1

Attachment 12: Description of Statistical Survey Design

The following represents an anticipated experimental design for survey implementation, along 

with the associated number of completed surveys that will be required. Part B of this supporting 

statement provides detail on the sampling design. The proposed design and sampling plan is based on 

standard design and sampling theory for choice experiments and population surveys, as outlined by 

Louviere et al. (2000), Kuhfeld (2009) and Dillman (2000). EPA notes that the anticipated experimental 

design described here is preliminary and it may be subject to refinements during design evaluations to 

account for issues such as dominant or dominated pairs, ecological feasibility, and to remove attribute 

combinations which do not provide information for estimation.

The purpose of the Chesapeake Bay survey is to calculate average per household parameters 

(e.g., willingness to pay and choice probabilities) within a given survey population. Additional analysis 

that differentiates per-household parameters may be conducted within groups of households which use 

or do not use the Chesapeake Bay.

Experimental design for the choice experiments

Based on focus groups and pretests, and guided by realistic ranges of attribute outcomes, the 

anticipated experimental design includes a fixed status quo or “no policy” option (Option A), and two 

multi-attribute choice options or alternatives, B and C. Choice options, named Option B and Option C, 

are characterized by three potential levels for environmental attributes and six different levels of annual 

household cost. Furthermore, the baseline environmental attribute levels vary over the split-sample 

experiments, with the Option A or status quo choice representing either a constant, declining, or 

improving baseline in the environmental attributes.

Different split-sample experiments will be produced in the three geographic divisions:

1. Bay States: Maryland, Virginia, District of Columbia

2. Watershed States: Delaware, New York, Pennsylvania, and West Virginia

3. Other East Coast States: Vermont, New Hampshire, New Jersey, Massachusetts, 

Connecticut, Rhode Island, Maine, North Carolina, South Carolina, Georgia, and Florida
2

Within these geographic divisions, the split-sample experiment cells will collect more detailed 

information in the Bay states, as stipulated in Table A15-1. 

Table A15-1. Split-sample design cells.

Geographic division Baseline factor

Cell 1 Bay States Declining

Cell 2 Bay States Constant

Cell 3 Bay States Improving

Cell 4 Watershed Declining

Cell 5 Watershed Constant

Cell 6 Watershed Improving

Cell 7 Other East Coast Declining

Cell 8 Other East Coast Constant

Cell 9 Other East Coast Improving

Options A and B are characterized by levels for the following five attributes:

1. Change in water clarity in A and B (x1A; x1B) – 3 possible levels

2. Change in blue crab abundance in A and B (x2A; x2B) – 3 possible levels

3. Change in striped bass abundance in A and B (x3A; x3B) – 3 possible levels

4. Change in oyster abundance in A and B (x4A; x4B) – 3 possible levels

5. Change in lake condition in A and B (x5A; x5B) – 3 possible levels

6. Cost in A and B (x6A; x6B) - 6 possible levels

This implies an experimental design characterized by [35×6] for each alternative, or [310×6

2

] for 

alternatives A and B.

To construct a preliminary main effects design with 72 profiles that is sufficiently flexible to 

estimate alternative specific main effects and response patterns (i.e., a non-generic design), we begin 

with a 35x6 orthogonal fractional factorial design with 144 profiles. We then combined the elements of 

this design into pairs that would reflect trade-offs at the margin (i.e., improvements in the attributes that 

are attained at the cost of decrease in other environmental attributes and/or increase of the overall cost of 

the program). Finally, these pairs were blocked1in such a way that variability of the environmental and 

 

1 EPA assigned each profile to an independent subset, or “block” of profiles. Blocking reduces the number of profiles each 

respondent sees, thus reducing respondent burden. 
3

cost attributes within a block would be maximized (and hence the main effects would not be confounded 

with the block effects). The result is a design with 72 profiles, with attributes labeled following the 

above notation, and levels indicated by integers 1...N, where N for each attribute is the number of levels 

identified above.

