasing

snag densities? (Wisdom and others, in prep.).

Monitoring requires both time and money. If resource specialists are to monitor woodpecker habitat, therefore, they need efficient and statistically valid methods to achieve

monitoring objectives. Key decisions managers must make before sampling snags and

large trees are the shape and size of plot that statistically is most efficient. Bull and 

others (1990) tested the efficiency and accuracy of both fixed- and variable-radius 

circular plots to determine snag densities. They found that 1-acre and variable plots,

with a factor-5 prism, worked best for areas with snag densities ranging from 0.7 to 2

snags per acre (1.7 to 4.9 snags per ha). In areas obscured by vegetation, or in steep, 

difficult terrain, however, it may be difficult to accurately count all snags in these plot

sizes. In addition, Krebs (1989) states that most ecologists have found that long, thin or

rectangular plots work better than circular or square plots in the same area. The habitat

components of a forest are never uniformly distributed; rather, there are often clumps, or

patches, of habitat components such as snags and trees. Consequently, rectangular

plots are better for sampling because they cross more clumps of snags or trees, rather

than encircling, or missing, them completely. This results in a lowered variance, which

translates into smaller sample sizes. Rectangular plots therefore are recognized as the

optimal plot shape for sampling in patchy habitats. For the optimal plot size, however,

each forest situation needs to be analyzed independently (Krebs 1989). 

This report provides resource specialists with efficient and accurate methods to sample

snags and large trees with the use of rectangular plots. This report also was written in

response to the concern that many National Forest subwatersheds fail to provide the

necessary densities of snags and large trees to maintain viable populations of cavitynesters (Bate 1995, Morrison and others 1986). Currently, most National Forests east of

the Cascade Range use the snag densities recommended by Thomas and others

(1979) for woodpecker management. Bull and Holthausen (1993), however, found that

pileated woodpecker densities were less than what this model would have predicted by

snag numbers alone. In addition, recent studies suggest that current snag density

guidelines may be too low to produce the desired levels of woodpecker abundance

because the guidelines focus only on their nesting needs (Bull and others 1997). The

primary purpose of these methods is therefore to conduct compliance and effectiveness

monitoring for woodpeckers in relation to the habitat standards and guidelines of

National Forests. 

The necessary spreadsheets and macros (Excel Version 5.0)3 to conduct all analyses

pertaining to snag and large tree densities and distributions on a landscape can be found

online at http://www.fs.fed.us/pnw/snags. Guidelines for stratification are included to

reduce sampling effort and to increase precision of an estimate (Krebs 1989). Methods

presented will help resource specialists to optimize their sampling effort by choosing a plot

size that minimizes the number of samples required for their specific forest conditions.

3

3 The use of trade or firm names in this publication 

is for reader information and does not imply endorsement

by the U.S. Department of Agriculture of any product or service.
Two methods are available for density analysis. Method one requires sampling until a

desired level of precision is obtained for a density estimate, for example, a density 

estimate that could be within 20 percent of the true mean, 90 percent of the time. 

The second density analysis method was developed for sampling in areas that have 

low snag densities compared to targeted densities. After taking a minimum of 60 samples, a resource specialist may test for a significant difference between the estimated

and targeted densities. In addition, resource specialists can use their data to calculate 

a distribution index. The Distribution Index will estimate how evenly distributed target

snags or large trees are across a landscape; this index is based on the proportion of 

the sampled landscape supporting target snags or large trees. 

Four files will accompany each report. They can be found online at http://www.fs.fed.us/

pnw/snags. Both English and metric versions are available. The file names for the

English versions are (1) Estimate.xls, (2) Single.xls, (3) Strate.xls, and (4) Append2.doc.

The file names for the metric version equivalents are (1) Estimatm.xls, (2) Singlem.xls,

(3) Stratm.xls, and (4) Append2.doc. Within these files are the data forms, data sets,

macros, and spreadsheets necessary for snag and large tree density and distribution

analyses on landscapes. The files named *.xls were created and are intended for use in

Microsoft Excel Version 5.0. The Append2.doc is a Microsoft Word Version 6.0c document. It contains detailed explanations of each item on the field form and has been

made available on disk for modification for specific forest conditions. Please make backup copies of all files before beginning any data entry or analyses.

The file Estimate.xls (Estimatm.xls) contains no data; this is where your own data

should be entered.

Two files containing data sets are provided for tutorial purposes: (1) Single.xls (Singlem.xls)

and (2) Strate.xls (Stratm.xls). The file Single.xls (Singlem.xls) contains a subset of the

data collected from a 900-acre (364-ha) old-growth ponderosa pine forest. It represents an

example of a landscape area smaller than the typical subwatershed. The file Strate.xls

(Stratm.xls) contains a subset of the data collected from a 4,347-acre (1760-ha) Douglas-fir

(Pseudotsuga menziesii (Mirb.) Franco)/western hemlock (Tsuga heterophylla (Raf.) Sarg.)

subwatershed. This subwatershed was delineated into three strata (Bate 1995). These two

files are identical in every way except for the data sets they contain.

All working spreadsheets are protected with the exception of the Optimal sheet. 

Only the shaded areas on each of these spreadsheets therefore can accept alphanumeric

information from you. This protects the formulas and format necessary to conduct all

analyses. In the “Computer Analysis” section of this report, users will find the background,

statistics and discussion of each macro and spreadsheet. In the “Tutorial” sections,

detailed operating instructions are given for using the two sample data sets provided.

Although these sampling techniques were designed to address objectives for the management of woodpeckers, these techniques may be used for any wildlife species associated with snags and large trees. For example, a manager may want to determine the

4

General

Information

Files Online

Sampling Applications
difference in large, hollow tree densities between two subwatershed areas for black

bears (Ursus americanus). These sampling techniques would be appropriate for this

objective.

In addition, these techniques may be used to complement the information collected in

other monitoring projects. For example, the USDA Forest Service’s current vegetation

survey (USDA Forest Service 1993) collects Forest habitat data from the same permanently established plots every 8 years. These plots are located on a 1.7-mile (2.7-km)

grid across Oregon and Washington on National Forest Service lands. The final product of both of these monitoring techniques could be converted to similar units of 

measurement (e.g., no. per acre [no. per ha]) to provide additional baseline data for

resource specialists. 

A condensed outline of the guidelines for sampling snag and large trees can be found in

appendix 1. A more detailed discussion of the topics in the outline follows. 

The first step in sampling snags and large trees is to select the area to be surveyed.

Our snag and large tree sampling methods were developed to be compatible with the

intended sampling unit for the Forest Service’s woodpecker monitoring program, which

was defined as a landscape ranging from 3,000 to 7,000 acres (1215 to 2834 ha) (Bull

and others 1991). Our sampling methods also are intended for use on a subwatershed

scale with some slight modifications. See the “Establishing Transects” and “Compare to

Target” sections for details. Subwatersheds average nearly 20,000 acres (8097 ha)

within the interior Columbia basin (Quigley and others 1996) but can be as small as

1,000 acres (405 ha). 

The area to be sampled, however, need not be a delineated subwatershed. For example, a manager may want to know the estimated snag and large tree density within an

old-growth Research Natural Area that comprises only 900 acres (364 ha). These

methods will work for this situation as well. Our sampling methods, however, are not

intended for small-scale sampling such as an individual stand (<100 acres [40 ha]);

complete counts are more appropriate in individual stands. 

After a landscape area has been selected for sampling, the next step is to specify the

sampling objectives. Doing this will dictate the stratification process and can aid in the

decisionmaking process for optimal plot size. The following questions should be

answered before sampling begins: (1) What size class of snags or large trees will be

surveyed (e.g., what d.b.h. and height)? (2) What condition of snags and large trees will

be surveyed? (e.g., both hard and soft snags? Hollow trees? All trees?) (3) Should any

species be excluded (e.g., if a particular tree species is known to provide little, if any,

wildlife value, should it be excluded from your sampling program)? and (4) Should signs

of wildlife use be recorded (e.g., woodpecker foraging and nesting signs)? Your choices

will ultimately determine the amount of time and resources needed to obtain a density

estimate with a desired level of precision. In addition, several of these choices will

affect the outcome of the Compare to Target density estimate test and the Distribution

Index found in the “Computer Analysis” section of this paper.

5

General Snag and

Large Tree Sampling

Guidelines

Landscape Definition

and Selection

Sampling Objectives
Perhaps the most critical step in any snag or large tree sampling program is deciding 

on the stratification process. Although the initial investment of time spent in the stratification process can be large, if done correctly, this process should reduce the final

requirement of resources and provide a more precise density estimate (Krebs 1989).

Before stratification of a landscape begins, however, we recommend checking with 

local foresters. Field-level foresters often stratify for other sampling needs, and their

delineations may work well for purposes outlined here.

If the landscape is homogeneous throughout in regard to snag or large tree densities,

there is probably little to be gained by stratifying. Whether a landscape should be stratified before sampling begins, however, depends on several factors. Cochran (1977) 

presents the three most common reasons:

1. Stratification may produce a gain in precision of the estimate. If the landscape 

is heterogeneous in regard to its snag or tree densities, creating individual 

strata, which are homogeneous within themselves, can improve the precision 

of an estimate.

2. Sampling problems can differ for different parts of the landscape because of 

forest community type, timber harvest method, or seral stage.

3. Resource specialists may want to obtain separate estimates for certain subdivisions of the landscape. For example, if part of a subwatershed is managed 

for 40 percent PMP, compared to another, which is managed for 100 percent 

PMP, stratification can provide separate estimates for each stratum.

If one or more of the above reasons applies to your situation, it would probably be 

beneficial to stratify. The spreadsheets contained within this report can accommodate

up to four strata.

To stratify your survey area, use the following steps: 

1. Visit the area if you are unfamiliar with it. Landscape patterns unclear on maps 

may become apparent from an initial ground survey. What differences are visible in

the vegetative structure across the landscape? What similarities exist? Begin to

think about strata that are homogeneous in regard to snag and large tree densities

or forest structure. 

2. Obtain reference maps for use in the field. Use whatever maps are available. For

example, either geographical information system (GIS), or orthoquad maps, or both,

can contain the following necessary information: (a) current road system with all

detectable roads drawn, (b) stand units and their unique numeric identifier for each

stand, and (c) current seral stage of vegetation. We recommend using maps scaled

to 1:31,680 or less. This information may be contained on one or several maps.

Make several copies of a map with the stand units delineated.

6

Landscape

Stratification
3. Obtain the most current aerial photographs of the survey area.

4. Run a query by using either the GIS or any stand exam database available.

Because each local area (district) has its own approach to the storage of stand

data, we recommend first checking with the data specialist to develop the most efficient approach to obtaining this information if you are unfamiliar with its recovery.

You are interested in what each stand supports in regard to (a) the current community type, (b) the management history, (c) seral stage, and (d) snag and large tree

densities. For example, Has the stand ever been harvested? Was regeneration

successful? Has it been thinned? If harvested, what method was used? Were

snags retained? Were large trees retained? Use the aerial photographs to confirm

the database information. 

5. Visit the area with the above information.

6. Assign each stand to a stratum. Plan on spending at least one day in the field to

validate the information you have received from the GIS or stand exam database.

Generally, the amount of time spent in the field for stratification purposes will be

directly related to the quality of the information collected from the GIS or stand

exam database. Additional field days may be required to complete the stratification

work. This is case-specific and depends on the resource specialist’s knowledge of

the area.

7. Estimate the number of acres (ha) within each stand or stratum.

We assume that most landscapes surveyed for snags and large trees will have undergone some amount of timber harvest. Consequently, depending on the primary method

of timber harvesting, the placement of each stand unit within a stratum may or may not

be straightforward. For example, on the west side of the central Oregon Cascade Range

where clearcutting has been the primary method of timber harvest, the delineation of

strata for a snag survey should be relatively apparent.

For this situation, combine all unharvested, old-growth stands into a single stratum.

Then consult the silviculturist, and conduct a groundcheck to determine at what age tree

and shrub growth are great enough to interfere with the sightability of snags within the

harvested stands. Separate all harvested stands with overgrown vegetation from those

that remain visually open. These overgrown stands would be your second-growth

stands. Finally, combine all stands that have been harvested more recently where the

line of vision still extends out to at least 66 feet (20 m). This should give you three 

strata: (1) recent clearcut stands, (2) second-growth stands, and (3) old-growth stands.

Then generate a map with each stand assigned to one of the three strata for use in 

the field.

By contrast, in areas where selective logging has occurred, the designation of individual

strata takes more time, especially where no GIS layers are available. In this situation,

first place stands into strata based on ocular estimation. This can usually be done from

7
stationary viewpoints within or near the edge of stands, oftentimes without having to

venture far from roads. For example, in a subwatershed composed of a mix of ponderosa pine and lodgepole pine (Pinus contorta Dougl. ex Loud.) stands, three strata

might be possible, based on various tree composition and varying snag densities: (1)

stands dominated by ponderosa pine with few snags observed; (2) stands represented

by codominance of ponderosa and lodgepole pine trees, with usually one or two snags

per acre observed; and (3) stands dominated by lodgepole pine tree with two or more

snags per acre observed. 

Remember, the main criteria in making the decision to stratify a subwatershed are the

sampling objectives. For example, if the sample is designed exclusively for estimating

the density of large trees, the stratification can be dictated solely by this variable. If both

large trees and snags are of interest, stratification should be done based on which of

the two (trees or snags) appears to be more variable. In areas where clearcutting is the

common method of timber harvest, the density of snags and large trees often is highly

correlated, and stratification can be done reliably by using either variable.

The second criterion should be either seral stage or timber harvest technique. Do you

expect that certain stands will be more difficult to survey than others? If so, separate

these out. The final criterion should be forest community. This is especially important for

snags in areas undergoing insect or disease events. Certain tree species are more susceptible to insects or diseases; therefore, where these trees are located, you can expect

higher densities of snags. This may be the situation where lodgepole pine trees intersperse with ponderosa pine.

Field equipment—Surveyors will require some or all of the field equipment in the 

list following: 

Item Use 

1. Accurate map showing stand units 

with stratum number Record correct stratum number

2. Road map Determine location and access

3. Aerial photographs Determine stratum and locations

4. Orthophoto quads Determine stratum and locations

5. Field data forms Record survey information

6. Hip-chain Measure transect distances; mark 

center line of transect

7. Biodegradable hip-chain line Same as above

8. Diameter or Biltmore stick Measure diameter of snags or trees

9. Clinometer Measure heights of snags or trees

10. Compass Determine bearings 

11. Meter tape >66 feet (20 m) long Measure perpendicular distances from 

the center line

12. Pocket knife Determine species and decay class 

of snags

13. Flagging Mark ends of subsegments, if necessary 

14. Stake Secure end of tape measurer if only 

one observer

8

Methods

General Surveying

Procedures
Field forms—Standardized field forms are provided to record the necessary snag and

large tree information for density and distribution analyses. If both snag and large tree

data are recorded simultaneously, these data should be entered into separate files. All

data entered into the spreadsheet should be numeric, following the format shown on the

sample sheet (fig. 1). If available, hand-held computers can be used for data entry 

in the field. The spreadsheets were created with this purpose in mind and data can 

be entered directly onto Sheet 1. This eliminates the need to enter the data from the 

field forms.

If hand-held computers are not used, however, field forms can be produced by using the

macro Dataform. It will create data forms on a blank worksheet for use in the field. 

To create a data form (1) open the Estimate.xls (Estimatm.xls) file; (2) select any blank

sheet in the file (e.g., Sheet 4); (3) select Macro from the Tools menu; (4) highlight

Dataform; (5) choose Run; (6) highlight entire page with mouse; and (7) then choose

Selection, instead of Sheet, under the Print options. This will create data forms with 

grid lines (fig. 1). 

Appendix 2 provides detailed explanations for the correct input of snag and large tree

habitat information. It is also online (filename: Append2.doc) so that it can be customized for different areas; each forest will most likely have different snag and tree

species encountered. Resource specialists also have the option to alter the requirements for each field variable to meet their objectives. For example, should heights 

be recorded to the nearest foot or meter? What wildlife signs should be recorded? 

Option 1: landscape method—Use the following steps to establish transects by using

the entire landscape: (1) randomly place a grid over the subwatershed map; (2) randomly

select five grid points within each stratum that will be used to establish starting points for

each transect; (3) randomly select compass bearings for each of the five transect starting points; and (4) determine if each of the five transects within each stratum fall within

sufficient area of the stratum to allow four sample subsegments (one subsegment = 

164 feet [50 m]) to be placed; if not, select additional transects and starting points until 

a total of 20 samples (subsegment lengths), from a minimum of five stands, have been

located within each stratum (fig. 2). 

Use a random numbers table for any of the selections above, or generate random numbers using the second hand of a watch. If a watch is used to generate random starting

direction, multiply the number of seconds by six to obtain any of 360 random numbers

that can be used as compass bearings for the starting point.

Option 2: stand method—In areas composed of highly fragmented small stands, it may

be more efficient to dispense with the grid method for establishing transects. For example, some clearcut stands in western Oregon are just large enough to accommodate 654

feet (200 m), or four subsegments of randomly established transect. To establish transects in highly fragmented areas (1) select stands for sampling by randomly picking

stand unit numbers from the complete list of stands within that stratum; (2) select a 

random point along the road bordering the stand as an entry point into the stand; and

9

Establishing Transects
10

Figure 1–Sample data form.
11

Figure 2—Example of pilot survey transect establishment on landscape with three strata. A maximum of four

subsegments should be surveyed along each transect within each stand. A minimum of 20 subsegment samples should be taken within each stratum for the pilot survey. Each subsegment is given a unique numeric

identifier (e.g., 1.1, 1.2, 2.1, and 2.2). Two subsegments comprise one segment. Segments are identified by

the whole number associated with the subsegment number.

(3) from the point along the road, randomly select a starting point from which to establish a transect within 164 feet (50 m) of the road. In this way, you can usually sample 

at least four subsegments within each clearcut stand.
12

The pilot survey should include a minimum of 20 samples taken within each stratum.

For nonstratified landscapes, 20 total samples are needed for the pilot survey.

Subsegment plots are 164 feet (50 m) long. One subsegment is considered one 

sample for the pilot survey. Segment plots are 328 feet (100 m) long. Two consecutive

subsegments constitute one segment (fig. 3). The 20 samples should be taken from 

at least five different stands for each stratum, or four subsegments (656 feet [200 m])

within each stand (fig. 2). This is necessary to ensure that the variability within each

stratum is adequately represented and will provide a better estimate of the sample size

required for your objectives.

On large subwatersheds, the stands in which the pilot samples are taken should not be

near each other. This is especially important on subwatersheds that encompass several

plant communities because of an elevational gradient. In this situation, divide the subwatershed into three sections and equally divide your samples throughout these sections.

Once the requirements of the pilot survey have been met and the optimal plot size within each stratum has been selected, transects longer than four subsegments in length

(656 feet [200 m]) may be established. Transects within a stand should not exceed 12

subsegment lengths (1,968 feet [600 m]). If the transect crosses through many stands

(and consequently different strata), however, this distance may be increased up to 24

subsegment lengths (3,936 feet [1200 m]) if large samples are required. Use your best

judgment in how long a transect should be to ensure that you adequately sample the

natural variability of the landscape. For landscapes >7,000 acres (2834 ha), it would be

best to continue to establish short transects (four subsegment lengths) after the pilot

survey if your only objective is to compare the estimated density to the targeted density

of snags or trees. See the “Compare to Target Density” section for details.

