### 1

**Attachment 15**  **: 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, Options B and C
. These alternatives, Option B and Option C, are characterized by three potential levels for environmental attributes and six different levels of annual household cost. The study design will employ

two split samples . The first consists of three different baselines, where Option A or the status quo choice represents either a constant, declining, or improving baseline in the environmental attributes , relative to current levels
. The second experimental treatment involves two different reference years for predictions of the attribute levels (2025 or 2040).
Each of these 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, S outh 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. Based on the three geographic strata, three baseline versions, and two reference years for environmental conditions, the study will consist of the following 18 cell design: **Table A15** **- 1**  **. Split -** **sample design cel l** **s.**

Geographic division Baseline factor Reference year for environmental conditions Cell 1 Bay States Declining 2025 Cell 2 Bay States Constant 2025 Cell 3 Bay States Improving 2025 Cell 4 Watershed Declining 2025 Cell 5 Watershed Constant 2025 Cell 6 Watershed Improving 2025 Cell 7 Other East Coast Declining 2025 Cell 8 Other East Coast Constant 2025 Cell 9 Other East Coast Improving 2025 Cell 10 Bay States Declining 2040 Cell 11 Bay States Constant 2040 Cell 12 Bay States Improving 2040 Cell 13 Watershed Declining 2040 Cell 14 Watershed Constant 2040 Cell 15 Watershed Improving 2040 Cell 16 Other East Coast Declining 2040 Cell 17 Other East Coast Constant 2040 Cell 18 Other East Coast Improving 2040 Options B and C, the alternatives to the status quo baseline (option A) , are characterized by different levels for the following six attributes, including cost. The number of levels corresponding to each of these attributes is depicted below :

1. Change in water clarity in Options B and C (x 1B 

### ; x 1C

### )

– 3 possible levels

### 3

2. Change in adult blue crab abundance in Options B and C (x2B 

### ; x2C

### )

– 3 possible levels 3. Change in adult striped bass abundance in Options B and C (x3B 

### ; x3C

### )

– 3 possible levels 4. Change in oyster abundance in Options B and C (x4B 

### ; x4C

### )

– 3 possible levels 5. Change in lake condition in Options B and C (x5B 

### ; x5C

### )

– 3 possible levels 6. Cost in Options B and C (x6B 

### ; x6C

### )
- 6 possible levels This implies an experimental design characterized by three levels for each of the five attributes and six levels for costs [3 5 

### × 6] for each alternative option, or [3 10 

### × 62

### ] for Options B and C together
. 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 3 5

### x6 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 blocked 1 

### in such a way that variability of the environmental and 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 and reference year**  **by baseline cell.** Booklet X1 B X2B X3 B X4B X5 B X6B X1 C X2 C X3 C X4C X5 C X6 C 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

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.

### 4 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 9 1 2 2 1 1 6 1 1 1 1 1 3 9 3 1 1 2 2 1 2 1 3 2 2 3 10 1 2 1 3 1 1 1 3 1 3 2 3 10 1 3 3 2 3 3 2 3 3 3 3 5 10 3 1 2 1 2 6 1 1 2 1 1 3 11 2 1 3 1 3 1 2 2 2 1 3 1 11 2 3 1 2 2 6 1 3 2 2 2 5 11 3 2 3 1 3 3 3 2 3 2 2 4 12 2 2 1 1 1 3 2 1 1 3 1 4 12 3 1 2 2 2 1 2 2 2 2 2 1 12 3 3 2 3 3 2 3 2 3 3 3 1 13 1 3 1 1 3 1 3 3 1 2 3 4 13 2 2 2 1 3 6 2 2 2 2 1 4 13 2 3 1 3 2 5 3 1 1 3 2 3 14 1 3 1 2 3 1 2 2 1 2 3 2 14 2 1 2 1 2 4 2 1 2 3 1 6 14 3 2 2 2 1 6 3 1 3 2 1 5 15 1 2 1 3 3 5 3 2 1 1 3 4 15 2 3 2 3 2 3 2 3 3 2 2 4 15 3 1 1 2 1 6 3 1 1 1 2 6 16 1 2 3 1 1 5 1 3 2 1 1 6 16 2 2 3 3 3 6 3 2 3 1 3 5 16 3 1 1 2 3 1 3 3 1 1 3 2 17 1 1 3 2 2 5 1 2 3 2 1 6 17 2 3 2 1 3 6 1 3 3 1 3 6 17 3 1 1 3 1 6 2 1 1 1 1 4 18 1 2 2 2 3 3 1 1 1 2 3 1

### 5 18 2 3 3 1 2 2 2 2 3 2 2 3 18 3 2 2 2 1 2 3 2 3 3 1 3 19 1 1 3 3 2 1 3 1 3 3 1 2 19 1 3 2 3 1 4 1 2 2 2 1 2 19 3 2 2 1 3 5 3 3 1 1 3 6 20 1 2 2 3 2 2 1 2 1 3 3 4 20 2 3 2 2 1 5 2 2 1 2 1 2 20 3 3 3 3 3 4 2 3 3 3 1 2 21 2 3 2 1 1 1 1 3 3 1 1 1 21 3 2 3 2 2 6 3 2 3 1 1 3 21 3 3 1 3 3 4 3 2 1 3 2 2 22 1 3 1 1 1 1 2 3 1 1 2 3 22 2 1 3 3 3 6 1 1 3 1 3 2 22 2 3 2 3 3 5 1 2 2 3 3 4 23 2 1 2 2 1 5 2 1 1 1 1 2 23 3 1 1 3 3 5 1 1 2 3 3 4 23 3 2 2 1 2 4 3 3 2 1 1 3 24 1 2 3 1 2 5 1 1 3 3 2 6 24 1 3 1 2 1 2 3 3 1 2 2 4 24 3 3 2 1 1 5 3 3 1 1 2 5 

### 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) 2 3 3. 5 4.5
- - - Adult Striped Bass (millions) 21 24 30 36
- - - Adult Blue Crab (millions) 235 250 28 5 3 28
- - - Oysters (tons) 2,800 3,300 5,500 10,000
- - - 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 3. 5 4.5
- - - Adult Striped Bass (millions) 24 24 30 36
- - - Adult Blue Crab (millions) 250 250 285 328
- - - Oysters (tons) 3,300 3,300 5,500 10,000
- - - 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) 3.3 3.3 3.5 4.5
- - - Adult Striped Bass (millions) 26 26 30 35
- - -

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Adult Blue Crab (millions) 260 260 312 340
- - - Oysters (tons) 4,300 4,300 5,500 10,000
- - - 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 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 1,728 3,17 1 0.017 0.010 Watershed 13,442,787 1,728 7,779 0.017 0.010 Other East Coast 25,431,478 1,728 14,717 0.017 0.010 Overall 44,353,441 5,184 8,556 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/
.

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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).
**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 458 488 304 324 Maryland 3,696 3,948 2,462 2,622 Virginia 5,238 5,596 3,490 3,714 Delaware 240 256 160 170 New York 5,112 5,462 3,406 3,626 Pennsylvania 3,506 3,746 2,336 2,486 West Virginia 534 570 356 378 Connecticut 506 540 340 360

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Florida 2,740 2,930 1,826 1,946 Georgia 1,324 1,414 882 940 Maine 206 220 138 146 Massachusetts 940 1,004 626 668 New Hampshire 192 204 128 136 New Jersey 1,186 1,268 790 842 North Carolina 1,382 1,478 922 982 Rhode Island 152 164 102 108 South Carolina 666 710 444 472 Vermont 94 102 64 68 Total: 28,172 30,100 18,776 19,988 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.