Following common practice in the environmental economics literature, we anticipate three 

choice questions per survey. This allows the 72 profiles to be included (orthogonally blocked) in 24 

unique survey booklets, as illustrated in Table A15-2. The attribute levels applied within surveys are 

summarized in Table A15-3. Monte Carlo evidence suggests that 6 to 12 completed responses are 

required for each profile in order to achieve large sample statistical properties for choice experiments 

(Louviere et al. 2000, p. 104, citing Bunch and Batsell 1989). Following this guidance, the above design 

will require 24×12 = 288 completed surveys, or 12 completed surveys for each unique survey booklet. 

This will provide a total of 864 profile responses per cell.

Table A15-2. The set of 72 design profiles within each geographic division by 

baseline cell.

Booklet X1A X2A X3A X4A X5A X6A X1B X2B X3B X4B X5B X6B

1 1 2 1 2 2 6 2 1 1 1 2 5

1 2 1 2 3 3 3 3 1 2 3 1 1

1 3 3 3 1 2 2 3 3 2 2 2 1

2 1 1 2 2 2 4 1 1 3 1 2 5

2 2 2 1 3 1 5 1 2 1 3 2 6

2 3 3 3 2 3 3 3 3 2 3 2 2

3 2 2 2 1 2 2 1 2 1 3 2 5

3 2 3 1 2 3 6 1 1 1 2 3 2

3 3 1 3 3 1 1 2 1 3 3 3 2

4 1 1 2 2 3 3 1 3 3 2 1 4

4 2 3 3 3 1 1 2 2 3 3 2 1

4 3 1 2 2 3 5 3 1 2 1 2 2

5 1 1 3 1 1 4 1 2 1 1 2 4

5 2 3 3 2 3 6 1 3 3 2 1 2

5 3 2 3 2 3 3 3 3 2 3 2 3

6 1 1 2 1 3 3 2 2 3 1 3 4

6 2 1 1 2 2 3 2 3 1 2 1 5

6 3 1 3 3 1 6 3 2 3 2 1 5

7 1 1 2 2 3 2 2 1 3 2 1 4

7 1 3 3 1 2 1 1 2 3 3 2 2

7 2 2 1 3 1 3 3 2 1 1 1 1

8 2 1 1 1 3 2 2 1 3 1 2 4

8 2 2 2 2 3 1 2 2 2 3 2 1

8 3 3 2 3 1 4 1 3 1 3 1 3

9 1 1 2 3 3 5 1 3 2 3 2 6
4

9122116111113

9311221213223

10121311131323

10133233233335

10312126112113

11213131222131

11231226132225

11323133323224

12221113211314

12312221222221

12332332323331

13131131331234

13222136222214

13231325311323

14131231221232

14212124212316

14322216313215

15121335321134

15232323233224

15311216311126

16123115132116

16223336323135

16311231331132

17113225123216

17232136133136

17311316211114

18122233111231

18233122223223

18322212323313

19113321313312

19132314122212

19322135331136

20122322121334

20232215221212

20333334233312

21232111133111

21323226323113

21331334321322

22131111231123

22213336113132

22232335122334

23212215211112

23311335112334

23322124332113

24123125113326

24131212331224

24332115331125
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Table A15-3: Attribute Levels Included in Each Survey Version.

Attribute

Attribute Levels

Baseline 1 2 3 4 5 6

Declining Baseline

Water Clarity (feet) 1.5 3 5 6 - -

-

Striped Bass (millions) 21 24 28 30 - -

-

Blue Crab (millions) 235 250 280 312 - -

-

Oysters (tons) 2,800 3,300 4,300 5,250 - -

-

Low Algae Level Lakes 2,300 2,900 3,300 3,850 - -

-

Annual Household Cost - $20 $40 $60 $180 $250 $500

Constant Baseline

Water Clarity (feet) 3 3 5 6 - -

-

Striped Bass (millions) 24 24 28 30 - -

-

Blue Crab (millions) 250 250 280 312 - -

-

Oysters (tons) 3,300 3,300 4,300 5,250 - -

-

Low Algae Level Lakes 2,900 2,900 3,300 3,850 - -

-

Annual Household Cost - $20 $40 $60 $180 $250 $500

Improving Baseline

Water Clarity (feet) 4 4 5 6 - -

-

Striped Bass (millions) 26 26 30 35 - -

-

Blue Crab (millions) 260 260 312 340 - -

-

Oysters (tons) 4,300 4,300 5,250 6,500 - -

-

Low Algae Level Lakes 3,100 3,350 3,600 3,850 - -

-

Annual Household Cost - $20 $40 $60 $180 $250 $500

Realized Sample Sizes for Maximum Acceptable Sampling Error

The goal of the choice experiment is to estimate regression coefficients from mixed or 