Presampling selection–In some situations, it may be more practical to preselect a plot

size for sampling, rather than conducting the Optimal Plot Size analysis (see “Optimal

Plot Size” in the “Computer Analysis” section). This can often be determined based on

information gathered during the stratification process. For example, in low-density (<1

snags per acre [0.4 snags per ha]) clearcut strata where travel is easy, a statistical

review of the data reveals little about the optimal plot size. Rather, wider plots should be

used to collect data on as many snags or large trees as possible. 

In steep, rugged terrain, or in densely overgrown forest, the wider plots should not be

used because they are inefficient and prone to inaccuracies in these conditions. By contrast, the narrower plots make it easier to detect snags and large trees within the plot

boundaries and to measure their distances. Then, in areas where snag numbers tend to

be low, but clumps of snags are present because of disease or insect events, the

longer, narrower plots work best to minimize the variance. See appendix 3 for additional

information on presampling plot size selection in various forest conditions.

Postsampling selection–In most forested conditions, the optimal plot size to use for

sampling is unknown until a pilot sample has been collected. Then you have estimates of

the density and distribution of the snags or trees in the area. Then use the pilot-sample

Plot Size Selection
Figure 3—The eight plot sizes available for sampling snags and large trees: two possible lengths and four

possible widths. During the pilot survey, the smallest plot size is nested within the larger plots until an optimal

plot size is selected. Then the optimal plot size is used for the remainder of the survey. The Width33(10) -

Width132(40) plots refer to the entire width (feet [m]) of the plot. Therefore, only snags or trees whose measured distance from the center line is ≤ half of the width qualify for a specific plot size when determining the

optimal plot size. For example, a snag that is 23 feet (7 m) away from the center line qualifies for the

Width66(20), Width99(30), and Width132(40) plot sizes. It does not qualify, however, for the Width33(10) plot

because its measured distance is not ≤16.5 feet (5m), which is half-width of the Width33(10) plot.

13
data to determine which plot size minimizes your sampling effort to obtain your desired

objectives. See the “Optimal Plot Size” analysis section for details. Then the Optimal

plot size can be used for the remainder of the survey. 

One of the most critical steps of any snag and large tree survey is to conduct a pilot

survey. The two main objectives in conducting a pilot survey are to (1) collect preliminary data by which to identify the optimal plot size and (2) obtain an estimate of the total

number of samples required to meet your objectives. It is important to recognize that

pilot data are not extraneous data to be discarded. Rather, they are the first samples

collected and to be included in the density and distribution estimates for the entire subwatershed. In areas where snag and large tree densities are high, the pilot survey in

itself may provide an adequate number of samples to meet objectives. By contrast, in

areas where snag and large tree densities are low, analyzing pilot data for the optimal

plot size can greatly reduce the number of samples needed to obtain a desired level of

precision. The optimal plot size can then be used to collect the remainder of the data.

Follow these steps to conduct the pilot survey: (1) use a hip-chain to establish transects;

start transects from the randomly selected points described above, (2) delineate subsegment lengths (164 feet [50 m]) and segment lengths (328 feet [100 m]) along the

transect as you walk, (3) assign a unique numeric identifier to each segment and subsegment as you establish them, and (4) conduct a complete count of all qualifying snags

or trees out to 66 feet (20 m) from the center line. The hip-chain line functions as the

center line. A snag or tree is considered “in” if its midpoint is <66 feet (20 m) from the

center line. 

Exceptions to this procedure occur when the stratum to be surveyed has reduced 

visibility (<33 feet [10 m]) or high densities (>15 snags or trees per plot are consistently

counted). In these conditions, snags and trees should be counted to 33 feet (10 m)

either side of the center line. See “Presampling Selection” for selecting plot size for

other exceptions to this procedure. After the pilot survey is completed, snags and trees

should be counted to the boundary of the plot size selected rather than 66 feet (20 m)

either side of the center line.

Samples are taken along the transects you have established as described above.

During sampling, it will always be necessary to survey subsegments (164 feet [50 m]) in

sets of two so that combined, they equal one segment (328 feet [100 m]). If at any time

it is not possible to survey two consecutive subsegments, because of stratum changes,

discard the single subsegment plot from the data set. This is critical for the analyses.

Otherwise the spreadsheets will yield erroneous results about optimal transect sizes,

densities, and distributions.

There are four possible widths for both subsegments and segments resulting in a total

of eight possible plot sizes (fig. 3). The four widths available are 33, 66, 99, and 132

feet (10, 20, 30, and 40 m, respectively). These are the whole widths of the plots.

These are referred to as Width33, Width66, Width99, and Width132 plots, respectively,

14

Snag and Large Tree

Survey Techniques
in the English version of these spreadsheets. In the metric version, these plots are

referred to as the Width10, Width20, Width30, and Width40 plots, respectively. The half

width of each of these plots is then 16.5, 33, 49.5, and 66 feet (5, 10, 15, and 20 m,

respectively). The half width is the distance out from the center line to which all snags or

trees are counted for each chosen plot width size (fig. 3). All snags and trees should be

measured to their midpoints.

A snag or tree qualifies if it meets stipulated criteria. For each snag or tree encountered,

record the following information: (1) stratum number, (2) segment number, (3) subsegment number, (4) perpendicular distance of the midpoint of the snag or tree in feet (m)

from the center line, (5) species, (6) decay, (snags) or structural (large tree) class, (7)

d.b.h., and (8) height (fig. 1). These fields must be entered for the spreadsheets to operate correctly. Refer to appendix 2 for details about each field variable. The location,

cavity and forage fields are optional. The location field can correspond to (1) the stand

number from which the transect originates, (2) the transect starting position determined

by a global positioning system (GPS), or (3) the Universal Transverse Meridian (UTM)

coordinates of the transect starting point. The Width33(10)-Width132(40) fields are to

be left blank while in the field. These will be automatically filled in by the spreadsheets

during the computer analysis (fig. 1).

Other field variables also may be recorded during surveys. For example, the seral

stage of the stand, distance to the nearest edge, and immediate habitat surrounding a

snag or tree can influence whether it is used by wildlife species. Resource specialists

therefore, may want to include additional habitat variables to measure. Note, however,

that spreadsheet columns to record additional habitat information should be placed at

least four columns to the right of the foraging field before any cavity or foraging analyses occur. Columns “A-S” should not be altered if the macros are to properly operate. 

In addition to the field variables listed above, several header row variables must be 

filled in for each snag or tree encountered: (1) forest, (2) district, (3) subwatershed, 

(4) observer, (5) date, and (6) pages. Because the information recorded for each of

these variables may be the same for each row, data columns are set to the far right of

the data entry spreadsheet. This allows for easy viewing of the data while providing a

permanent record of each of these variables for future referencing. Note that field

names for these header variables begin in column “T.” The columns for these header

rows can be moved.

The numbering system for segments and subsegments is important to follow to maintain

accuracy in all analyses. Each new segment should be given a unique whole number

even if it is a new segment within a different stratum, e.g., 1, 2, 3, etc. Two subsegments are nested within a segment. The subsegments therefore should have the same

whole number as the segment, plus a decimal number indicating whether it is the first 

or second subsegment. For example, for Segment 1, there should be a Subsegment

1.1 and a Subsegment 1.2. On each new day in the field, numbering of segments and

subsegments should follow consecutively from the previous day (fig. 2). If several

15
groups of observers are conducting surveys simultaneously, however, the numbering

sequence does not have to be consecutive; again, what is important is that each segment and subsegment plot has a unique numeric identifier. For example, if three groups

are surveying on the same day, one group can number plots in the single digits; another

can number plots in the 100 series, and so on.

Of all the fields found on the data sheet, Distance is the most important variable to

record accurately. In cases where no snags or trees are encountered, it is critical to

record a “9999” in the distance column. This allows the macros to distinguish between

plots without snags or trees versus plots that have snags or trees with a distance of “0”

because they are located directly on the center line. Periodically, supervisors should

calibrate measurements of the distance variable to ensure accurate collection of data.

Even small but consistent, overestimation or underestimation of this variable will yield

different results. Attention especially should be given to borderline cases. A borderline

case is one in which the distance of the snag or tree being surveyed falls on the edge

between two width intervals. For example, if a tree is estimated to be 33 feet (10 m)

away from the line, it is important to measure this distance exactly. To record 33 feet

(10 m) when the actual distance is 36 feet (11 m) will bias the accuracy of the data. 

We found that we could consistently pace the distance accurately in open, flat areas,

but borderline cases still should be measured. When vegetation or steep terrain make

pacing difficult, distances need to be measured with a tape to maintain accuracy.

In this section, we provide the background, statistics and discussion of each macro 

and spreadsheet. Refer to the “Tutorial” section for detailed operating instructions.

Appendix 4 contains frequently used Excel commands. No two data sets will be the

same size, and all macros have been written to accommodate this variation. Data set

lengths will differ depending on the overall densities of qualifying snags and trees, the

number of strata, and the total number of samples taken in a pilot survey.

Users should enter data into the file Estimate.xls (Estimatm.xls). To prepare for data

entry and analysis follow these steps: (1) open the Estimate.xls (Estimatm.xls) file; 

(2) rename the Estimate.xls (Estimatm.xls) file with the subwatershed name or another filename; (3) use the newly named file for your own data entry and analysis; this

preserves the file Estimate.xls (Estimatm.xls) in its original format for analysis of other

landscapes; (4) make backup copies of the Tutorial files, Single.xls (Singlem.xls) and

Strate.xls (Stratm.xls); this will preserve the original files for reference and tutorial purposes; (5) enter your data onto Sheet 1; several of the macros need to reference

Sheet 1 to work properly; and (6) double check here to ensure that the number “9999”

has been entered in each subsegment where no snags or trees were encountered;

failing to enter the number “9999” in these rows will cause miscalculations to occur.

Run the macro Consecutive before beginning any computer analysis. It will sort your

data set by segments and subsegments. This is important because data from the same

subsegment plots, entered accidentally or out of sequence, will be analyzed as a separate plot. After running this macro, it is extremely important to scroll through the entire

16

Computer Analysis

Consecutive Plots

Data Entry
data set to ensure that two subsegment plots are entered for each segment. For example, segment 13 should contain subsegments 13.1 and 13.2. If segment 13 only has

subsegment 13.1 listed but no subsegment 13.2, this entire segment and subsegment

should be deleted. Otherwise, the analyses for optimal plot size and a distribution index

will be inaccurate.

Filling the width columns, Width33(10)-Width132(40), with the appropriate formulas is

the first step performed by the computer analysis. You do not have to write the formulas

in the Width columns yourself. Rather, the macros Formula (Formmulti and Formsingle)

will create the appropriate formulas based on the information you supply in each of four

input boxes. These boxes will appear once the macro has begun running. Refer to the

“Tutorial” section for detailed operating instructions.

There are five criteria for which each snag or large tree is evaluated before a formula is

placed in each of the width columns: (1) d.b.h., (2) height, (3) decay (snags) or structural (trees) class, (4) species, and (5) distance. The first four criteria are relative fields;

the values accepted are those entered by the user. By contrast, the distance criterion is

an absolute field; the macro truncates the distances for each snag or tree in 16.5-foot

(5-m) intervals. Thus, four plot widths are created: 33, 66, 99, and 132 feet (10, 20, 30,

and 40 m, respectively). Again, these four plot widths correspond to the four blank

width columns: (1) Width33(10), (2) Width66(20), (3) Width99(30), and (4) Width132(40), 

respectively. 

The formulas are “If, then” statements. Therefore, if the snag or tree meets all the 

target criteria specified by the user, plus meets the distance requirement, then a “1” is

placed in the column by the macro. By contrast, if the snag or tree fails to meet all the

target criteria, then a “0” is placed in the column. Only those snags or trees that meet

all the requirements of the formula created by the user are given the value “1.”

Consequently, these are the only snags or trees that will be included for the statistical

analysis for each plot size. For example, if the perpendicular distance of a snag from

the center line was measured at 23 feet (7 m), it will qualify in the Width66(20),

Width99(30), and Width132(40) columns if it meets all other criteria. It will not be considered, however, for the Width33(10) column. This is because the Width33(10) column

represents a plot with a 33-foot (10-m) total width, or a 16.5-foot (5-m) half width.

Therefore, only snags or trees <16.5 feet (5 m) away from the center line, in either

direction, will be accepted within the Width33(10) column. See figure 3 for an example.

Two macros are available for entering the formulas for snag analyses. The macro

Formmulti can evaluate several species of snags. It also has the option of excluding a

single species from the analysis. For example, if a manager is interested in the snag

replacement potential provided by large trees, and knows that a species in the area is

not used for nesting purposes, this species may be excluded from the analysis by entering its numeric code when the species input box appears. By contrast, if a manager is

only interested in the density of a single large tree species, the macro Formsingle

allows for this narrowed focus in an analysis. Formsingle is identical to Formmulti (we

refer to both of these as the Formula macros) in every way except that it will evaluate

only a single snag or tree species at a time.

17

Formulas
The Formula macros will evaluate d.b.h. and height characteristics based on a minimum value you provide. By contrast, decay or structural classes are evaluated based

on a maximum value that you want considered for analysis. For example, in the

“Tutorials” provided, decay classes I-III are considered hard snags, and decay classes

IV-V are considered soft snags. This is based on the five-decay class system developed by Cline and others (1980). By entering the number three as the maximum decay

class value, therefore, only hard snags are included in the analysis. 

Parks and others (1997) have simplified this system by reducing the number of decay

classes to three. This has been done by combining Cline and other’s (1980) decay

classes II and III together, and classes IV and V together. Both systems are compatible.

The division between hard and soft snags therefore remains the same. We recommend

using the new system developed by Parks and others (1997) for future subwatershed

surveys for its simplicity to new users. 

Bull and others (1997) also provide descriptions of large tree structural variations important to wildlife. For example, hollow trees, trees with partial decay, and trees with

brooms provide a valuable wildlife resource. We recommend referring to Bull and others (1997) therefore before beginning a large tree survey to ensure that large tree structural classes are designed to meet your objectives. Refer to appendix 2 for an example.

Large tree numeric values should be arranged so that with increasing values, the tree is 

increasingly sound. This is the opposite of the decay class values for snags.

It is important that the width formulas are entered precisely because the macro uses

these columns to calculate the means and standard deviations of the data. When the

Formula macro is finished running, therefore, scroll down throughout each of the width

columns to ensure that they contain an “If, then” statement that looks like the following:

=IF(AND(I2<=16.5, K2<=5, L2>=10, M2>=6, J2<>9999),1,0) formula 1 (English).

=IF(AND(I2<=5, K2<=5, L2>=25, M2>=1.8, J2<>9999),1,0) formula 1 (metric).

This is the proper syntax for the formula in the Width33(10) column, for snags <16.5

feet (5 m) away from the line (cell range = I2), in all decay classes (cell range = K2),

with a d.b.h. >10 inch (25 cm [cell range = L2]), height >6 feet (1.8 m [cell range = M2]),

and all species (cell range = J2). If some cells are missing a formula, rerun the macro.

In addition, this macro must be run every time new data are added to the data sheet.

The macro should be run before the strata are separated to avoid having to run it multiple times. Double check that a “9999” is placed in the distance cell whenever a subsegment does not register any snags or trees. This will allow the macro to distinguish

between subsegments with zero snags or trees versus subsegments with a snag or a

tree on the line and a resulting distance of zero feet (m).

The Formula macros can take only maximums and minimums. If, however, you want to

determine the density of snags in a particular size class, these formulas can be edited.

For example, to determine the density of snags that are ≥10 inches (25 cm) d.b.h. and

<12 inches (31 cm) d.b.h., follow these steps: (1) run one of the Formula macros if they

18
have not been run already to create the proper syntax (see Formula 1) for the “If, then”

formula; (2) highlight the cell E2; (3) press the function key F2. This will allow you to

edit the formula; (4) insert L2<12 to the “If, then” statement (Formula 2); and (5) press

Enter. This will create the formula:

=IF(AND(I2<5, K2<=5, L2>=10, L2<12, M2>=6, J2<>9999),1,0) formula 2.

(6) Copy the formula in cell range E2; (7) paste this newly edited formula throughout the

E column; and (8) repeat this procedure for each Width column so that the macro maintains the distance requirement within each Width column. Similarly, if you are interested

in only one decay class of snags, or one structural class of large trees, run one of the

formula macros and edit it to conduct this narrower analysis. For example, if you are

interested in the density of hollow trees within a stratum, and hollow trees are identified

by the numeric code = 1, edit the “K” column in formula 1 shown above to the following:

=IF(AND(I2<=5, K2=1, L2>=10, M2>=6, J2<>9999),1,0) formula 3.

Next, copy and paste this formula throughout the Width33(10) column. Then repeat this

procedure for all width columns before running further analyses.

Depending on the objectives of your snag and large tree surveys, you may want to take

your analysis beyond densities and distributions. For example, if you want to determine

what snag species most of the cavities were found in, use the macro Cavity. Or, if you

are interested in what tree species exhibit the most foraging signs, you can analyze this

situation by using the macro Forage. Each of these macros can evaluate every snag or

large tree for five factors: (1) d.b.h., (2) height, (3) decay (snag) or structural (tree)

class, (4) species, and (5) cavity or foraging use. The main function of both of these

macros is to provide the user with a percent use value. This is calculated by taking the

number of snags or trees with cavities or foraging signs and then dividing this by the

total number of snags or trees encountered:

where

Pu = percent use;

Ss = number of snags or trees with nesting or foraging signs;

St = total number of snags or trees encountered; and

U = unknowns: entire snag or tree could not be examined or unknown whether 

foraging or nesting signs were present.

A separate column to the right of the cavity and forage columns is created for these

analyses (labeled “QUALIFYING”). Here you will find the formulas that are created and

placed into the spreadsheet by the macros. These formulas are also “If, then” statements. They evaluate each snag or tree for the target criteria you stipulate. Similar to

19

Cavity and 

Foraging Signs

Ss

St – U

Pu = , (1)
the Formula macros, these macros accept only one value for each input box. These

formulas, however, also can be edited to obtain the precise information on cavities or

foraging you desire. Please refer to the “Cavity” section in “Example I” of the “Tutorial”

for detailed instructions on operating the Cavity macro. 

Before conducting any cavity or foraging analyses, check to make sure that no zeros

are found in rows under the Cavity or Forage columns where no snags or trees were

encountered. The value zero is not acceptable here because the macros will view these

as data values in the analysis.

Few subwatersheds will be homogeneous enough to forgo stratification. In addition, the

optimal plot size likely will differ among heterogeneous strata, as will the means and

variances. Consequently, first separate the strata to analyze each stratum individually.

For nonstratified landscapes, proceed to the “Analysis by Segment” section.

The macro Sort will first sort the data set by stratum in ascending order. Then you will

be prompted to enter the ranges of each stratum. Use the scroll bar to determine the

ranges. Using the mouse to highlight the range will cause the macro to abort. The

macro will place each stratum on a separate sheet. These can be found by clicking on

the tabs labeled Stratum1, Stratum2, etc. If the names of these sheets are not in view,

use the arrows in the bottom left hand corner to tab left, or right, until they appear.

As additional data are collected, they should be entered directly onto Sheet 1 of your

file. Then rerun the Consecutive, Formula, and Sort macros. If for some reason you

have fewer rows of data for a stratum the second time you run the Sort macro, you

should first activate that stratum’s sheet and clear or delete all data on that page. The

macro will then place the correct number of rows of data on the sheet.

When the macro moves the data for each stratum, it takes with it the necessary format

and formulas to conduct all analyses. Simultaneously, it keeps the entire data set in its

original format on Sheet 1.

The macro Segment will compute averages, standard deviations, and sample sizes

based on plot lengths of 328 feet (100 m) or segments for each of the four plot widths.

When initiated, this macro will first sum the number of qualifying snags or trees within

each segment. The macro will then condense the spreadsheet and show only the number of trees or snags within each segment. These will be labeled as Totals but are also

referred to as Subtotals by Excel. We refer to these condensed rows as Subtotals.

After condensing the Subtotals, the macro will move them to a new area. This is necessary or else the macros will calculate averages and standard deviations by using the

original data rows and the Subtotals.

If at any time the Segment macro stops with an error message, restore the sheet to its

original state before running the macro again. To restore the sheet to its original format,

(1) press End within the Error message box if macro stops, (2) highlight all rows below

20

Sorting Data Sets

Analysis by Segment
the Grand Total Row, (3) select Delete from the Edit menu, and (4) click on Entire Row.

Then to remove the subtotals, (1) click on the field name SEGMENT, (2) from the Data

menu, select Subtotals, and (3) choose Remove All. With the exception of the first step,

these same steps must be performed whenever a new analysis is run using a different

macro.

There are several ways to determine the range of subtotals to be copied but only one

correct way to enter it into the input box. The proper syntax for a cell range is:

“E2:E213.” The range can be determined either by using the scroll bar or the arrow

keys and visually noting the end cell in the column. If you try to determine the range by

dragging the mouse, the cell range will look like this: =$E$2:$E$213. The “dollar” and

“equal” signs, however, need to be removed or the macro will abort; the macros work on

relative cell ranges to accommodate data sets of different lengths and the “$” refers to

an absolute cell range. If an input box ever blocks the view of the cell ranges, you can

move it by clicking on the title bar and dragging it to a new position.

Once the subtotals have been moved, you will then be prompted to enter the ranges 

of each of the newly pasted columns. The macro will then calculate averages and 

standard deviations for each segment plot width size:

Averages in Excel Version 5.0 are calculated by using the equation: 

where 

= sample mean,

xi = value of x observed in sample i, and

n = total number of samples.

Excel standard deviations are obtained by the equation: 

where

s = sample standard deviation.

The results will be placed both below the condensed rows of information at the cell

address you give, and in the appropriate columns on the Optimal sheet. Always direct

the macro to place the table of results at least three rows below the newly pasted data.

The macro also will provide you with the sample size (N) for this data set. This value is

not, however, automatically transferred to any other spreadsheet. It is good practice to

print out your results before continuing. At the end of this macro, you will be asked if

you want to be transferred to the Optimal sheet. Choosing “No” will keep you on the

active sheet.

21

∑ xi

n

–

x = , (2)

n ∑x i

2 – (∑x i)2

n (n–1 )

s = , (3)

x
To compute averages and standard deviations for subsegments, use the macro

Subsegment. Operation of this macro is identical to the Segment macro, but sums on

plot lengths of 164 feet (50 m) rather than 328 feet (100 m). To remove the Subtotals,

however, highlight the field name SUBSEGMENT rather than SEGMENT before selecting Subtotals from the Data menu.

To begin analysis to determine the optimal plot size within a stratum, bring up the

Optimal sheet by clicking on the tab with this label in the lower left screen. Any gray

boxes on this sheet require input from the user. (Note: This sheet could not be protected; please make backup copies in case of accidental entries.) The Stratum box in the

upper left portion of the sheet allows for a written description of the stratum. 

This is useful in situations where resource specialists want to determine what the 

optimal transect is for both hard snags and large trees. We recommend running the

optimal plot size analysis several times if more than one habitat variable is the focus of

the survey. The Minimum Sample Size Required box just below should contain one of

two numbers, 60 or 20. These numbers correspond to the minimum sample size

required for a simple-random, or stratified-random sampling design, respectively, within

each stratum. See the “Compare to Target” section for an exception to the minimum 

sample size required.

There are two options to determine the optimal plot size for a stratum or area. The first

option, the sample size option, examines the number of plots required for sampling in

comparison to the number of acres that would be sampled for the same plot size. 

The second option is based on Wiegert’s (1962) method, which incorporates a cost 

factor into the analysis. Both methods evaluate the estimated number of samples 

needed to obtain a density estimate that is within 20 percent of the true mean, 

90 percent of the time. 

The sample size option considers three factors: (1) the sample size required in plots 

(2) the sample size required in acres (ha), and (3) whether the estimated sample size 

(n) meets the minimum requirements. The required sample size is determined by

(Cochran 1977):

where

n = sample size required to estimate the mean density,

s = standard deviation of the mean within each plot size,

ta = Student’s t-value for a 90 percent confidence interval (a = 0.10), and

d = desired absolute error (calculated as 20 percent of the pilot mean).

First look at the number of sample plots required for each size. Then look at the estimated number of acres (ha) required for each specific plot size to obtain the same level

of precision. The optimal plot size is often that which requires the minimal number of

22

Optimal Plot Size

tas

d

2

( ) n = , (4)

Analysis by

Subsegment
plots and acres (ha) to be sampled, once the minimum sample size requirements have

been met. Often, several plot sizes will be appropriate. This is where the person who

has conducted the pilot sample needs to examine numbers given on the Optimal sheet

and consider, Would it be more efficient and accurate to use a wider or a narrower plot

width, given the forest conditions of this stratum? For example, the results on the

Optimal sheet may estimate that a Subsegment132(40) plot requires 20 more acres (49

ha) than a Subsegment66(20) plot to obtain the same level of precision. This seems like

a large difference, but what really matters is whether it will take a considerable amount

of extra time to survey to 66 feet (20 m) in a Subsegment132(40) plot, as opposed to

sampling only 33 feet (10 m) out from the line in a Subsegment66(20) plot. In areas

where snags or trees are present in low densities, and visibility is open to 66 feet (20 m)

from the center line, the Subsegment132(40) plots would probably be the best choice.

In contrast, if snag or tree densities are moderate or high, narrower plots are likely the

better choice. This will reduce sampling effort by decreasing the amount of time it takes

to complete each plot. In addition, users need to consider how easy or difficult it is to

see and reach snags or trees out to a specified distance. In steep terrain where shorter

snags may be obscured by vegetation, it is important to select a narrower plot size to

maintain accuracy.

The second option, which incorporates Wiegert’s (1962) method, can aid the decisionmaking process. Wiegert demonstrates that the optimal plot size is that which minimizes the product of the relative cost and the relative variance. Given that you have the

data necessary to determine both relative costs and variances, Wiegert’s method is considered preferable (Krebs 1989). It would be the most accurate to conduct time trials (to

estimate costs) to measure the amount of time it takes to survey each plot size within

your area. Then assuming that costs are directly related to time, relative costs could be 

incorporated into the optimal plot analysis. There are, however, some logistical difficulties with conducting time trials because only one plot size can be surveyed at a time. In

addition, time trials cannot be conducted simultaneously while conducting the pilot survey, which requires surveying snags or large trees to 66 feet (20 m) from the center line.

Consequently, the time (and costs) to conduct time trials may quickly offset any benefits

gained by acquiring this information because of the separate field efforts required

beyond the pilot survey.

We therefore recommend that resource specialists not conduct time trials. Rather, we

suggest that if a manager wants to include a cost factor, it is reasonable to use the general costs-per-sample guidelines that we developed. These costs are all built on a relative scale. We have outlined our methods for developing cost estimates, however, so

that resource specialists may understand how the costs were derived. Subsequently,

resource specialists may adjust these costs for their survey areas, or conduct their own

time trials, if they believe their surveys would benefit from the effort.

If resource specialists prefer to incorporate a cost factor into the analysis, six costs per

plot scenarios are listed at the bottom of the Optimal sheet under the General Cost per

Sample Guidelines based on the conditions listed in table 1. These have been made

23
available for demonstration. To understand how the relative cost affects the outcome 

of your decision about the optimal plot size, pick the category that best describes the

forest situation within the current stratum. Then copy and paste the information within

this column into the Cost per Sample above it. We encourage resource specialists 

to try several Cost per Sample categories if their forest conditions fall between the 

categories described.

24

Table 1—Cost estimates based on time trials to conduct snag (>10-inch [25-cm]

d.b.h.) surveys in different forest conditions

Time to walk plot Average

length number of Time per Total

Plot dimensions ( no snags)a snags per plot snaga timea Total costb

High visibility (>66 feet [20 m]); easy terrain (<30% slope); low (2 snags/acre [0.8/ha]) density

Subsegment33(10) 2 0.25 2 2.50 0.43

Subsegment66(20) 2 .50 2 3.00 .51

Subsegment99(30) 2 .75 2 3.50 .60

Subsegment132(40) 2 1.00 2 4.00 .68

High visibility (>66 feet [20 m]); easy terrain (<30% slope); high (8 snags/acre [3.2/ha]) density

Subsegment33(10) 2 1.00 2 4.00 .68

Subsegment66(20) 2 2.00 2 6.00 1.02

Subsegment99(30) 2 3.00 2 8.00 1.36

Subsegment132(40) 2 4.00 2 10.00 1.70

Medium visibility (a16.5 yards [15 m]); moderate terrain (<50% slope); low (2 snags/acre [0.8/ha])

density

Subsegment33(10) 3 .25 3 3.75 .64

Subsegment66(20) 3 .50 3 4.50 .77

Subsegment99(30) 4.5 .75 3 6.75 1.15

Subsegment132(40) 6.75 1.00 3 9.75 1.66

Medium visibility (a16.5 yards [15 m]); moderate terrain (<50% slope); high (8 snags/acre [3.2/ha]) 

density

Subsegment33(10) 3 1.00 3 5.00 .85

Subsegment66(20) 3 2.00 3 8.00 1.36

Subsegment99(30) 4.5 3.00 3 13.50 2.30

Subsegment132(40) 6.75 4.00 3 18.75 3.19
25

Estimating Costs

Table 1—Cost estimates based on time trials to conduct snag (>10-inch [25-cm]

d.b.h.) surveys in different forest conditions (continued)

Time to walk plot Average

length number of Time per Total

Plot dimensions ( no snags)a snags per plot snaga timea Total costb

Low visibility (<33 feet [10 m]); difficult terrain (>50% slope); low (2 snags/acre [0.8/ha]) density

Subsegment33(10) 6 0.25 4 7.0 1.19

Subsegment66(20) 6 .50 4 8.0 1.36

Subsegment99(30) 24 .75 4 27.0 4.59

Subsegment132(40) 30 1.00 4 34.0 5.78

Low visibility (<33 feet [10 m]); difficult terrain (>50% slope); high (8 snags/acre [3.2/ha]) density

Subsegment33(10) 6 1.00 4 10.0 1.70

Subsegment66(20) 6 2.00 4 14.0 2.38

Subsegment99(30) 24 3.00 4 36.0 6.12

Subsegment132(40) 30 4.00 4 46.0 7.82

a Time in minutes. b Cost calculated at $10 per (hour*person). Units in dollars.

In addition, we have taken Wiegert’s method one step further by calculating the Total

Cost a resource specialist might expect for each plot size selected. We have found this

to be the most valuable piece of information, because all costs are relative to each other

within the same area.The Total Cost also incorporates the Minimum Sample Size

required. Although, the actual cost for sampling may be more or less in a particular

area, selecting the plot size that demonstrates the lowest Total Cost will likely result in

selection of the Optimal plot size for your current forest conditions.

The cost per plot, or time, seems to be a function of three factors: (1) visibility, (2) terrain, and (3) density. Visibility refers to the unobstructed viewing distance within a stratum; visibility is most strongly affected by the seral stage, or amount of shrub cover,

within a stand. Terrain includes such things as the slope, shrub cover, and the amount

of downed woody debris. All of these factors affect how easy or difficult it is to walk

through an area. Density is dictated by the target criteria of the snags or trees being

censused and the natural occurrence of these target snags or trees.

Cost estimates per plot were calculated at $10 per observer-hour. In addition to costs

per plot, each survey will have associated fixed cost. Fixed cost is the time spent selecting and locating each beginning transect point and then returning to a vehicle after the

surveying has been completed. This cost can be minimal in clearcut areas or quite high

in areas with difficult terrain. We therefore calculated a fixed cost based on a moderate

situation with a low snag density, which averages the cost per plot in this category for

Subsegments and Segments. This assumes that observers choose the quickest route to

the beginning point of a transect. 
Out cost estimates were based on time trials conducted in forests in northern Idaho 

and then adjusted based on cost estimates from a snag study in the central Oregon

Cascade Range. During the time trials, all snags >10 inches (25 cm) d.b.h. were 

surveyed. For each, we recorded the following information: (1) species, (2) d.b.h. 

(measured by using a Biltmore diameter stick), (3) decay class, (4) height (ocular 

estimate), (5) distance of the midpoint of the snag from the center line, (6) nesting 

evidence (ocular), and (7) foraging signs (ocular).

In flat, open areas, distances for each snag were either paced or determined by using a

measuring tape. Paced distances were accepted only after accuracy and consistency in

the estimation of distances of snags not considered to be marginal could be demonstrated. A snag was considered marginal, for example, if its distance of 16.5 or 18 feet 

(5 or 5.5 m) away from the line was uncertain. For these cases, all distances were

measured. In addition, periodic calibration of pacing was conducted. In steep areas, 

all distances >12 feet (3.5 m) were measured.

We developed six hypothetical situations based on our experience surveying snags.

“Easy” refers to an area that is relatively flat (<30 percent slope) and where snags or

trees are easily observed out to 66 feet (20 m) in both directions. “Moderate” refers to

situations where the slope is <50 percent and visibility of snags or trees averages 50

feet (15 m). “Difficult” describes situations in which a combination of factors makes 

travel difficult and slow, and visibility is low. For example, in dense regeneration stands,

it is not possible to accurately detect snags beyond a particular distance. Travel could

be difficult as a result of slope (>50 percent), type of seral stage, or the amount of shrub

cover or downed woody debris. Cost estimates were developed for each forest situation

given two densities: (1) two snags per acre (0.8 snags per ha) and (2) eight snags per

acre (3.2 snags per ha) as shown in table 1.

To develop the costs, we first determined the average amount of time required for an

observer to walk a 164-foot (50-m) line looking for snags in the various forest conditions

but without encountering any target snags. Then we estimated the average amount of

time per snag in the different forest conditions required to record the snag characteristics listed above. Next we summed the time required to walk a transect without snags,

with the time per snag given the two densities. Total time was then multiplied by $10

per hour to obtain the cost (table 1). Costs for all Segment plots were derived by simply

doubling the cost of a Subsegment plot with the same width.

Within the moderate and difficult categories, costs jump considerably for the

Width99(30) and Width132(40) plot sizes. This is a result of the observer having 

to periodically leave the center line to survey beyond the point of visibility.

For unstratified subwatersheds, the estimated sample size is given on the optimal sheet

under “Sample Size (plots).” For stratified subwatersheds, go to the sheet Sample Size.

This sheet provides two methods for estimating the total sample size required on a 

stratified subwatershed: (1) optimal and (2) proportional allocation. It also breaks down

the total sample size required into the number of plots required for sampling within 

each stratum.

26

Sample Size

Determination
Proportional allocation of the sample size allocates the samples among the strata based

on the proportion of the total area in each stratum (weight Wi). In contrast, optimal allocation incorporates both the stratum proportional area (Wi ) and variance (si

2 ) to determine how many samples are required within each stratum (Krebs 1989). Both methods

calculate the number of samples required to obtain a density estimate that is within 20

percent of the true mean, 90 percent of the time.

The sample size (Krebs 1989) required by the proportional allocation method is determined by the equation:

Then the number of samples within each stratum (ni) is determined by multiplying the

total number of samples needed (n) by the weight (Wi) of each stratum. 

Sample size for the optimal allocation method (Krebs 1989) is found by the following

equation:

Then the number of samples needed within each stratum is estimated by: 

where

B = desired bound for 1 - a (xst * 20 percent),4

ta = Student’s t -value for 90 percent confidence limits (1 - a),

n = total sample size required in stratified sampling,

Wi = stratum weight (Ai/A),

si = standard deviation in stratum i,

s2

i = variance in stratum i,

A = total number of acres (ha) in subwatershed,

Ai = number of acres (ha) in stratum I, and

ni = total sample size required in stratum i.

27

B2 1

ta A

(∑Wisi)

2

+ (∑Wisi

2 )

n = , (7) ( () )

Aisi

∑Aisi

ni = n , (8) ( )

4 We have substituted the symbol B (to denote bound) 

for the d listed in Krebs’ (1989) equations.

ta

2 ∑ Wisi2

B2 n = , (5)

ni = nWi , (6)
There are advantages and disadvantages to each of the allocation methods.

Proportional allocation offers the advantage of dropping the strata and combining all

samples after the sampling is done. You would do this in cases where you found little 

or no difference in densities between strata. This will yield both a larger sample size 

(n) and a smaller variance (s2). By contrast, this option is not available if the optimal

allocation method is used. The optimal allocation method, however, provides the best

estimate for the least cost in situations where large differences in density exist between

strata. With this method, sampling is concentrated in the stratum that has the highest

variance. By contrast, proportional allocation concentrates sampling effort in the largest

stratum, regardless of the variance within each stratum.

It is important to remember that the sample sizes given are only estimates of the number required to obtain a desired level of precision. Consequently, we recommend that

data be analyzed in the macros periodically to gauge the precision of estimates.

After a minimum of 60 samples (See the “Establishing Transects” section for an exception to the minimum number of samples required.) have been collected (or 20 samples

per stratum), the mean density of snags or trees can be estimated; resource specialists

may then decide whether enough samples have been collected to achieve their objectives. The two density options provided are (1) Estimate Average Density and (2)

Compare to Target Density. These allow the user to either obtain an average snag or

tree density that is within 20 percent of the true mean at a desired confidence level or

determine whether the estimated density is significantly different from the targeted density, respectively. Users can choose both options. For the Estimate Average Density

option, use the Densities sheet. For the Compare to Target Density option, you must

first obtain a density estimate from the Densities sheet, and then use this information on

the Statistical Test sheet.

Estimate average density—To meet the requirements of the Estimate Average Density

option, two equations are available on the Density sheet based on two sampling methods: (1) simple and (2) stratified random sampling. For the simple random sampling

method, the average is calculated in the normal way (equation 1). Then the variance is

calculated by:

and the standard error of the mean is then determined by:

where

x = population mean,

xi = observed x value in sample i,

n = sample size,

s2 = variance of the measurements,

sx = standard error of the mean x, and

ta = Student’s t-value for 90 percent confidence limits (1 - a ).

28

∑(xi – x)2

n – 1

s2 = , (9)

s2

n

s x = , (10)

Estimating Densities
The confidence interval is then calculated by using a normal approximation 

(Krebs 1989) :

As in the previous sheets, all shaded boxes require input from the user. The t-value is

preset at 1.67 for a sample size equal to 60 to obtain a 90-percent confidence interval.

If a different level of confidence is desired, however, the t-value may be changed. In the

first section of the Densities sheet, an estimated mean is given based on simple random

sampling methods.