conditional logit models that may be used to estimate willingness to pay for multi-attribute policy 

alternatives, or the likelihood of choosing a given multi-attribute alternative, following standard random 

utility modeling procedures (Haab and McConnell 2002). Hence, the sample size requirements are 

determined by the accuracy of the parameter estimates in the WTP models.

The resulting sample design will be a single stage stratified sample. No clustering (multiple 

stages of selection) will be necessary. Unequal probabilities of selection will result in different 

geographic divisions defined in Part B, Section 2 “Survey design”, and lead to varying sampling 

weights, as demonstrated in Table A15-4 (assuming that the design contains 9 cells). Due to these 
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varying weights, under assumptions of constant response rate and fixed sample size, the expected design 

effect due to differential baseline weights is 1.75. The realized design effect will likely be higher due to 

extra variability of weights within cells due to non-response adjustments.

Table A15-4. Sample size and accuracy projections.

Geographic 

division

Population 

size

Expected 

sample size

Expected 

weights

Standard 

error, 

50% 

incidence

Standard 

error, 10% 

incidence

Bay States 5,479,176 864 6341 0.017 0.010

Watershed 13,442,787 864 15,559 0.017 0.010

Other East Coast 25,431,478 864 29,434 0.017 0.010

Overall 44,353,441 2,592 17,081 0.011 0.007

Source: The household population size for each region was obtained from U.S. Census Bureau 

(2012). 2010 Census Summary File 1. Retrieved May 31, 2012 from http://factfinder2.census.gov/.

The maximum acceptable sampling error for predicting response probabilities (the likelihood of

choosing a given alternative) in the present case is ±10%, assuming a true response probability of 50% 

associated with a utility indifference point. Given the survey population size, this level of precision 

requires a minimum sample size of approximately 96 observations. The number of observations 

(completed surveys) required to obtain large sample properties for the choice experiment design provide 

more than sufficient observations to obtain this required precision for population parameters.

Projected sample sizes given the potential non-response

Survey non-response is a common phenomenon. The sample design must be proactive and 

account for the potential non-response. Based on recent experience with surveys of similar nature, EPA 

expects the response rate for the Chesapeake Bay survey to be close to 30%. Additionally, the expected 

eligibility rate for a mail survey is 92%, and accounts for vacant, seasonal, non-existent, and otherwise 

ineligible units. The projected number of required mailings is given in Table A15-5 for different 

scenarios (response rates of 20% and 30%) and different sample size determination methods (expected 

number of mailings vs. the number of mailings that ensures 90% probability of reaching the cell target 

sample size).
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Table A15-5. Required sample size.

Target cell size: 

n=288

r=20% response rate r=30% response rate

Mean 

projection, n/r

90% prob 

to achieve 

cell size

Mean 

projection, 

n/r

90% prob to 

achieve cell 

size

Required cell size 1,565 1,672 1,043 1,111

District of Columbia 229 244 152 162

Maryland 1,848 1,974 1,231 1,311

Virginia 2,619 2,798 1,745 1,857

Delaware 120 128 80 85

New York 2,556 2,731 1,703 1,813

Pennsylvania 1,753 1,873 1,168 1,243

West Virginia 267 285 178 189

Connecticut 253 270 170 180

Florida 1,370 1,465 913 973

Georgia 662 707 441 470

Maine 103 110 69 73

Massachusetts 470 502 313 334

New Hampshire 96 102 64 68

New Jersey 593 634 395 421

North Carolina 691 739 461 491

Rhode Island 76 82 51 54

South Carolina 333 355 222 236

Vermont 47 51 32 34

Total: 14,086 15,050 9,388 9,994

The sample size required for 90% probability of achieving the cell size is computed as the 90-th 

percentile of the negative binomial distribution with success probability equal to the response rate and 

the number of successes equal to the target cell size.