In the second section, a density estimate with a bound is calculated based on stratified

random sampling methods. The stratified mean density is computed by the following

equation:

To calculate a confidence interval, the stratified variance must first be determined:

Variance of

Then the confidence interval is calculated by the normal approximation:

where

x st = stratified population mean (number per acres [ha]),

x i = observed mean in stratum i,

Ai = number of acres (ha) in stratum i,

A = total number of acres (ha) in subwatershed,

ni = number of samples in stratum i,

i = stratum number,

L = number of strata,

si

2 = variance in stratum i, and

Wi = stratum weight or proportion of area in stratum i (Ai/A).

Because this section is designed to accommodate landscapes with different numbers 

of strata, the user must enter the correct number of strata in the column Stratum Number. The macro counts the number of rows within this column that contain a value corresponding to the number of strata within the landscape. It then selects the appropriate

equation for the given number of strata. For example, for a subwatershed with four strata, enter the numbers 1, 2, 3, and 4 in each of the rows under the column heading

Stratum Number.

29

∑i=1Aix i

A

x st =

L

, (12)

Wi

2 si2

ni

L

∑

i=1

(x st) = , (13)

x±tasx , (11)

( )

x st ± ta var(x st) , (14) ( )
Compare to target density test—The second density option is an informal statistical

test that allows resource specialists to determine whether the estimated snag or tree

density is significantly different from the targeted density identified as part of their standards and guidelines. A minimum of 60 samples for the landscape, or 20 samples from

each stratum (whichever is higher), are required. For subwatersheds >7,000 acres

(2834 ha) increasing your sampling effort may be necessary to compensate for the 

natural variability of snags and trees because of an elevational gradient. For example, 

a 20,000-acre (8097-ha) subwatershed, which encompasses three distinct forest community types, may require about 100 samples to adequately conduct the Compare 

to Target Density test. This translates into an increase of about three sample plots 

for every 1,000 acres (405 ha) surveyed above 7,000 acres (2834 ha). See the

“Establishing Transects” section for details in plot establishment. This option is especially useful in situations where densities are low and the sampling effort to obtain an

estimate within 20 percent of the true mean (90 percent of the time) is extremely high.

It is intended for surveys where the main objective is determining whether the subwatershed meets the targeted guidelines for snags or large trees. Note here that 

recent data suggest that snag targets set in National Forest plans are too low (Bull 

and others 1997).

The most common way to test for a significant difference between two means is to conduct a t-test that compares the mean within each plot to the target mean. Although this

would work for our purposes, in single-stratum landscapes, there are some problems

with this approach on stratified landscapes. Consequently, we chose to use the confidence interval statistical test. This test determines whether the targeted density value

falls within the confidence interval of the estimated density. Because the bound on the

density estimate is calculated by using a t-statistic, it is essentially the same as a t-test.

This t-statistic has the same distribution as the Student’s t-test statistic. In addition, this

approach simplified the process and made it possible to use with stratified landscapes. 

Resource specialists can use this same statistical comparison after the minimum number of samples has been met. The spreadsheet labeled Statistical Test then allows

resource specialists to visually assess whether the estimated and targeted densities 

of a survey are significantly different from each other (fig. 4). Users need only enter the

targeted density and the estimated density and its bounds from snag or tree survey; the

resulting graph is automatically plotted. For example, on a homogeneous 6,044-acre

(2447-ha) study site in ponderosa pine forest in the Oregon Cascade Range, one objective was to determine whether the study area met the targeted hard snag densities listed 

in the Forest plan. The Forest plan guidelines (Deschutes National Forest plan 1992;

see footnote 1) for this area stipulated it support at least 0.9 hard snags per acre (2.2

hard snags per ha). On this site, the estimated (n = 175) hard snag density was 0.11 +

0.04 snags per acre (0.3 + 0.1 snags per ha [Bate 1995]). It was obvious that the study

area did not meet the targeted snag densities listed in the Forest plan; this could be

demonstrated statistically. The null hypothesis for this test was:

Ho: There is no difference between the targeted and estimated hard snag densities.

30
31

Distribution Analysis

Numbers per acre

Confidence interval

1.00

0.90

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00

90

Target density

Estimated density

Upper limit

Lower limit

Figure 4—Statistical Test sheet. Results of the statistical test found a difference between the targeted density

of 0.9 snags per acre (2.2 snags per ha) and the estimated density of 0.11 snags per acre (0.3 snags per ha).

Data from intensively harvested landscape in ponderosa pine forest on the Deschutes National Forest.

To evaluate the results, we checked whether the target value (0.9 hard snags per acre

[2.2 snags per ha]), fell between the values 0.07 and 0.15. These values are the upper

and lower limits on the density estimate 0.11 hard snags per acre (0.27 hard snags per

ha). If so, we could fail to reject the null hypothesis. In this case, however, the targeted

density did not fall within the confidence interval of the estimate (fig. 4). We therefore

rejected the null hypothesis. These are the results when a 90 percent confidence interval is used. If there is any uncertainty at the 90 percent confidence level as to whether

there is a difference between the targeted and estimated densities, resource specialists

may select a narrower confidence interval to decrease the possibility of a type I error. 

If after this step, a manager still questions the results, more samples should be taken

before repeating this test. By contrast, resource specialists should be aware that the

biological consequences of having a type II error occur may be more serious. We therefore recommend consulting with a statistician so that you are aware of the biological

consequences of each of these types of errors before implementing any major management actions as a result of this test.

The Distribution Index sheet estimates how evenly distributed target snags or large

trees are across a landscape; this is based on the percentage of the sampled landscape

supporting target snags or large trees. To obtain a distribution index, users must first

obtain two values: (1) present value and (2) count value. These are calculated by using Numbers per acre
the macro Pres_Abs. These values are the number of Segment33(10) plots supporting

a target snag or tree, and the total number of plots sampled, respectively. These values

are then entered onto the Distribution Index sheet. The macro Pres_Abs runs similarly

to the Segment and Subsegment macros in that it will sum the number of target snags

or trees within each row. It will only do this, however, for the Width33(10) column. It will

then condense the information into rows of Subtotals. Next, the condensed Subtotals

will be pasted to another area for analysis. As with the Segment macro, it is necessary

to enter the range by using the following format:

C1:F334

Symbols within the range will cause the macro to abort.

For single stratum landscapes, use the first section on this sheet. For stratified subwatersheds, use the second section and run the macro Pres_Abs on each stratum. 

In addition, you will need to know the total number of acres (ha) within each stratum.

Subsequently, a stratified distribution index is produced. Follow the directions given 

in the “Tutorial” for complete details about proper cell entries.

While calculating a stratified Distribution Index, it is critical to enter the correct number 

of strata by deleting the empty cells. This is similar to the Densities sheet where the

equation used is driven by the numbers in the Stratum column. Otherwise, the macro

selects the wrong equation. Highlight the unused stratum cells under Stratum and 

press Delete.

As the name of the macro Pres_Abs suggests, the Distribution Index is a presenceabsence analysis. It determines the proportion of plots with a qualifying snag or tree,

divided by the total number of plots sampled. The proportion of plots containing a qualifying snag or tree is then adjusted to compensate for the small amount of area sampled

relative to the critical area of 10 acres (4 ha). This result can then be extrapolated

across the entire landscape.

We chose 10 acres (4 ha) as the critical area to evaluate for the distribution analysis,

because it approximates the average home range size of the red-breasted nuthatch

(Sitta canadensis) (Raphael and White 1986). This primary cavity-nester has the smallest home range of the primary cavity-nesters. In addition, 10 acres (4 ha) is often 

recommended as an appropriate size area on which to evaluate the distribution of 

snags for cavity-nesters (Raphael 1997). In choosing this size area, we assume that 

if snags and large trees are adequately distributed to meet the needs of red-breasted

nuthatches, this distribution will also meet the needs of cavity-nesters that have larger

home ranges.

We theorized that if snags are adequately distributed on a landscape, we should find a

hard snag present within nearly every 10-acre (4-ha) circular area. To test our theory, we

used snag data collected from three old-growth strata in the central Oregon Cascade

Range (Bate 1995). Then we approximated the diameter of an area of this size by joining

32
33

two Segments (656 feet [200 m]) together. The diameter of a 10-acre (4-ha) circle is

738 feet (225 m). Combined with a 66-foot (20-m) width we were sampling about 10

percent of a 10-acre (4-ha) area. In the two old-growth stands of Douglas-fir/western

hemlock forests, target snags (>18 inch [46 cm] d.b.h., >20 foot [6 m] height, decay

classes I-III [Cline and others 1980]) were present in an average of 88 percent of these

two Segment66(20) plots joined together. On a landscape with old-growth ponderosa

pine forest present, we found that 90 percent of these double Segment66(20) plots had

a target snag (>10 inch [25 cm] d.b.h., >6-foot [1.8-m] height, decay classes I-III [Cline

and others 1980]) present. When all decay classes were included, the proportion

increased to nearly 100 percent in both forest types. We then used these results as 

the baseline from which the proportions from smaller plot sizes were adjusted.

We wanted to conduct the distribution analyses by using the narrowest plot size (33 feet

[10 m]) so that a distribution index could be calculated regardless of the optimal plot

size selected for density analyses. We also wanted to avoid having to collect information with plots 656 feet (200 m) in length. To do this, we looked at the relation between

the proportion of larger plots with a snag present compared to the proportion of the

smaller plots with a snag present (1 minus proportion of plots with snags absent). 

We then used a fractal dimension to adjust for the change in the proportions because of 

the change in the scale (Milne 1991). The proportions found in each of the plot sizes

are related by:

where 

Pabs = proportion of larger plots with snag or tree absent,

p = proportion of smaller plots with snag or tree absent, and

n = fractal dimension.

Next, we calculated the value “1 -p ” (proportion of plots with a target snag present) by

using the old-growth sites described above. We used this as a baseline value. Then

we divided the proportion of smaller plot sizes supporting a target snag for sites in 

various conditions: lightly, moderately, and intensively harvested. This gave us what 

we termed the Distribution Index. We found that old-growth areas had an index of 1.00

or greater. This translated into about 90 percent of the larger plot sizes supporting a

hard target snag. In contrast, intensively harvested areas, where large areas were

devoid of snags, had a Distribution Index of 0.40 or less. Given that woodpeckers are

territorial, we questioned the level at which these areas could support breeding populations of woodpeckers. Realize that the Distribution Index for both hard and soft snags

would be higher.

The need for a Distribution Index became apparent after a study done on a subwatershed in the Willamette National Forest found that only about 28 percent of the landscape supported any qualifying snags (Bate 1995). This subwatershed had a stratified

Distribution Index of 0.39. Although clearcut and second-growth areas did have some

Pabs = pn , (15)
large, soft remnant snags and smaller diameter hard snags, most snags that met the

target criteria were encountered only in the remaining old-growth forest. In a situation

like this, the stratified snag density becomes irrelevant because of the poor distribution 

of snags.

Background information—You are the manager of a stand of old-growth ponderosa

pine located on the east side of the central Oregon Cascade Range. The entire oldgrowth area comprises 900 acres (364 ha). You need to estimate the density of hard

snags to determine whether the area meets the targeted densities listed in the Forest

plan. Only hard snags (decay classes I-III [Cline and others 1980]) that are ≥10 inch

(25 cm) d.b.h. and ≥6 feet (1.8 m) tall qualify. You are also interested, however, in determining the density of soft snags in this same size class to provide baseline data 

for resource specialists in adjacent areas. They are interested in mimicking old-growth

characteristics in this region. You therefore plan on sampling all decay classes but with

hard snags as the primary objective. In addition, you want to assess how evenly qualifying hard snags are distributed across the landscape. Finally, you would like to obtain

some information on the percentage of snags that are used for nesting.

Stratification—To start the snag surveying project you use aerial photographs and

stand maps to determine whether any apparent strata can be delineated. The area

appears patchy in regards to the seral stage because of management actions; some

areas have undergone controlled burns, whereas others have not. You think therefore

that this may mean very different snag densities. A more thorough ground check, however, reveals a relatively homogeneous forest in regard to snag densities based on 

1-acre (0.4-ha) ocular estimates. Consequently, the area was not stratified. Visibility

averages about 49 feet (15 m), and the area is flat and easy to traverse.

Pilot survey—Five transects were established within the area. Placement was determined by randomly placing a grid over a map and then randomly selecting five grid

intersection points for the starting point of each transect. The compass direction was

then also chosen randomly. Each transect was delineated into two segments or four

subsegments. Two consecutive subsegments constitute one segment. A hip-chain was

used to delineate each 164-foot (50-m) subsegment plot.

Field forms were created by using the macro Dataform (fig. 1) to record all information

gathered in the field. (See “Field Forms” under “General Surveying Procedures” for complete details.) To explain to observers what information was required under each field

heading, you customized the file called Append2.doc. This file contains the basic field

descriptions and the numeric codes for each habitat variable. 

Once in the field, all qualifying snags within each subsegment were counted out to 66

feet (20 m) from the center line. Snags were measured to their midpoints. The d.b.h.

and height of each snag were measured. Diameters were measured in inches (cm) and

heights in feet (m). In addition, for each snag encountered, you recorded the perpendicular distance of the midpoint of the snag in feet (m) away from the center line, the

numeric code for species, its decay class (Cline and others 1980), and the numeric

code to indicate evidence of nesting or foraging.

34

Tutorials

Example I: Density and

Distribution Analysis

for Single-Stratum

Landscape
35

Data entry—To enter your own data, you open the file Estimate.xls (Estimatm.xls) and

go to Sheet1. For this example, however, the data are already entered and can be

found in the file Single.xls (Singlem.xls). Open this file in the spreadsheet program Excel

for Windows, Version 5.0. On Sheet 1 you will find the data from the pilot survey

described above. Twenty subsegments, nested within 10 segments, of data have been

entered. Note that the data have been entered into the spreadsheet following the same

format provided on the field form and are always entered on Sheet 1 (fig. 1). If these

were your own data, you would need to run the macro Consecutive before beginning

computer analyses. For this example, it is not necessary. Please refer to the

“Computer Analysis” section for information on this macro.

You now want to run the analyses to determine which of the eight available plot sizes

minimizes your sampling effort for snags that meet the target criteria. However, you

have two objectives: (1) hard snag density and (2) the density for snags in all decay

classes. First, run the analysis on qualifying hard snags. The first step is to run the

Formula macros.

Formula entry—The first step in the computer analysis is to place the appropriate formulas within each of the Width columns. This is done by the macro Formmulti using

the distances you recorded in the field. To activate the macro, (1) click on Macro from

the Tools menu, (2) highlight Formmulti, and (3) press Run. 

To create the correct formula for each of the Width columns follow these steps: (1)

When an input box appears with the message, “Please enter the minimum d.b.h. you

want to consider for this analysis,” enter the number 10 (25). This is because target

snags are ≥10 inch (25 cm) d.b.h. For the metric version, the correct entry is in the

parentheses: (2) Then press the OK button when a message box appears to confirm

that this is the correct value; (3) When the height input box appears, enter 6 (1.8) to

specify that only snags with heights ≥6 feet (1.8 m) tall should be considered; (4) Press

OK after the message box appears to confirm your entry; (5) For the Class input box,

enter “3.” This is based on the decay class descriptions of Cline and others (1980),

where hard snags were those in the Decay Classes I-III; and (6) Finally, when the

macro asks if you want to exclude any species from the analysis, enter “9999” to 

specify that you want all species of snags to be considered in the analysis.

To have these formulas entered throughout the Width columns, (1) enter E2:E50 for the

range of the Width33(10) column. Use the scroll bar on the right side of the screen to

determine the last cell row in the Width33(10) column; then (2) enter F2:F50, G2:G50,

and H2:H50 for the ranges of the Width66(20), Width99(30), and Width132(40) columns,

respectively; and (3) check to ensure that each row in the width columns contains either

a “0” or a “1.”

Analyzing by segment for single stratum—The next step is to calculate averages and

standard deviations for each plot size. The macro Segment will do part of this; first, it

will sum the total number of qualifying snags within the segment plot sizes that are 
328 feet (100 m) in length. To obtain these statistics, follow these steps: (1) select

Macro from the Tools menu; (2) highlight the Segment macro; (3) press Run. You will

see the macro create rows of Totals. Excel refers to these as Subtotals; for clarity, we

also refer to these as Subtotal rows. Then the spreadsheet is condensed so that only

the Subtotals are shown.

The next step is to move only the visible Subtotals rows to a new area for analysis.

Otherwise, the macro will calculate averages and standard deviations on both the individual data rows and the Subtotal rows. To transfer these Subtotal rows, (1) enter

C1:H60, when an input box appears with the message “Please enter the range which

includes the Segment and Width columns, but excludes the Grand Total row (C1:H?).”

If the input box interferes with the range determination, just click on the title bar Copy

Range and drag it out of the way. Then use the scroll bar to determine the range. Do

not use the mouse because it will include absolute range symbols in the value, which

will cause the macro to abort. Refer to the directions given below to restore the sheet

back to its original format if an error occurs. (2) Then a message box will appear to verify that the range you entered is correct; click OK, and then Yes if the range is accurate.

If not, click No and a second input box will appear for the correct range; and (3) enter

the cell range C64 for the input box labeled Paste Range. The table of results should

always be at least three rows below the newly pasted data.

The next steps will build the table of SEGMENT Results and place it below the newly

pasted data. To do this, (1) enter the cell range E65:E74 when asked for the “range of

the newly pasted Width33(10) column”; (2) direct the macro to place the table at the cell

range E77 by entering this value into the input box labeled Segment Results. Here is

where the macro will insert the averages, standard deviations, and sample size into a

table for the various widths of the segment plots; and (3) enter the ranges of the newly

pasted Width66(20), Width99(30), and Width132(40) columns. The correct ranges for

this sample data set are F65:F74, G65:G74, and H65:H74, respectively. After the

ranges have been entered a message box will appear with each value you have given.

Click OK or enter to proceed.

Finally, the macro presents you with another input box: "Do you want to switch to the

Optimal sheet to see your results? Please record your current results for use in further

analyses. Remember, to analyze by Subsegment, you must first restore the data set to

its original format." Click on No. This will keep you on Sheet 1. Now scroll down below

the newly pasted Subtotals. There you will find a table with the segment averages,

standard deviations, and number of samples for this data set (table 2). The row labeled

Segment33(10) gives you the average snag density and standard deviation for plots that

are 328 feet (100 m) long by 33 feet (10 m) wide. Segment66(20), Segment99(30), 

and Segment132(40) rows refer to plots that are also 328 feet (100 m) long, but either

66 feet (20 m), 99 feet (30 m), or 132 feet (40 m) wide, respectively. These results are

based on the pilot sample of 20 samples. The “N” is “10,” however, because the macro

lumped two consecutive subsegments together to determine whether longer plots would

be more efficient than shorter (164-feet [50-m]) plots. The averages and standard 

36
37

Table 2—Segment plot statisticsa

Standard

Plot dimensions Average deviation

Segment33(10) 0.8 0.789

Segment66(20) 1.8 1.874

Segment99(30) 2.4 3.098

Segment132(40) 2.8 3.615

N 10 

a Averages and standard deviations for each segment plot size, along with total sample size, using 

the Single.xls (Singlem.xls) data set. Values calculated by the macro Segment. Analysis for hard 

snags from old-growth ponderosa pine landscape.

to its original format so that you can run an analysis based on Subsegment plots. 

To restore the sheet to its original format, (1) select all rows containing data beneath 

the Grand Total row, (2) select Delete from the Edit menu, (3) press on Entire Row, 

(4) activate the cell with the field name SEGMENT, (5) choose Subtotals from the Data

menu, and (6) select Remove All. This will return the data set to its original format. 

If the macro ever stops because of a cell range entered incorrectly, you will receive 

an error message box. Click End within the message box and proceed with the steps

listed above to restore the sheet to its original format.

Analyzing by subsegment for single stratum—The next step is to estimate the averages and standard deviations for the subsegment plot sizes that are 164 feet (50 m)

long. Refer to the directions given above to restore the sheet to its original format, if

Subtotals or results remain from any other analyses. To start the Subsegment macro,

(1) select Macro from the Tools menu, (2) highlight Subsegment, and (3) press Run.

Similar to the Segment macro, the macro will first sum the number of qualifying snags 

in each plot and then present these results in condensed Subtotal rows. 

deviations from this analysis also will be placed in the appropriate cells on the Optimal

sheet for analysis. You may want to print these results for your own records. To print

the results, (1) highlight the range with the mouse by clicking and dragging; (2) select 

Print from the File menu; and (3) Choose Selection. Also note that the “N” is not 

recorded elsewhere.

After recording or printing the results of this analysis, you need to restore Sheet 1 back
38

Table 3—Subsegment plot statisticsa

Standard

Plot dimensions Average deviation

Subsegment33(10) 0.4 0.681

Subsegment66(20) .9 1.21

Subsegment99(30) 1.2 1.795

Subsegment132(40) 1.4 2.01

N 20 

a Averages and standard deviations for each subsegment 

plot size, along with total sample size, using the Single.xls 

(Singlem.xls) data set. Values calculated by the macro 

Subsegment. Analysis for hard snags from old-growth 

ponderosa pine landscape.

The next steps involve transferring the Subtotals to a new area for analysis. Enter

D1:H70 into the input box titled Copy Range. A message box will appear with this range

value. If correct, click on Yes. If not, click No and a second input box requesting the

same range will appear and you can enter it correctly this time. Enter D73 into the input

box titled Paste Range. This is where the Subtotals will be pasted.

To have the macro create the Subsegment statistics table, (1) enter E74:E93 into the

input box labeled Width33(10) Statistics; (2) enter the value E96 into the input box titled

SUBSEGMENT Results. The Subsegment Statistics table will be placed here; and (3)

enter the ranges of each of the newly pasted Width66(20), Width99(30), and

Width132(40) columns when you are prompted. The correct entries for these input

boxes are F74:F93, G74:G93, and H74:H93, respectively.

Finally, the macro will bring up an input box with "Do you want to switch to the Optimal

sheet to see your results? Please record your current results for use in further analyses.

Remember, to analyze by Segment you must first restore the data set to its original format." Choose Yes. This will transfer you to the Optimal sheet. On Sheet 1 below the

newly pasted data, however, you will still find a table of Subsegment results. Table 3

shows the correct averages and standard deviations for each of the 164-foot (50-m)

subsegment plots. For example, Subsegment33(10) refers to a plot that is 164 feet (50

m) long by 33 feet (10 m) and its estimated average and standard deviation for the 20

pilot samples. In addition, the table gives you “N” which is the number of subsegments

for this data set.
39

Optimal plot size—The next step is to determine which plot size optimizes sampling in

the current forest conditions. This is done on the Optimal sheet. (If you chose not to be

transferred to the Optimal sheet after running the Subsegment analysis, you can switch

to it now by clicking on the Optimal tab in the lower left hand corner of the screen.) 

The shaded boxes on this sheet are those requiring input from you. First, write a brief

description of the study area in the shaded box labeled Stratum. For example, for this

analysis you might write: 

“Stratum: Old-growth P.Pine; ≥10 in (25 cm) d.b.h.; ≥6 ft (1.8 m) tall; Hard snags.”

Then look under the column heading Mean Density (no. per plot). Here you will find the

estimated average for each of the eight plot sizes. These values were automatically

transferred when you ran the Segment and Subsegment macros. Similarly, you will find

the appropriate standard deviation values under the column heading Standard Deviation

(no. per plot). Table 4 shows the correct entries and resulting calculations.

In the first section of the Optimal sheet, you will find that the Mean Density (no. per plot)

has been converted to the number of snags per acre (ha) under the column heading

Mean Density (no. per acre [no. per ha]). Similarly, the standard deviation of each plot

has been squared to get the variance, and then converted to the no. per acre (no. per ha)

under the Variance column. Then, beneath the Variance column you will find a value

with the label Lowest Variance = 10.08 (62.22). The Optimal spreadsheet uses the lowest variance calculated among the eight plot sizes as the divisor for all the variances.

These values are used to calculate the relative variances; they are then used to fill the

Relative Variance column. The next two columns of this section, Sample Size (plots),

Sample Size (acres [ha]), calculate the total number of plots and acres (ha), respectively, needed to obtain a density estimate that is within 20 percent of the true mean 90 percent of the time. Finally, the last column, Number of Acres (ha) Required, gives the minimum number of acres (ha) required for sampling (table 4). This value includes the pilot

sample data. This is based on the value entered into the cell labeled “Minimum Sample

Size Required.” For a single stratum landscape, a minimum of 60 samples are required.

For landscapes with two or more strata, the minimum sample size within each stratum is

20. See the “Establishing Transects” section for exceptions to the minimum number of

samples required. For this data set, enter “60” into the box labeled “Minimum Sample

Size Required” in the upper left corner of the sheet. 

To select the optimal plot size, first look at the number of plots required for each plot

size. Which plot sizes require the smallest number of samples? Then consider the plot

size in terms of area (acres or ha). Segment33(10) plots require both the lowest number of plots (68) and acres (17) to be sampled. (For the metric version, 6.8 ha are

required.) It is important, however, to remember that a minimum of 60 samples are

required for these methods regardless of the plot size used.
40

Table 4—Optimal sheet: optimal plot size analysis for hard snags in single-stratum ponderosa pine landscapeaPlot Mean Standard Mean Relative Sample Sample Numberdimensions Plot size density deviation density Variance variance(RV)= Size Size required

Feet2 (m2) No./plot No./acre (no./ha) No. of plots Acres (ha)

Subsegment33(10) 5,412 (500) 0.4 0.681 3.22 (8) 30 (185.3) 2.98 202 25 (10.1) 7.4 (3)Subsegment66(20) 10,824 (1000) .9 1.21 3.62 (9) 23.7 (146.3) 2.35 126 31 (12.6) 14.8 (6)Subsegment99(30) 16,236 (1500) 1.2 1.795 3.22 (8) 23.2 (143.2) 2.3 156 58 (23.4) 22.2 (9)Subsegment132(40) 21,648 (2000) 1.4 2.01 2.82 (7) 16.4 (101.1) 1.62 144 71 (28.8) 29.6 (12)Segment33(10) 10,824 (1000) .8 .789 3.22 (8) 10.1 (62.2) 1 68 17 (6.8) 14.8 (6)Segment66(20) 21,648 (2000) 1.8 1.874 3.62 (9) 14.2 (87.8) 1.41 76 38 (15.1) 29.6 (12)Segment99(30) 32,472 (3000) 2.4 3.098 3.22 (8) 17.3 (106.7) 1.71 116 87 (34.9) 44.5 (18)Segment132(4) 43,296 (4000) 2.8 3.615 2.82 (7) 13.2 (81.7) 1.31 116 115 (46.5) 59.3 (24)

Lowest variance 10.08 (62.22)

Total cost

Plot Plot Relative Fixed Cost per per plotdimensions size variance cost sample unit Relative cost Product Total cost

Feet2 (m2) Dollars Dollars

Subsegment33(10) 5,412 (500) 2.98 1.06 .64 1.7 1.00 2.98 343 Subsegment66(20) 10,824 (1000) 2.35 1.06 .77 1.8 1.08 2.53 230Subsegment99(30) 16,236 (1500) 2.3 1.06 1.15 2.2 1.30 2.99 345 Subsegment132(40) 21,648 (2000) 1.62 1.06 1.66 2.7 1.60 2.6 391 Segment33(10) 10,824 (1000) 1 2.11 1.28 3.4 1.99 1.99 230 Segment66(20) 21,648 (2000) 1.41 2.11 1.54 3.7 2.15 3.03 276 Segment99(30) 32,472 (3000) 1.71 2.11 2.30 4.4 2.59 4.45 512 Segment132(40) 43,296 (4000) 1.31 2.11 3.32 5.4 3.19 4.19 631 

Lowest total cost 1.70

a Cost estimates taken from the General Cost per Sample Guidelines. A minimum of 60 samples is required.
41

This is where consideration of a cost factor can aid the decisionmaking process. 

On the Optimal sheet are six estimated costs for conducting surveys. These are 

listed under the General Cost per Sample Guidelines lower on the Optimal sheet. 

(See “Estimating Costs” in the “Computer Analysis” section for additional details). 

We decided that the survey area could be easily walked, but visibility averaged 49 feet

(15 m). This puts us in a moderate situation because of the visibility restrictions. 

Two density options are provided. Select the low density because our means appear 

to be closer to two snags per acre (0.8 snags per ha) then to eight snags per acre (3.2

snags per ha). Now, copy the column values under Moderate; Low Density. Then paste

these values into the column titled Cost per Sample in the row above. Table 4 demonstrates the results when these values have been entered correctly. Refer to appendix 4

for Copy and Paste instructions.

The spreadsheet then calculates a relative cost for each of the eight plot sizes by 

dividing the cost for each plot size by the lowest cost among them, which is 1.70. 

Then, following Wiegert’s method (1962), we multiply the relative variance by the 

relative cost. The plot size that minimizes the product of these two factors is considered

to be the optimal plot size. Once again, Segment33(10) plots appear to be Optimal

because they have the lowest relative variance and relative cost product (1.99). Now,

however, look at the column labeled Total Cost. This column calculates the cost based

on the minimum number of samples required; this is the lowest of either the recommended number of samples (Sample Size [plots]), or the cost to meet the minimum

sample size requirement of “60.” The spreadsheet bases the cost on the lowest of

these two values. For Segment33(10) plots, you could expect to spend about $230. 

If Subsegment66(20) plots were used, however, the estimated total cost also is $230.

Subsequently, it is not clear which of these two plots would be optimal. We are also

interested in snags of all decay classes, however, and running the optimal plot analysis

on both hard and soft snags may aid in the decisionmaking process.

To run the analysis for snags in all decay classes, first return to Sheet 1. If necessary,

restore the data sheet to its original format by following the instructions given above in

the “Analyzing by Segment” section. Then you will need to rerun the Formmulti macro.

Refer to the “Formula” section above and enter everything exactly the same with the

exception of the decay class. When the input box asking for the maximum decay class

to consider appears, enter “5” instead of “3” this time. This will include both hard and

soft snags in the analysis. Then rerun the Segment and Subsegment macros exactly

as you did above. Make copies of both results’ tables and then transfer over to the

Optimal sheet. Then copy and paste the values under the Moderate; High Density 

column in the General Cost per Sample Guidelines into the Cost per Sample column.

Use the High Density column this time. This high density choice will help to compensate for additional time spent sampling because of more snags encountered. Table 5

shows the results for both hard and soft snags. 

In the analysis for both hard and soft snags, Segment33(10) plots again seem to be the

best choice in regards to the number of plots required for sampling. They require the

lowest sample size in plots (19) and in acres (5). (For the metric version, 1.9 ha are

required.) If this was one of multiple strata, this plot size would be the best. This is

best demonstrated by entering “20” in the box labeled Minimum Sample Size Required

to simulate this as one of three strata within a landscape, instead of a single stratum.
42

Table 5—Optimal plot size analysis for both hard and soft snags in single stratum ponderosa pine landscapeaPlot Mean Standard Mean Relative Sample Sample Number dimensions Plot size density deviation density Variance variance(RV)= size size required

Feet2 (m2) No./plot No./acre (no./ha) Plots Acres (ha)

Subsegment33(10) 5,412 (500) 0.6 0.754 4.83 (12) 36.8 (227.4) 5.68 110 14 (5.5) 7.4 (3)Subsegment66(20) 10,824 (1000) 1.4 1.188 5.63 (14) 22.8 (141.1) 3.53 50 12 (5) 14.8 (6)Subsegment99(30) 16,236 (1500) 1.85 1.814 4.96 (12.33) 23.7 (146.3) 3.66 67 25 (10.1) 22.2 (9)Subsegment132(40) 21,648 (2000) 2.25 2.124 4.53 (11.25) 18.3 (112.8) 2.82 62 31 (12.4) 29.6 (12)Segment33(10) 10,824 (1000) 1.2 .632 4.83 (12) 6.5 (40) 1 19 5 (1.9) 14.8 (6)Segment66(20) 21,648 (2000) 2.8 1.549 5.63 (14) 9.7 (60) 1.5 21 11 (4.3) 29.6 (12)Segment99(30) 32,472 (3000) 3.7 2.791 4.96 (12.33) 14 (86.5) 2.16 40 30 (11.9) 44.5 (18)Segment132(40) 43,296 (4000) 4.5 3.274 4.53 (11.25) 10.9 (67) 1.68 37 37 (14.8) 59.3 (24)

Lowest variance 6.48 (40)

Total cost

Plot Plot Relative Fixed Cost per per plot dimensions size variance cost sample unit Relative cost Product Total cost

Feet2 (m2) Dollars Dollars

Subsegment33(10) 5,412 (500) 5.68 1.06 0.85 1.9 1.00 5.68 210 Subsegment66(20) 10,824 (1000) 3.53 1.06 1.36 2.4 1.27 4.47 145 Subsegment99(30) 16,236 (1500) 3.66 1.06 2.30 3.4 1.76 6.43 225 Subsegment132(40) 21,648 (2000) 2.82 1.06 3.19 4.3 2.23 6.28 264 Segment33(10) 10,824 (1000) 1 2.11 1.70 3.8 1.99 1.99 229 Segment66(20) 21,648 (2000) 1.5 2.11 2.72 4.8 2.53 3.79 290 Segment99(30) 32472 (3000) 2.16 2.11 4.60 6.7 3.51 7.6 403 Segment132(40) 43296 (4000) 1.68 2.11 6.38 8.5 4.45 7.45 509 

Lowest total cost 1.91

a Cost estimates taken from the General Cost per Sample Guidelines. A minimum of 60 samples are required.
43

Figure 5—Density sheet. Estimated density results for single-stratum ponderosa pine landscape by

using optimal plot size: Subsegment66(20) plots. Results for qualifying hard snags in the Single.xls

(Singlem.xls) data set.

Nevertheless, a minimum of 60 samples is recommended to ensure that the assumptions of normality are met and the variability of the study area is adequately represented.

In situations like these, therefore, it is important to consider alternative plot sizes that 

may require less sampling effort. Examine the Total Cost column to see that this time

Subsegment66(20) plots seem to be the optimal plot size because they are the least

expensive ($145). This result corroborates the results of the optimal plot analysis for

hard snags alone, which found that either Subsegment66(20) or Segment33(10) plots

would be optimal based on the estimated Total Cost. Consequently, Subsegment66(20)

plots seem to be the best plot size for sampling snags in this area; we will use this plot

size for the remainder of our analyses.

Density analysis—Now switch to the spreadsheet Densities by clicking on the tab with

this label in the Single.xls (Singlem.xls) file. Here a density estimate is calculated.

Begin with hard snags. Again, the shaded boxes are those that require input from you.

Leave the t-value at 1.67 even though this is the value that provides a 90 percent confidence level with 60 samples. Next enter 900 acres (364 ha) into the box labeled

Landscape Area. To obtain a density estimate and its bound, use the “Simple Random

Sampling Equation” section. Enter Subsegment66(20) in the gray box under the column

heading Plot Dimensions (name). The spreadsheet will then give you “10824” under

Plot Size (feet2). (For the metric version, under Plot Size (meters2) you will get “1000.”)

This will then convert the Plot Size into “Plot Area (acres [ha]).” Then input the estimated average density and standard deviation in snags per plot into the appropriate locations: “0.9 and 1.21” snags per plot, respectively. Finally, enter the number 20 into the

shaded box under the column heading “Sample Size.” The results are shown immediately below your entered values (fig. 5).
44

The landscape supports 3.62 + 1.81 hard snags per acre (9.00 + 4.51 hard snags per ha).

To determine the precision of your estimate, the bound is divided by the mean. For this

example, the bound 1.81 is divided by the mean of 3.62 and the result is 50. This says

that you are 90 percent confident that your density estimate is within 50 percent of the

true mean. After obtaining the density results for hard snags, enter the average and

standard deviation of the Subsegment66(20) plots for both hard and soft snags.

These values are “1.4” and “1.188,” respectively. This results in a density estimate of 

5.63 + 1.78 snags per acre (14 + 4.42 snags per ha).

Distribution analysis—The final objective for this snag survey is to determine whether

hard snags are adequately distributed to meet the needs of territorial cavity-nesters.

The Distribution spreadsheet bases its calculations on the percentage of the sampled

landscape with at least one qualifying snag present. The presence or absence of a

qualifying snag is evaluated on plots that are a subsample of an area about 10 acres 

(4 ha) in size. Details about this index are given in the “Computer Analysis” section

under “Distribution Analysis.” 

To begin (1) switch to Sheet 1; (2) make sure the data set is in its original state by deleting any results from the Segment or Subsegment macros and removing all Subtotals 

following the instructions given above; (3) click on the width columns to ensure that the

formulas within these cells are for hard snags only (e.g., within the formula you should

find K<=3). If not, rerun the Formmulti so that only snags with the maximum decay

class III are counted following the instructions given above in the Formula section; 

(4) then choose Macro from the Tools menu; (5) select Pres_Abs; and (6) click on Run.

Once the macro begins, (1) Enter: C1:E60 into the first input box labeled Copy Range.

(2) Press OK when the message box appears with this cell range. (3) For the next input

box, labeled Paste Range, enter the cell range C64. This will place the Subtotals below

the condensed rows. Then the macro will count how many segments were counted with

at least one qualifying hard snag present. (4) Another input box labeled Width33(10)

Range will come to the screen requesting the range of the newly pasted Width33(10)

column. Enter E65:E74. (5) Then you will notice that two additional column headings

are added to the right of the Width33(10) column. These are the Present and Count

fields. They should have the values “6” and “10,” respectively. Record these values to

enter onto the Distribution Index sheet.

Now bring up the Distribution Index sheet by clicking on the tab with this title. If this

sheet is not readily visible, use the right arrow keys at bottom left until it appears. 

Enter the values for the Present and the Count shaded boxes (6 and 10, respectively).

Once adjusted, the Distribution Index for this example is 1.37 (table 6). Values of 1.00

or greater reflect a hard snag distribution similar to that found in old-growth forested

areas. This index value suggests, therefore, that the distribution of snags in this area 

is adequate to meet the needs of territorial cavity-nesters.
45

Table 6—Distribution spreadsheet: the distribution index for qualifying 

snags for the single-stratum ponderosa pine landscapea

Proportion of plots

Proportion of with with snag/tree present

Present Count(N) snag/tree (adjusted)

6 10 0.6 1.37

Distribution Index DI = 1.37

a Data from the Single.xls (Singlem.xls) file. Distribution Index values of 1.00 or greater 

reflect a snag distribution similar to that found in old-growth forested areas. 

Cavity analysis—To conduct cavity analyses, first return to Sheet 1 and restore the

data set to its original format by removing all results below the Grand Total row and the

Subtotals. Refer to directions given in the “Analyzing by Segment” section above for

complete details. The data in the Single.xls (Singlem.xls) file have been given codes for

cavity and forage use based on definitions described in appendix 2 (note: the cavity and

forage data have been created for demonstration purposes). To create the correct formula to determine the percentage of snags sampled that have been used for nesting

(either recently or in the past), (1) select Cavity from the Tools menu under Macro; (2)

then select Run; (3) enter 10 inches (25 cm) when an input box appears asking for the

minimum d.b.h. to consider for the analysis; (4) then enter 6 feet (1.8 m) when asked for

the minimum height; (5) for the maximum decay or structural class, enter “5”—this will

evaluate snags in all decay classes; (6) then when prompted for any species to exclude

enter “9999”—this will allow all species of snags to be included in the analysis; and (7)

finally, you will be asked for a cavity code: enter “1,” the code for any snag with a new

cavity (see appendix 2). 

After building the correct formula, complete the following steps: (1) enter P2:P50 when

asked for the range of the Qualifying column; (2) when asked for the range of the

Cavity column, enter N2:N50; (3) then enter the range of the Qualifying column again.

Enter P2:P50 once more.

Now scroll to the top of the spreadsheet. There you will find three additional column

headings: (1) TOTAL, (2) UNKNOWNS, and (3) CAVSIGNS. You should find the values “45,” “8,” and “4,” in these columns, respectively. In addition, just below these field

names will be a row labeled Percent Use (Cavity) =. This will divide CAVSIGNS by the

(TOTALS-UNKNOWNS) to get the percent use. You should find the value “10.8.” This

means that 10.8 percent of the snags surveyed showed new signs of nesting.

Now to determine what percentage of the snags show both new and old cavity signs, (1)

first activate the cell P2 by clicking on it; (2) press the function key F2 at the top of your

keyboard. This allows you to edit the formula within this cell; (3) change the portion of

this formula that says N2=1 to N2<=3;

=IF(AND(K2<=16.5, L2>=10, M2>=6, J2<>9999, N2<=3),1,0) (English version)

=IF(AND(K2<=5, L2>=25, M2>=1.8, J2<>9999, N2<=3),1,0) (metric version)
(4) then press Enter. This will cause the macro to include snags that have either new or

old cavities, or both (codes 1-3); and (5) copy and paste (see the Excel Commands

sheet [appendix 4] if necessary) this revised formula in cell P2 throughout the P column

under QUALIFYING (P3:P50). Notice that values in both the TOTAL column and in the

UNKNOWN column stay the same. The CAVSIGNS column, however, has changed to

“14.” Now your results should show that about 37.8 percent of the snags surveyed

showed some kind of nesting activity, at some point in time. 

Conclusions for single stratum—Based on the 20 samples collected thus far, the

results are inconclusive as to whether the estimated density of hard snags (3.62 + 1.81

snags per acre [9.00 + 4.51 snags per ha]) on this landscape meets, or exceeds, the

targeted densities (2.2 snags per acre [5.4 snags per ha]) listed in the Forest plan.

More sampling is required, therefore, using the optimal plot size selected,

Subsegment66(20) plots, before any conclusions about density can be drawn. Results

from the distribution analysis suggest that hard snags are distributed evenly enough

across the landscape to meet the needs of cavity-nesters, but again are inconclusive

until 60 samples have been collected.

Background information—You are required to conduct a snag survey on one representative subwatershed to determine how effective management actions have been in

maintaining the desired snag densities. This is part of the compliance monitoring project

taking place forest-wide. The stands are dominated by Douglas-fir/western hemlock 

forest communities. Because of limited resources, you are mainly interested in determining whether the subwatershed meets the guidelines for hard snags outlined in the

Forest plan. In addition, you would like to assess the distribution of the qualifying snags

encountered, and judge whether or not this distribution addresses the territorial needs 

of cavity-nesters.

Subwatershed stratification—Aerial photographs show that the subwatershed is highly

fragmented. Information from the Forest’s GIS informs you that clearcutting has been

the primary method of timber harvesting. In addition, a snag-retention program was 

initiated only 6 years ago. For a snag to meet the target criteria on this subwatershed, 

it must have a d.b.h. ≥18 inches (46 cm), be ≥20 feet (6.1 m) tall, and be in the decay

classes I-III (Cline and others 1980). Because of the timber harvesting techniques used

within this area, and recent initiation of the snag retention program, you expect snag

densities to be low in second-growth and most clearcut stands. In the old-growth stands,

you expect to find high densities of target snags.

Based on snag densities alone, you think that two strata may be appropriate: (1) oldgrowth stands and (2) second-growth and clearcut stands combined. A thorough

ground check, however, reveals that although all old-growth stands may be combined

into one stratum, lumping the second-growth and clearcut stands would not be ideal. 

It seems that once the clearcut stands reach a certain age, mobility and visibility away

from a center transect line are greatly decreased. You therefore decide to place all

clearcut stands that have been harvested in the past 10 years into their own stratum,

and to lump all older cut stands into another stratum labeled second growth.

46

Example II: Density and

Distribution Analysis for

Subwatershed with

Multiple Strata
47

You now have three strata delineated: (1) clearcut, (2) second-growth, and (3) oldgrowth stands. You use the GIS to print out a map with all stands designated into one

of the three strata. These are color coded for quick, easy referencing. In addition, the

GIS output gives you the number of acres (ha) within each stand, and within the entire 

subwatershed. Strata one, two, and three, have 1,759 acres (712 ha), 1,381 acres

(559 ha), and 1,243 acres (503 ha), respectively, for a total of 4,383 acres (1775 ha).

You then spend a day in the field, validating that each stand has been placed in the

proper stratum.

Pilot survey—The topography of the subwatershed differs from flat benches to steep

(>100 percent) slopes. Clearcutting has occurred predominantly on the flat areas.

Visibility within the clearcut stratum is unobstructed, travel is easy, and snag densities

seem low. You therefore preselect a plot size for sampling within this stratum to meet

your objectives. Subsegment132 (40) plots are the best choice to increase the probability of detecting a target snag, while minimizing the amount of sampling effort resulting

from the shorter plot size selected.

A preliminary review of the second-growth stands reveals difficult travel conditions and

low visibility. In addition, few, if any, target snags are expected because of a zero snag

retention policy when these stands were harvested. You therefore also preselect a plot

size for use within this stratum. Subsegment66 (20) plots are narrow enough to ensure

that any target snags out to 33 feet (10 m) from the center line are detected. Again, the

shorter plots will meet the requirement of a minimum sample size more quickly.

By contrast, it is not clear what plot size would be the best choice within the old-growth

stratum where snag densities appear highly variable. Visibility averages about 49.5 

feet (15 m), and mobility varies from moderate to difficult, because of large volumes of

downed woody debris and dense tree and shrub regeneration in places. Consequently,

you will conduct a formal Optimal Plot Size analysis within this stratum.

Five stands within each stratum were randomly selected for the establishment of transects across the subwatershed. Random starting points for each transect were selected

by placing a grid over each stand and then randomly selecting a grid intersection for the

starting point. The compass direction was also randomly determined. Each transect

was then delineated into four subsegment plots for a total of 20 samples within each

stratum. As described above in “Example I,” two consecutive subsegments make up

one segment. A hip-chain was used to measure the 164-foot (50-m) plot lengths and to

function as the center line of the plots. 

All qualifying snags within each subsegment were counted out to 66 feet (20 m) from

the center line in strata 1 and 3, following the methods described in “Example I” of 

the “Tutorial.” By contrast, target snags were only counted out to 33 feet (10 m) 

within stratum 2.
Data entry—Data for all strata within this subwatershed were entered onto Sheet 1 of 

the file named Strate.xls (Stratm.xls). It may be accessed in the spreadsheet program

Excel for Windows, Version 5.0. Open this file and you will find that 20 subsegments,

nested within 10 segments, of data have been entered for each stratum. There are a

total of 60 subsegment samples. (If these were your own data, you would run the macro

Consecutive before beginning any computer analyses. Please refer to the “Computer

Analysis” section for information on this macro.) You now want to run the analyses necessary to determine which of the eight available plot sizes minimizes your sampling

effort for snags within each stratum.

Formula entry—As in the single stratum example, the first step in the computer analysis is to fill in the appropriate formulas for each of the Width columns. This is done by

the macro Formmulti. To activate the macro, (1) find Macro under the Tools menu, (2)

highlight Formmulti, and (3) press Run.

To create the correct formula for a target snag analysis, (1) enter 18 inches (45 cm) into

the DBH input box; (2) press OK to continue; (3) next, enter 20 feet (6.1 m) into the

height input box; (4) the next input box will ask for the maximum decay class to consider

in the analysis. Enter the number “3.” This is based on the decay class descriptions 

of Cline and others (1980), where hard snags were those in Decay Classes I-III; and 

(5) enter “9999” into the species input box to specify that you want all snag species 

considered in the analysis.

Now to paste the correct formula for target snags into the Width columns, enter E2:E116

when asked for range of the Width33(10) column. Use the scroll bar on the right side of

the screen to determine the last row in the Width33(10) column. You will be prompted to

enter the individual ranges of the Width66(20), Width99(30), and Width132(40) columns.

Your entries should be F2:F116, G2:G116, and H2:H116, respectively. The spreadsheet

will then enter “1s” and “0s” into each cell within these columns. A “0” is given if the

snag within that row fails to meet all of the target qualifications. A “1” is given if the snag

meets all the specifications you entered into the Formmulti macro above.

Sorting strata—The next step is to sort, and then to separate, the main data set on

Sheet 1 into the three individual strata. This is necessary to obtain estimates of the

averages and standard deviations for each stratum. To begin, (1) select Macro from the

Tools menu; (2) click on Sort; and (3) click on Run. This macro will first sort the data, in

ascending order, by stratum number.

The macro will then copy each stratum’s data rows onto a separate sheet. Follow these

steps to complete this process. First, enter A2:O21 into the input box requesting the

“range of Stratum 1.” Use the scroll bar to determine the range. As stated above, using

the mouse will cause the macro to abort. Then another input box will come up asking

for the “range of Stratum 2 (A?:O?).” Enter A22:O41. The next input box will ask Do

you need to move another stratum? Click on Yes. Enter A42:O116 into the input box

requesting the “range of Stratum 3.” Finally, when the message box asking Do you

need to move another stratum? appears, press No. Now the data rows for each stratum 

have been copied and pasted onto three individual sheets within this same file: (1)

Stratum1, (2) Stratum2, and (3) Stratum3.

48
49

Table 7—Segment plot statisticsa

Plot dimensions Average Standard deviation

Segment33(10) 0.7 0.675

Segment66(20) 1.6 1.174

Segment99(30) 2.2 1.476

Segment132(40) 2.7 1.889

N 10

a Averages and standard deviations for each plot size in stratum 

three, along with total sample size, using the Strate.xls (Stratm.xls) 

data set. Analysis for hard snags from old-growth Douglas-fir/

western hemlock forest subwatershed.

Analyzing by segment and subsegment with multiple strata—When working with

multiple strata, it is important to run both the Segment and Subsegment macros on 

each stratum to obtain averages and standard deviations before proceeding to the next

stratum, unless a plot size was chosen before sampling began. This is necessary

because both macros transfer results directly to the “Optimal” sheet on completion. 

If you switch to a different stratum before running both the Segment and Subsegment

macros on one stratum, you will get mixed results from two different strata. To ensure

that the correct values are transferred to the “Optimal,” always print out the Segment

and Subsegment plot statistics on completion. See tables 7 and 8 for examples of

these results. 

Table 8—Subsegment plot statisticsa

Plot Dimensions Average Standard deviation

Subsegment33(10) 0.35 0.489

Subsegment66(20) .8 .894

Subsegment99(30) 1.1 1.021

Subsegment132(40) 1.35 1.387

N 20

a Averages and standard deviations for each plot size in stratum 

three, along with total sample size, using the Strate.xls (Stratm.xls) 

data set. Analysis for hard snags from old-growth Douglas-fir/

western hemlock forest subwatershed.
Stratum 1 analysis—Using the arrow keys in the bottom left corner of the screen, click

several times in the right direction until you see a sheet labeled Stratum1. Click on this

tab. Here are the 20 subsegment samples taken during the pilot survey from Stratum 1,

composed of the clearcut stands. Scrolling down through the data you will quickly notice

that only one qualifying snag was encountered during the pilot survey. You still need to

run, however, the Subsegment macro to get a snag average and 

standard deviation for the Subsegment132(40) plot size.

To begin, (1) click on Macro from the Tools menu, (2) select Subsegment, and (3) Click

on Run. Next, follow these steps for the correct entries into each of the input boxes: 

(1) For the first input box, Copy Range, enter D1:H41. Press OK when each of the message boxes throughout this section appear with the correct cell addresses for confirmation. (2) Enter D45 into the second input box titled Paste Range. The summed rows will

be pasted here. (3) The next input box, Width33(10) Statistics asks for the “range of the

newly pasted Width33(10) column.” Enter E46:E65. (4) Then, enter E68 into the input

box labeled SUBSEGMENT Results. The table of results will be placed here. 

(5) Three additional input boxes will appear asking for the ranges of the newly pasted

Width66(20), Width99(30), and Width132(40) column ranges. Enter F46:F65, G46:G65,

and H46:H65, respectively. And (6) finally, a message box labeled “More Analysis” will

appear. Click on No. Clicking Yes will transfer you to the Optimal sheet. The Optimal

Plot Size analysis, however, is not necessary because we preselected the plot size to

use within this stratum.

Now scroll down to find a table with the Subsegment results. Only the Subsegment99(30)

and Subsegment132(40) plot sizes have values other than “0.” Both of these plot sizes

will have 0.05 (snags per plot) for their averages and 0.224 (snags per plot) for their

standard deviations. Because the center of the single snag encountered had a distance

greater than 33 feet (10 m) from the center line, it did not qualify for the Width33(10) 

or Width66(20) plot sizes. Therefore, each of these plot sizes have the value 0.0 for

both their averages and standard deviations. Print, or record these values for further

analysis. To print the results, (1) highlight the range with the mouse, (2) select Print

from the File menu, and (3) choose Selection.

If the macro ever stops because a cell range was entered incorrectly, you will see an

error message box. Click End within the message box and then proceed with the 

following steps to restore the sheet to its original format: (1) select all rows containing

data beneath the Grand Total row (2) select Delete from the Edit menu (3) click on

Entire Row (4) then activate the cell with the field name SUBSEGMENT (5) from the

Data menu choose Subtotals; and (6) select Remove all. This will return the data set 

to its original format.

Stratum 2 analysis—Click on the tab labeled Stratum2; this contains data from the 

second-growth stratum. Scroll down through the data set. Note that no target snags

were encountered during the pilot survey within this stratum. Subsequently, it is not

necessary to run either the Segment or Subsegment macros for this stratum. 

50
51

Stratum 3 analysis—Now click on the tab labeled Stratum3 in the lower left corner of

the screen. These are the data from the old-growth stratum. Begin your analysis by

obtaining averages and standard deviations for each 328-foot (100-m) long Segment

plot within this stratum. To begin this process, (1) choose Macro from the Tools menu,

(2) click on Segment, and (3) highlight Run. After the macro sums and condenses the

rows, a series of input boxes will appear. Follow these steps for the correct entries: 

(1) For the Copy Range input box enter C1:H86. Then the macro double checks to see

that you entered the correct range. Click on Yes if correct, otherwise click No and reenter the range. (2) Then the Paste Range will come up. Enter C90 as the location to

paste the data rows. (3) For the Width33(10) Statistics input box, enter E91:E100. 

(4) For the SEGMENT Results input box, enter the cell range E103. Your table of results

will be placed here. (5) Then for the ranges of the Width66(20), Width99(30), 

and Width132(40) newly pasted columns, enter F91:F100, G91:G100, and H91:H100,

respectively. (6) When asked whether you want to switch to the Optimal sheet, 

click on No. Now scroll down to examine, and record the results (table 7). Follow the

directions given above to print your results. You will find that an average of 0.7 snags

per plot were found in the Segment33(10) plot size. This is for a plot size 328 by 33 feet

(100 by 10 m). The standard deviation was 0.675 snags per plot. Segment66(20),

Segment99(30), and Segment132(40) plots each had an average of 1.6, 2.2, and 2.7

snags per plot, respectively. The column to the right of the averages lists the corresponding standard deviation for each plot size (table 7).

The next step in the Stratum 3 analysis is to obtain the averages and standard deviations for each Subsegment plot 164 feet (50 m) in length. To begin this process: (1)

Remove any results from the Segment macro analysis following the directions given

above with the exception of “Step 4.” Here you should highlight the field name SEGMENT, rather than SUBSEGMENT. (2) Then select Macro from the Tools menu. (3)

Highlight Subsegment. And (4) Click on Run.

Follow these steps so that correct cell ranges are entered within each of the input

boxes. Enter D1:H96 into the input box labeled Copy Range. When asked by the next

input box whether the range you entered was correct, press Yes if it was, No if not.

Reenter the correct range if necessary. The Paste Range input box should appear.

Enter D100 to have the newly pasted data rows copied here. For the Width33(10)

Statistics input box type in E101:E120. Then direct the macro to place the SUBSEGMENT Results table in the cell E123. Next, for the ranges of the newly pasted

Width66(20), Width99(30), and Width132(40) columns, enter F101:F120, G101:G120,

and H101:H120, respectively. Finally, a More Analysis? input box will appear. Choose

No to first print the results from your Subsegment analysis before transferring to the

Optimal sheet. Table 8 shows the correct averages and standard deviations for each 

of the Subsegment plot sizes. 

Optimal plot size—For this example, only the old-growth stratum is available for the

Optimal plot size analysis because plot sizes were preselected for the clearcut and 

second-growth strata. To begin the Optimal Plot Size, first transfer to the Optimal sheet
if you have not already. Use the tabs in the lower left corner of the screen to activate

the Optimal sheet. The averages and standard deviations for the old-growth stratum 

for each of the eight plot sizes available should have already been transferred by the

Segment and Subsegment macros (table 9). 

Now follow these steps to furnish the necessary information to aid in the decisionmaking

process: (1) Enter the number “20” into the box labeled Minimum Sample Size

Required. You enter “20” because you have three strata and need a minimum of 20

samples within each stratum for stratified landscapes. (2) Next, examine the values in

the Mean Density (no. per acre) column. Are they closer to two snags per acre (0.8

snags per ha) or eight snags per acre (3.2 snags per ha)? They are closer to two snags

per acre (0.8 snags per ha). Therefore, copy the estimated prices for a difficult, low

snag density situation and then paste these into the Cost per Sample column above

(table 9). (Note: If both hard and soft snags were included, the density would be high).

Select the difficult category because of large amounts of downed woody debris and

dense shrub cover in mainly steep areas.

To choose the Optimal plot size, consider these factors: (1) Segment99(30) plots require

the lowest number of plots (31) to be sampled, whereas Segment33(10) plots require

the smallest amount of acreage (16 acres [6.5 ha]) to be sampled. (2) Now look at the

values listed in the Product column. When the relative costs have been multiplied by

the relative variances, we find the Segment66(20) plots have the lowest product (3.32)

of the eight plot sizes. Therefore, based on Wiegert’s (1962) method, this is the optimal

plot size to use to sample for snags in this forest stratum. (3) Now look at the column

Total Cost. Do the results within this column support what we found in the Product 

column? Yes, they do. If we use this plot size, we would minimize our costs ($181) 

to obtain the desired level of precision. In addition, we would not be jeopardizing our

accuracy by trying to sample beyond the point of clear visibility from the center line.

Segment66(20) plots therefore seem to be the optimal plot size to use within stratum

three, and we will use this plot size for the remainder of the analyses.

Stratified density analysis—Your next objective in this process is to obtain an estimate 

of the required sample size for this subwatershed. To accomplish this, however, we

must first have an estimate of the stratified mean density to enter into the Sample Size

equation. To obtain the stratified density estimate follow these steps: (1) Click on the

tab labeled Densities. (2) Go to the section titled Stratified Random Sampling Equation.

(3) Enter the number of strata within the subwatershed in the shaded box labeled

Stratum. For this example, there are three strata so enter the numbers 1, 2, and 3. (4)

Enter the name of each plot size selected for sampling within each stratum under Plot

Dimensions (name). Stratum one used Subsegment132(40) plots, stratum two used

Subsegment66(20) plots, and three used Segment66(20) plots. The spreadsheet will

then provide the area in square feet (m) under the Plot Size column. This translates

into 21,648 feet2 (2000 m2) for the Subsegment132(40) and Segment66(20) plots and

10,824 feet2 (1000 m2) for the Subsegment66(20) plots, respectively. Notice that the

default area here is 5,412 feet2 (500 m2). Double-check to ensure that the correct area

52
53

Table 9—Optimal spreadsheetaPlot Mean Standard Mean Relative Sample Sample Number Dimensions Plot size density deviation density Variance variance(RV)= size size required 

Feet2 (m2) No./plot No./acre (no./ha) Plots Acres (ha)

Subsegment33(10) 5,412 (500) 0.35 0.489 2.82 (7) 15.5 (95.8) 4.3 136 17 (6.8) 2.2 (0.9)Subsegment66(20) 10,824 (1000) .8 .894 3.22 (8) 13 (80) 3.59 87 22 (8.7) 4.4 (1.8)Subsegment99(30) 16,236 (1500) 1.1 1.021 2.95 (7.33) 7.5 (46.3) 2.08 60 22 (9) 6.7 (2.7)Subsegment132(40) 21,648 (2000) 1.35 1.387 2.72 (6.75) 7.8 (48.1) 2.16 74 37 (14.7) 8.9 (3.6)Segment33(10) 10,824 (1000) 0.7 0.675 2.82 (7) 7.4 (45.6) 2.04 65 16 (6.5) 4.4 (1.8)Segment66(20) 21,648 (2000) 1.6 1.174 3.22 (8) 5.6 (34.4) 1.55 38 19 (7.5) 8.9 (3.6)Segment99(30) 32,472 (3000) 2.2 1.476 2.95 (7.33) 3.9 (24.2) 1.09 31 23 (9.4) 13.3 (5.4)Segment132(40) 43,296 (4000) 2.7 1.889 2.72 (6.75) 3.6 (22.3) 1.00 34 34 (13.6) 17.8 (7.2)

Lowest variance 3.61 (22.29)

Total cost

Plot Plot Relative Fixed Cost per per plot dimensions size variance cost sample unit Relative cost Product Total cost

Feet2 (m2) Dollars Dollars

Subsegment33(10) 5,412 (500) 4.3 1.06 1.19 2.3 1.00 4.3 307 Subsegment66(20) 10,824 (1000) 3.59 1.06 1.36 2.4 1.08 3.86 211 Subsegment99(30) 16,236 (1500) 2.08 1.06 4.59 5.7 2.51 5.22 339 Subsegment132(40) 21,648 (2000) 2.16 1.06 5.78 6.8 3.04 6.56 503 Segment33(10) 10,824 (1000) 2.04 2.11 2.38 4.5 2.00 4.08 291 Segment66(20) 21,648 (2000) 1.55 2.11 2.72 4.8 2.15 3.32 181 Segment99(30) 32,472 (3000) 1.09 2.11 9.18 11.3 5.02 5.45 354 Segment132(40) 43,296(4000) 1.00 2.11 11.56 13.7 6.08 6.08 466 

Lowest total cost = 2.25

a Optimal plot size analysis for hard snags in stratum three of the Douglas-fir/western hemlock forest subwatershed. Data from the

Strate.xls (Stratm.xls) file. Cost estimates taken from the Optimal spreadsheet in the General Cost per Sample Guidelines section.
54

size is being used. Also make sure you use the appropriate Plot Size name depending

on if you are using the metric or English spreadsheet. (5) Enter the number of acres

(ha) found within each stratum under Stratum Size (acres [ha]). There were 1,759,

1,381, and 1,243 acres (712.1, 559.1, and 503.2 ha, respectively), for strata one, two,

and three, respectively. (6) Enter the estimated densities and standard deviations for

each plot size within each stratum under Average Density (no. per plot) and Standard

Deviation (no. per plot), respectively. For stratum one, enter 0.05 for the average density

and 0.224 for the standard deviation. For stratum two, enter 0.00 for both of these values. For stratum three, enter 1.6 and 1.174 for the average and standard deviation,

respectively. (7) Finally, enter the number of samples you have for each stratum in the

column Sample Size. This should be “20” for strata one and two. You should enter “10”

for stratum three. The results from the Densities spreadsheet, shown in figure 6, 

estimate the average density on this subwatershed to be 0.953 + 0.359 target snags 

per acres (2.37 + 0.89 snags/ha).

Sample size determination—The next step in the analysis for multiple strata is to

obtain an estimate of the required sample size to obtain your desired level of precision.

The sample sizes required for stratified subwatersheds are calculated on the sheet

labeled “Sample Size.” Click on the tab in the lower left of the screen to bring up this

spreadsheet. Again, all shaded boxes require values to be entered. Notice that one of

the first pieces of information required is an estimate of the stratified mean. This was

estimated for you on the spreadsheet labeled Densities (fig. 6). Enter this value (0.953

snags per acre [2.37 snags per ha]) into the Pilot Sample Mean box.

Next, follow these steps to supply the correct information to the sample size spreadsheet: (1) Enter the number of strata you have under Stratum Number. For this example, there are three strata, so enter the numbers 1, 2, and 3. (2) Highlight the box where

the number “4” would go if there were four strata and press Delete. This is to ensure

that the spreadsheet uses the appropriate sample size equation. (3) Enter the number

of acres found within each stratum under Stratum Size (acres [ha]). There were 1,759,

1,381, and 1,243 acres (712.1, 559.1, and 503.2 ha), for strata one, two, and three,

respectively. (4) Enter the name of each of the plot sizes selected for sampling within

each stratum under Plot Dimensions (name). Stratum one used Subsegment132(40) plots,

stratum two used Subsegment66(20) plots, and stratum three used Segment66(20) plots.

(5) Finally, enter the estimated average densities and standard deviations 

for each plot size within each stratum under Average Density (no. per unit) and Standard Deviation (no. per unit). These should be 0.05 and 0.224, 0.00 and 0.00, and 1.6

and 1.174 for strata one, two, and three, respectively.

For the results, scroll to the bottom of the Sample Size page (fig. 7). First, look in the

section under the heading Optimal Allocation. This method, which incorporates the stratum variances into its calculations, estimates that only 54 (52) samples will be required 

to obtain a stratified mean that is within 20 percent of the true mean, 90 percent of the

time. These 54 (52) samples are then divided among the three strata. It estimates that

only 11 plots are needed in stratum one (clearcuts), none in stratum two (second

growth), and 43 (41) are required in stratum three (old growth).
55

Now look in the section under the heading Proportional Allocation. This method uses

the overall variance of the subwatershed and then allocates the samples based on the

size of each stratum. Here it is estimated that 128 samples must be taken to obtain the

same level of precision. This translates into 51, 40, and 36 plots, of the appropriate

size, to be sampled within each stratum. 

Figure 6—Densities spreadsheet. Stratified mean density estimate with a 90 percent confidence interval for qualifying hard snags for the Douglas-fir/western hemlock forest watershed. Data from Strate.xls (Stratm.xls) file.
56

Figure 7—Sample Size spreadsheet. Optimal and proportional sample size calculations for 

sampling hard snags in each of the three strata on the Douglas-fir/western hemlock 

subwatershed. Data from the Strate.xls (Stratm.xls) file.
57

You will notice that the two sample size equations are close in agreement about the

number of samples to take in stratum three. Within strata one and two, however, there

are large discrepancies. The optimal method suggests focusing most of the sampling

effort in stratum three (n = 43), which has the largest variance relative to the other strata. The optimal method recommends no samples should be taken in stratum two,

whereas the proportional method suggests 40 sample plots.

The results of the optimal allocation method recommending zero samples in stratum two

is a problem. Although on subwatersheds where clearcutting has been the primary

method of timber harvesting, and target snags within cut stands may be rare or nonexistent, it is still necessary to sample stands within these strata. Small values for both

the average and standard deviation within this stratum therefore should be entered. For

example, enter 0.01 for the average and 0.05 for the standard deviation. Examine figure 8 for the results. Now the optimal method requires four samples within stratum two.

We still recommend, however, that a minimum of 20 samples (from a minimum of five

stands) be taken within every stratum regardless of the estimated sample size required.

In this example, we would recommend not sampling within strata one and two anymore,

unless you think that encountering zero snags within these stands for the pilot sample

was an inaccurate representation of the conditions within these strata. Rather, focus

your sampling effort in stratum three by surveying 10 additional Segment66(20) plots.

These would best be distributed among three different stands. After these 10 plots have

been sampled, you will have met your minimum sample size requirement of 60. You

can then reanalyze the data to determine whether you want to continue sampling to

increase the precision of your estimate, or stop sampling because the estimate is precise enough to meet your objectives. It is important to remember that the most any

sample size equation can give you is an estimate of the number of samples required.

As additional data are collected, entered, and analyzed, therefore, you may find the variances, and consequently the required sample size, changing within a stratum. This

possibility increases if the pilot sample data turn out to be a poor representation of the

variation within a stratum. Consequently, the best way to avoid oversampling (where

large sample sizes are required) is to continually enter your data and periodically calculate a mean density and its bound to determine the current level of precision. 

Also, please refer to the discussion of Sample Size Determination in the “Computer

Analysis” section for a discussion of the advantages and disadvantages of optimal 

and proportional allocation methods for determining your sample size. 

Compare to target density—Let us now assume that 60 samples have been taken

and, therefore, it is possible to test whether the estimated density of qualifying snags

meets the targeted density listed in the Forest plan. You already have the bound on the

density estimate for the 90 percent confidence interval. See the Densities sheet. This

is 0.953 + 0.36 target snags per acre (2.47 + 0.90 snags per ha). Now bring up the sheet

labeled Statistical Test by clicking on this tab. To conduct the test, follow these steps: 

(1) Create your null hypothesis: Ho: There is no difference between the estimated and

the targeted hard snag densities. (2) Let us assume that the target density for hard

snags on this subwatershed is 1.51 snags per acre (3.73 snags per ha). Enter this

value into the shaded box labeled Target Density. (3) Enter the estimated snag density

of 0.953 snags per acre (2.37 snags per ha) into the shaded box labeled Estimated

Density. (4) Enter the estimated bound for a 90 percent confidence interval: 0.36 (0.89).

See table 10 for the correct entries.
58

Figure 8—Sample Size spreadsheet. Optimal and proportional sample size calculations for 

sampling hard snags in each of the three strata on the Douglas-fir/western hemlock forest 

subwatershed. Stratum two average density and standard deviation have been adjusted to 

compensate for zero snags encountered. Data from the Strate.xls (Stratm.xls) file.
59

Once the necessary information has been entered into the spreadsheet portion of the

Statistical Test sheet, a graph depicting the results is automatically created (fig. 9).

Looking at the graph, you can see that the line representing the target density for snags

does not enter within the upper and lower limits of the estimated density. You can therefore reject the null hypothesis, which states that “there is no difference between the 

estimated and targeted snag densities.” This test suggests that you can be 90-percent 

confident that the snag density on this subwatershed fails to reach the targeted density.

Now you have satisfied the requirements of your first objective: to determine whether 

or not the subwatershed met the targeted hard snag density. Subsequently, you can

decide whether or not to continue sampling to obtain a more precise density estimate.

Stratified distribution analysis—To obtain the necessary information to conduct a distribution assessment for this subwatershed, you will need to run the macro Pres_Abs

for each stratum with snags present. Details for this index are given in the “Computer

Analysis” section under “Distribution Analysis.” Numbers per acre

Confidence interval

1.60

1.40

1.20

1.00

0.80

0.60

0.40

0.20

0.00

90

Target density

Estimated density

Upper limit

Lower limit

Figure 9—Statistical Test spreadsheet. Graph depicting test for significant difference between estimated and

targeted densities of qualifying snags on Douglas-fir/western hemlock subwatershed. Input data from table 10. Numbers per acre

Percent Target Estimated

confidence density density

interval acre (no./ha) acre (no./ha) Upper limit Lower limit Bound

1.51 (3.73) .996 (2.47) 1.356 (3.37) .636 (1.57) .36 (.90)

90 1.51 (3.73) .996 (2.47) 1.356 (3.37) .636 (1.57) .36 (.90)

1.51 (3.73) .996 (2.47) 1.356 (3.37) .636 (1.57) .36 (.90)

Table 10—Statistical Test spreadsheet. The target density and the estimated snag

density and its bounds for qualifying hard snags for the Douglas-fir/western hemlock forest subwatershed. Data from the Stratify.xls file used to create figure 5.
60

Start with stratum one and complete these steps: (1) click on the Stratum1 tab to activate the sheet; (2) remove any subtotals that may be present (for detailed instructions

see “Restoring Sheet to Original Format” in appendix 4); (3) once the sheet is returned

to its original format, select Macro from the Tools menu; (4) click on Pres_Abs; (5) then

highlight Run. The macro will sum and condense the data rows for each Segment33(10)

plot; (6) then enter C1:E31 into the input box labeled Copy Range; (7) for the Paste

Range input box enter C34; (8) enter E35:E44 into the input box labeled Width33(10)

Range for the range of the newly pasted Width33(10) column; and (9) record the

Present and Count field values to enter onto the Distribution Index sheet. They should

have the values “0” and “10,” respectively. These fields are added to the right of the

Width33(10) column.

Skip the process for stratum two, because no target snags were encountered there.

Then repeat the above procedure for stratum three. For example: (1) click on the

Stratum3 tab to activate the sheet; (2) remove any subtotals that may be present (for

detailed instructions see “Restoring Sheet to Original Format” in appendix 4); (3) once

the sheet is returned to its original format, select Macro from the Tools menu; (4) click

on Pres_Abs; and (5) then highlight Run. The macro will sum and condense the data

rows for each Segment33 (10) plot. (6) When asked to enter the Copy Range, enter

C1:E86; (7) for the Paste Range enter C89; (8) enter E90:E99 for the newly pasted

Width33(10) Range; and (9) record Present and Count field values. They should be “6”

and “10,” respectively.

Now, to correctly enter the correct values onto the Distribution Index sheet follow these

steps: (1) activate the Distribution Index sheet by clicking on the tab with this title; (2) go

to Multiple-Strata Distribution Index section; (3) under Stratum enter the numbers 1, 2,

and 3 to indicate that there were three strata on this subwatershed; (4) in the cell where

the number 4 would go if there were four strata, press Delete; and (5) then enter the

number of acres of each stratum under Stratum Size (ac). These were 1,759, 1,381,

and 1,243 acres (712.1, 559.1, and 503.2 ha), for strata one, two, and three, respectively. (6) Next, enter the values “0” and “10” for the Present and the Count fields, respectively, for both strata one and two. (7) For stratum three enter “6” and “10” for the

Present and Count fields, respectively. Results show the distribution index for this subwatershed to be 0.39 (fig. 10). This means that it is questionable whether the habitat

needs of territorial cavity-nesters are being met on this subwatershed (see details in the

“Computer Analysis” section under “Distribution Analysis”).

Conclusions for multiple strata—The density and distribution results of this analysis

suggest that the necessary snag resources to sustain woodpecker populations may 

be inadequate on this subwatershed. Based on the results of the Compare to Target

analysis, estimated snag densities were less than the targeted snag densities listed in

the Forest plan. In addition, results from the distribution analysis indicate that large portions of the landscape do not support any snags at all. This can be a problem because

woodpeckers are territorial. These tests are not conclusive, however, unless a minimum

of 60 samples has been taken on a subwatershed of this size. 
61

At this point, you have several management options. First, you may want to continue

sampling to increase the precision of your estimates and to determine whether this

changes the results of your analyses. Second, you may want to examine recent

clearcut areas for the number, and quality, of the retention snags. Third, you may want

to work with foresters to increase snag retention efforts. Finally, you may want to initiate

snag creation programs to increase the density and improve the distribution of snags on

this subwatershed.

We thank Evelyn Bull, Trish Heekin, and Kim Mellen for reviewing our manuscript. Kirk

Steinhorst provided a thorough statistical review of our work. Will Hutchinson, Christine

Hunter, Phil Talbot, Kris Allison, Klaus Rossini, Ian Cole, and Adam Messer assisted in

data collection. Funding was provided by the Pacific Northwest Region and the

Washington Office of the USDA Forest Service. Lisa Norris and Richard Holthausen

were instrumental in obtaining funding from the Pacific Northwest Region and the

Washington Office.

When you know: Multiply by: To find:

Centimeters (cm) 0.394 Inches

Meters (m) 3.281 Feet

Hectares (ha) 2.471 Acres

Acknowledgments

Figure 10—Distribution Index spreadsheet. The distribution index for qualifying snags for the Douglas-fir/

western hemlock subwatershed. Data from the Strate.xls (Stratm.xls) file. Distribution Index values of 0.40

or less indicate a poor snag distribution.

Proportion of Proportion of plots Distribution

Stratum size in plots with with snag/tree present Index

Stratum acres (h/a) Present Count (N) snag/tree present (adjusted) equations

1 1,759 (712.1) 0 10 0 0

2 1,381 (559.1) 0 10 0 0 0.00

3 1,243 (503.2) 6 10 0.6 1.37 0.36

0 0 0.36

Total acres 4,383 (1,774.4)

Distribution Index: DIst = 0.39

English Equivalents
62

Bate, Lisa J. 1995. Monitoring woodpecker abundance and habitat in the central 

Oregon Cascades. Moscow, ID: University of Idaho. 116 p. M.S. thesis.

Beebe, Spencer B. 1974. Relationships between insectivorous hole-nesting birds 

and forest management. New Haven: Yale University, School of Forestry and

Environmental Studies. 49 p.

Bull, Evelyn L.; Carter, Bernie; Henjum, Mark [and others]. 1991. Monitoring 

protocol-October 1991. Protocol for monitoring woodpeckers and snags in the Pacific

Northwest region of U.S. Forest Service. 8 p. Unpublished report. On file with: 

U.S. Department of Agriculture, Forest Service, Pacific Northwest Forest and Range

Experiment Station, Forestry and Range Sciences Laboratory, La Grande, OR 97850.

Bull, Evelyn L.; Holthausen, Richard S. 1993. Habitat use and management of

pileated woodpeckers in northeastern Oregon. Journal of Wildlife Management.

57: 335-345. 

Bull, Evelyn L.; Holthausen, Richard S.; Henjum, Mark G. 1992. Roost trees 

used by pileated woodpeckers in northeastern Oregon. Journal of Wildlife

Management. 56(4): 786-793.

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among woodpeckers in northeastern Oregon. Res. Note. PNW-444. Portland, OR:

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19 p.

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Cochran, William G. 1977. Sampling techniques, 3d ed. New York: John Wiley 

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47(3): 799-804.

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66

I. Landscape definition and selection (these snag and large tree sampling methods are

intended for use on a landscape, or subwatershed, scale; they are not intended for

sampling on the individual stand (<100 acres [40 ha]) where complete counts are

more appropriate). 

A. Select landscape.

B. Delineate boundaries if necessary. 

II. Sampling objectives

A. Size and condition of snags and large trees to be surveyed

1. Decide what diameter of snags or large trees will be surveyed.

2. Decide what height of snags will be surveyed.

3. What condition of snags and large trees will be surveyed? 

a. Both hard and soft snags? 

b. All trees? Just hollow trees? 

4. Should any species be excluded? For example, if a particular tree species is

known to provide little, if any, wildlife value, should it be excluded from your

sampling program?

5. Should wildlife use signs be recorded (e.g., woodpecker foraging and nesting

signs)?

B. Density estimate objectives

1. Estimate average density.

2. Compare to target density.

C. Obtain a distribution index.

III. Landscape stratification

A. Visit the area if you are unfamiliar with it. Landscape patterns unclear on maps

may become apparent from an initial ground survey. What are the obvious differences visible across the landscape? What are the similarities? Would combining

stands into strata that are homogenous in regards to snag or large tree densities,

or forest structure, increase your precision? Decrease your sampling effort? If so,

begin the stratification process.

Appendix 1:

General Snag 

and Large Tree

Sampling

Guidelines
67

B. Obtain several reference maps of landscape for use in the field: geographical information system (GIS) or Orthoquad maps, or both, containing the 

following information:

1. Current road system (use maps scaled to 1:31,680 or less)

2. Stand units and their unique numeric identifier

3. Current seral stage of vegetation

4. Aerial photographs of the survey area.

C. Run a query by using either the GIS or any stand exam database available.

Obtain any, or all, of the following information for each stand if it will aid in the

stratification process:

1. Forest community type

2. Management history (i.e., harvest information, prescribed burns)

3. Seral stage

4. Predicted snag and large tree densities. 

D. Visit area with above information.

E. Assign each stand to a stratum. 

F. Obtain number of acres (ha) within each stand or stratum.

IV. Surveying procedures

A. Establishing transects

1. Option 1: randomly place transects across landscape.

a. Randomly place a grid over the subwatershed map.

b. Select five grid points within each stratum that will be used to establish 

starting points for each transect.

c. Randomly select five compass bearings for each of the transect 

starting points. 

d. Determine if each of the five transects within each stratum fall within sufficient area of the stratum to allow four sample subsegments (164 feet [50

m]) to be placed; if not, select additional transects and starting points until a

total of 20 samples (subsegment lengths), from a minimum of five stands,

have been located within each stratum.
68

2. Option 2: Randomly select stands. For use in highly fragmented landscapes with

many small stands.

a. Randomly pick stand unit numbers from the complete list of stands within that

stratum for sampling.

b. Select a random point along the road bordering the stand to use for entry into

the stand.

c. Then from the point along the road selected above, randomly select a starting

point from which to establish a transect perpendicular to the road within 164

feet (50 m) of the edge of the stand.

d. Continue stand selection until a total of 20 samples (subsegment lengths), from

a minimum of five stands, have been located within each stratum.

B. Plot size selection

1. Prepilot sampling plot size selection, for example: 

Based on information gathered during the stratification process, it may be 

beneficial to preselect a plot size for sampling. For example:

a. In open, clearcut strata supporting low densities (<1per acre [0.4 per ha]) 

of snags or trees, use Subsegment132(40) plots. 

b. In dense (visibility <33 feet [10 m]) strata supporting low densities (<1 per acre

[0.4 per ha]) of snags or trees, use Subsegment66(20) plots.

c. See appendix 3 for other situations where plot sizes may be preselected.

2. Postpilot sampling plot size selection

In most forested conditions, the optimal plot size to use for sampling is unknown 

until the density and distribution of the snags or trees can be evaluated. 

In these situations therefore:

a. Use pilot sample data to determine which plot sizes minimize 

sampling effort to obtain your desired objectives. See “Optimal Plot 

Size Analysis” section for details.

b. Use Optimal plot size for remainder of survey.

C. Field surveying techniques

1. Establish transects by using a hip-chain starting from the points selected above.

The hip-chain line also marks the center of the strip transect. 
69

2. Delineate subsegment lengths (164 feet [50 m]) along the transect. Assign 

a unique numeric identifier to each subsegment as you sample (see appendix 2

for details).

3. Always sample subsegment lengths in sets of two. Two subsegments equal one

segment. This will allow macros to help you determine whether shorter or longer

plots are more efficient for your specific forest conditions. This is a function of the

density and distribution of snags or trees in the area. This also allows you to

obtain a Distribution Index.

4. For each subsegment length during the pilot survey, conduct a complete count of

all qualifying snags or trees out to 66 feet (20 m) from the center line.

5. Record the perpendicular distance from the center line to the midpoint of each

snag or tree. This information will aid in the decision making process for the optimal plot width. 

6. Note: If after the survey begins, you realize visibility in stand is limited (<33 feet

[10 m]), count only snags and trees out to 33 feet (10 m) from the line. Wider

plots may be inaccurate in these conditions.

7. Note: If after the survey begins, you realize snag or tree densities are consistently

high (>15 snags or trees/plot), count only snags and trees out to 33 feet (10 m)

from the line. Wider plots may be inefficient in these conditions.

8. Refer to appendix 2 for details on other information collected for each snag 

or tree.

9. After pilot survey, count only snags and trees within the boundaries of the chosen 

plot size.

V. Data Entry

A. Make backup copies of all files before entering own data.

1. Open the Estimate.xls (Estimatm.xls) file. 

2. Rename the Estimate.xls (Estimatm.xls) file with the subwatershed name or

another file name. 

3. Enter your data into the newly named file on Sheet 1. 

4. Double check data to ensure that the number “9999” has been entered in each

subsegment where no snags or trees were encountered.
70

VI. Computer analysis for stratified landscapes

A. Run Consecutive macro.

1. This sorts data sets by consecutive Segments and Subsegments.

2. Scroll through the entire data set to ensure that two Subsegment plots are

entered for each Segment. For example, Segment 13 should contain

Subsegments 13.1 and Subsegments 13.2

B. Run Formula macro to have “If, then” formulas entered into Width columns. 

If a snag or tree meets the criteria that you specify, it will then be included 

in the analysis.

1. Specify minimum d.b.h. of snags or trees.

2. Specify minimum height of snags or trees.

3. Specify maximum decay (snags) or structural (trees) class.

4. Specify species of snags or trees.

C. Run Sort macro to separate strata for individual analysis.

D. Run Segment macro to obtain averages, standard deviations, and sample sizes 

for each of the four segment (328 feet [100 m]) plots widths based on the criteria 

you provided to the Formula macro.

E. Run Subsegment macro to obtain averages, standard deviations, and 

sample sizes for each of the four subsegment (164 feet [50 m]) plot widths based 

on the criteria you provided to the Formula macro.

VII. Optimal Plot Size Analysis

A. Given mean and variance of each plot size, which one of the eight possible plot

sizes minimizes the number of samples required? Note that if snags or trees were

counted only out to 33 feet (10 m) from the center line, only four 

possible plot sizes are available.

B. Given mean and variance of each plot size, which one minimizes the 

number of acres (ha) required?

C. Which plot size minimizes the product of the relative variance and 

relative cost?

D. Which plot size predicts the lowest Total Cost? 

E. Select plot size which seems Optimal given your specific forest conditions.
71

VIII. Sample Size Determination

A. Use Sample Size spreadsheet to obtain estimate of total sample size required by

using plot sizes selected above. 

B. Collect remaining number of samples, after pilot survey samples, to meet your

objectives.

C. Continue to enter additional data on Sheet 1 as collected.

IX. Density Analysis

A. Use Density spreadsheet to obtain density estimate and its bound.

B. Use Statistical Test spreadsheet to compare estimated density to targeted density

(optional).

X. Distribution Analysis

A. Use Distribution Index spreadsheet to assess the distribution of snags and trees

across the landscape.
72

1. Stratum: Enter the stratum number: 

1, 2, 3, or 4.

2. Location: Enter the stand number in

which the plot is contained.

3. Segment: Enter a single whole 

number to indicate which 328-foot 

(100-m) transect length is being surveyed

(e.g., 1, 2, 3, or 4). No two numbers

within a survey area should be the same.

4. Subsegment: Enter the corresponding

whole number of the Segment that this 

164-foot (50-m) transect length is nested

within. Then give the Subsegment an 

additional number after a decimal point to

indicate whether the Subsegment is the 

first, or second, within this Segment. For

example, the two Subsegments nested 

within Segment 1 should be identified as

Subsegment 1.1 and 1.2.

5. Width33(10): This column will be

filled in by the macro for all snags or

trees that meet the target criteria and 

are <16.5 feet (5 m) away from the 

center line.

6. Width66(20): This column will be filled

in by the macro for all snags or trees that

meet the target criteria and are <33 feet

(10 m) away from the center line.

7. Width99(30): This column will be filled

in by the macro for all snags or trees that

meet the target criteria and are <49 feet

(15 m) away from the center line.

8. Width132(40): This column will be

filled in by the macro for all snags or

trees that meet the target criteria and 

are <66 feet (20 m) away from the 

center line.

9. Distance: Enter the perpendicular 

distance between the midpoint of the

qualifying snag or tree and the center of

the transect line to the nearest foot (nearest halfmeter). If no snag is encountered

within the entire Subsegment, enter

“9999” under distance. It is critical to

measure distances precisely. If the midpoint of a snag or tree falls directly on the

boundary, include the first one, exclude

the second one, and so on.

10. Species: Enter the corresponding

numeric code of the snag or tree species

encountered (standardized species codes

taken from Stand Exam Program in the

Pacific Northwest Region [USDA Forest

Service 1991]). 

Douglas-fir/redwoods:

Douglas-fir (Pseudotsuga menziesii) 202

Redwood (Sequoia sempervirens) 211

True firs:

Pacific silver fir (Abies amabilis) 011

White fir (A. concolor) 015

Grand fir (A. grandis) 017

Subalpine fir (A. lasiocarpa) 019

California red fir (A. magnifica var.

magnifica) 020

Shasta red fir(A. magnifica var.

shastensis) 021

Noble fir (A. procera) 022

Cedars:

Port-Orford-cedar 

(Chamaecyparis lawsoniana) 041

Alaska cedar (C. nootkatensis) 042

Incense-cedar (Calocedrus decurrens) 081

Western redcedar (Thuja plicata) 242

Appendix 2:

Field Form

Explanations
73

Larch:

Western larch (Larix occidentalis) 073

Spruce:

Brewer spruce (P. breweriana) 092

Engelmann spruce (Picea engelmannii) 093

Sitka spruce (P. sitchensis) 098

Pines:

Lodgepole pine (Pinus contorta) 108

Jeffrey pine (P. jeffreyi) 116

Sugar pine (P. lambertiana) 117

Western white pine (P. monticola) 119

Ponderosa pine (P. ponderosa) 122

Hemlock:

Western hemlock (Tsuga heterophylla) 263

Mountain hemlock (T. mertensiana) 264

Hardwoods:

Bigleaf maple (Acer macrophyllum) 312

Red alder (Alnus rubra) 351

Western paper birch ( Betula papyrifera) 376

Pacific madrone (Arbutus menziessii) 361

Golden chinkapin (Castanopsis 

chrysophylla) 431

Oregon ash (Fraxinus latifolia) 542

Tanoak (Lithocarpus densiflorus) 631

Quaking aspen(Populus tremuloides ) 746

Black cottonwood (P. trichocarpa ) 747

Oregon white oak (Quercus garryana ) 815

California black oak (Q.. kelloggii ) 818

Oregon myrtle (Umbellularia californica) 981

Other conifers:

Subalpine larch (Larix lyallii ) 072

Cypress (Cupressus) 050

All junipers (Juniperus) 060

Pacific yew (Taxus brevifolia) 231

Knobcone pine (P. attenuata) 103

Limber pine (P. flexilis) 113

Whitebark pine (P. albicaulis) 101

11. Class: Enter the numeric value for

the appropriate decay or structural class

of the snag or tree encountered. Snag

data should be collected on a data form

separate from large trees. For snags, 

the numeric value should increase with

increasing amounts of decay. For 

example, Parks and others (1997) 

categorized snags into three structural

classes.

A. Snag structural classes

1. Snags that have recently died.

2. Snags that have been dead several

years and have lost some branches 

and bark.

3. Snags that have been dead a long

time and lack branches and bark

(except grand fir and Douglas-fir, 

which tend to retain bark). 

In contrast, numeric values for the 

structural class of trees should decrease

with increasing amounts of decay. 

For example:

Tree structural classes

1. Hollow

2. Some decay evidence (broken

branch or top, fungi, wildlife signs)

3. Broomed trees

4. Sound

Refer to Bull and others (1997) for

detailed information on delineating 

categories and identifying trees useful 

to wildlife in the field.

12. D.b.h.: Enter the diameter at breast

height of the snag or tree encountered

using a d.b.h., stick or tape, to the 

nearest inch (cm). 

13. Height: Enter the height of the snag

or tree to the nearest foot (m).
74

14. Cavity: Enter the appropriate numeric code to indicate any nesting use of the

snag or tree under consideration. 

1. New cavity indicated by one

or all of following: fresh wood

chips on ground below hole, light

colored wood around entrance,

bird occupying cavity (excavated

or natural).

2. Old cavity: Gray colored chips

on ground below hole, gray colored wood around entrance, no

sign of bird occupying cavity

(excavated or natural).

3. Both old and new cavities

4. Other wildlife use.

5. Unknown. It is not possible to

determine whether any cavities 

are present.

6. No cavities found.

15. Foraging: Enter the appropriate

numeric code to indicate any foraging use

of the snag or tree under consideration. 

1. New foraging indicated 

by light colored wood around 

foraging sign, recent scaling. 

2. Old foraging indicated by 

gray colored wood around 

foraging sign.

3. Both old and new foraging.

4. No foraging signs.
75

Appendix 3:

Recommended

Plot Sizes for

Presampling

Table 11–Recommeded plot sizes for presampling plot sizeaRecommendedplot size Forest conditionsb Density Distribution Examples

Subsegment132(4)c Easy Low (<1 snag/acre [0.4/ha]) Evenly scattered Recent clearcutsSegment66(20) Moderate Medium (5 snags per acre [2/ha]) Clumped Pockets of beetle killSubsegment66(20)d Moderate High (>8 snags per acre[3.2/ha]) Evenly scattered Widespread beetle kill or

stand replacement burns

Segment66(20) Easy-moderate Low (<2 snags per acre [0.8/ha]) Clumped Open grass areas 

with treed draws

Subsegment66(20) Difficult Low (<1 snag/acre [0.4/ha]) Scattered Dense regeneration standsa In most forested areas, however, the optimal plot size should be determined by evaluating the density and distribution of snags or trees within the areas

and then conducting an Optimal Plot Size Analysis

b Easy forest conditions refer to high visibility (>66 feet [20 m]), easy travel, little slope; moderate refers to medium visibility (approx. 49.5 feet [15m]), 

moderate travel conditions due to downed woody debris, high shrub cover, or moderate slope (≤50 percent slope); difficult refers to low visibility (<33 feet

[10 m]), difficult travel due to large amounts of downed woody debris, high shrub cover, or high slope (≥50 percent).

c If interested in foraging and nesting use in clearcuts, use Segment132(40) plots to encounter more snags.d If densities are extremely high such that >15 snags per plot are consistently encountered, Subsegment33(10) plots may be more appropriate.
76

Appendix 4:

Frequently Used

Excel Commands

in Computer

Analysis

I. To start a macro over:

1. Press Enter or OK until message box with Error appears.

2. Select End.

3. Follow directions to restore sheet to its original format.

II. To restore a sheet to its original format:

1. Select all rows containing data beneath the Grand Total row.

2. Select Delete from the Edit menu.

3. Click on Entire Row. 

4. Then activate the cell with the field name SEGMENT (SUBSEGMENT if you

are running the SUBSEGMENT macro).

5. From the Data menu choose Subtotals.

6. Select Remove all.

III. To print out results:

1. Use mouse to highlight area to be printed (Click and drag with mouse).

2. Select Print from the File menu.

3. Click on Selection.

4. Choose OK.

IV. To edit a formula:

1. Activate top cell in column with formula to edit.

2. Press the function key “F2” at the top of the keyboard.

3. Change formula to meet your criteria.

4. Press Enter. (Arrow keys do not work in Edit mode.)

5. Copy and paste top cell throughout the column.

V. To copy and paste:

1. Highlight range to copy using the mouse. Click and drag for large areas.

2. Select Copy from the Edit menu.

3. Highlight area where formula is to be pasted.

4. Choose Paste from Edit menu.

VI. To reverse out of a process:

1. Press Escape.
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Bate, Lisa J.; Garton, Edward O.; Wisdom, Michael J. 1999. Estimating snag and large tree

densities and distributions on a landscape for wildlife management. Gen. Tech. Rep. PNWGTR-425. Portland, OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest

Research Station. 76 p.

We provide efficient and accurate methods for sampling snags and large trees on a landscape to

conduct compliance and effectiveness monitoring for wildlife in relation to the habitat standards

and guidelines on National Forests. Included online are the necessary spreadsheets, macros, and

instructions to conduct all surveys and analyses pertaining to estimation of snag and large tree

densities and distributions at the subwatershed scale. The methods focus on optimizing sampling

effort by choosing a plot size appropriate for the specific forest conditions encountered. Two

methods are available for density analysis. Method one requires sampling until a desired precision level is obtained for a density estimate. Method two is intended for use in areas that have

low snag densities compared to Forest plan targeted densities. After taking a minimum of 60 samples, one may test for a significant difference between the estimated and targeted densities. In

addition, data can be used to calculate a distribution index. The value obtained from the distribution index indicates whether the current distribution of target snags and large trees across a subwatershed is adequate to meet the habitat needs of territorial cavity-nesters and other wildlife

species. Wildlife use also may be evaluated.

Keywords: Density, distribution, foraging, nesting, monitoring, sampling technique, snag, large

tree, woodpecker, wildlife management, wildlife use. 

The Forest Service of the U.S. Department of Agriculture

is dedicated to the principle of multiple use management

of the Nation’s forest resources for sustained yields of

wood, water, forage, wildlife, and recreation. Through

forestry research, cooperation with the States and private

forest owners, and management of the National forests

and National Grasslands, it strives—as directed by

Congress—to provide increasingly greater service to a

growing Nation.

The United States Department of Agriculture (USDA) 

prohibits discrimination in all its programs and activities on

the basis of race, color, national origin, gender, religion,

age, disability, political beliefs, sexual orientation, or marital

or family status. (Not all prohibited bases apply to all programs.) Persons with disabilities who require alternative

means for communication of program information (Braille,

large print, audiotape, etc.) should contact USDA’s TARGET Center at (202) 720-2600 (voice and TDD).

To file a complaint of discrimination, write USDA, Director,

Office of Civil Rights, Room 326-W, Whitten Building,

14th and Independence Avenue, SW, Washington, DC

20250-9410 or call (202) 720-5964 (voice and TDD).

USDA is an equal opportunity provider and employer.

Pacific Northwest Research Station

333 S.W. First Avenue

P.O. Box 3890

Portland, Oregon 97208-3890
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