3
                                                                              2
                                                                              1
                                                                              2
                                                                              6
                                                                             14
                                                                              3
                                                                              3
                                                                              3
                                                                              1
                                                                              1
                                                                              4
                                                                              2
                                                                              1
                                                                              3
                                                                              1
                                                                              5
                                                                             15
                                                                              1
                                                                              1
                                                                              1
                                                                              1
                                                                              3
                                                                              3
                                                                              2
                                                                              2
                                                                              3
                                                                              2
                                                                              1
                                                                             15
                                                                              2
                                                                              2
                                                                              2
                                                                              1
                                                                              2
                                                                              4
                                                                              1
                                                                              3
                                                                              1
                                                                              2
                                                                              2
                                                                             15
                                                                              3
                                                                              3
                                                                              2
                                                                              3
                                                                              1
                                                                              6
                                                                              2
                                                                              1
                                                                              2
                                                                              3
                                                                              5
                                                                             16
                                                                              1
                                                                              1
                                                                              1
                                                                              2
                                                                              3
                                                                              4
                                                                              2
                                                                              3
                                                                              2
                                                                              3
                                                                              5
                                                                             16
                                                                              2
                                                                              2
                                                                              3
                                                                              3
                                                                              3
                                                                              4
                                                                              1
                                                                              2
                                                                              2
                                                                              1
                                                                              3
                                                                             16
                                                                              3
                                                                              1
                                                                              2
                                                                              1
                                                                              2
                                                                              6
                                                                              3
                                                                              1
                                                                              3
                                                                              1
                                                                              2
                                                                             17
                                                                              1
                                                                              3
                                                                              2
                                                                              1
                                                                              3
                                                                              4
                                                                              3
                                                                              2
                                                                              2
                                                                              1
                                                                              6
                                                                             17
                                                                              2
                                                                              3
                                                                              2
                                                                              1
                                                                              2
                                                                              2
                                                                              2
                                                                              2
                                                                              3
                                                                              3
                                                                              1
                                                                             17
                                                                              3
                                                                              1
                                                                              3
                                                                              2
                                                                              3
                                                                              1
                                                                              2
                                                                              3
                                                                              1
                                                                              2
                                                                              5
                                                                             18
                                                                              1
                                                                              3
                                                                              1
                                                                              1
                                                                              2
                                                                              4
                                                                              1
                                                                              1
                                                                              2
                                                                              2
                                                                              3
                                                                             18
                                                                              2
                                                                              2
                                                                              2
                                                                              1
                                                                              3
                                                                              1
                                                                              1
                                                                              3
                                                                              3
                                                                              3
                                                                              6
                                                                             18
                                                                              3
                                                                              1
                                                                              1
                                                                              3
                                                                              1
                                                                              2
                                                                              3
                                                                              3
                                                                              1
                                                                              1
                                                                              1
                                                                             19
                                                                              1
                                                                              3
                                                                              1
                                                                              3
                                                                              1
                                                                              1
                                                                              1
                                                                              3
                                                                              3
                                                                              2
                                                                              3
                                                                             19
                                                                              2
                                                                              3
                                                                              2
                                                                              1
                                                                              2
                                                                              5
                                                                              3
                                                                              1
                                                                              1
                                                                              1
                                                                              3
                                                                             19
                                                                              3
                                                                              1
                                                                              3
                                                                              2
                                                                              2
                                                                              6
                                                                              1
                                                                              2
                                                                              2
                                                                              2
                                                                              2
                                                                             20
                                                                              1
                                                                              1
                                                                              1
                                                                              3
                                                                              2
                                                                              5
                                                                              1
                                                                              3
                                                                              3
                                                                              1
                                                                              4
                                                                             20
                                                                              2
                                                                              3
                                                                              2
                                                                              3
                                                                              1
                                                                              1
                                                                              2
                                                                              2
                                                                              2
                                                                              2
                                                                              2
                                                                             20
                                                                              3
                                                                              2
                                                                              3
                                                                              2
                                                                              3
                                                                              3
                                                                              1
                                                                              1
                                                                              1
                                                                              2
                                                                              1
                                                                             21
                                                                              1
                                                                              3
                                                                              3
                                                                              1
                                                                              1
                                                                              6
                                                                              1
                                                                              3
                                                                              1
                                                                              3
                                                                              1
                                                                             21
                                                                              2
                                                                              1
                                                                              2
                                                                              3
                                                                              3
                                                                              2
                                                                              2
                                                                              1
                                                                              1
                                                                              2
                                                                              3
                                                                             21
                                                                              3
                                                                              3
                                                                              1
                                                                              2
                                                                              2
                                                                              2
                                                                              3
                                                                              3
                                                                              2
                                                                              1
                                                                              2
                                                                             22
                                                                              1
                                                                              2
                                                                              1
                                                                              1
                                                                              1
                                                                              5
                                                                              1
                                                                              1
                                                                              2
                                                                              3
                                                                              1
                                                                             22
                                                                              2
                                                                              3
                                                                              1
                                                                              3
                                                                              3
                                                                              6
                                                                              2
                                                                              2
                                                                              1
                                                                              2
                                                                              4
                                                                             22
                                                                              3
                                                                              1
                                                                              3
                                                                              1
                                                                              2
                                                                              1
                                                                              3
                                                                              1
                                                                              3
                                                                              1
                                                                              3
                                                                             23
                                                                              1
                                                                              1
                                                                              1
                                                                              1
                                                                              1
                                                                              2
                                                                              1
                                                                              1
                                                                              2
                                                                              2
                                                                              4
                                                                             23
                                                                              2
                                                                              3
                                                                              3
                                                                              1
                                                                              2
                                                                              1
                                                                              3
                                                                              3
                                                                              3
                                                                              1
                                                                              1
                                                                             23
                                                                              3
                                                                              2
                                                                              3
                                                                              2
                                                                              1
                                                                              4
                                                                              3
                                                                              2
                                                                              3
                                                                              3
                                                                              3
                                                                             24
                                                                              1
                                                                              2
                                                                              2
                                                                              2
                                                                              2
                                                                              5
                                                                              2
                                                                              3
                                                                              3
                                                                              3
                                                                              1
                                                                             24
                                                                              2
                                                                              2
                                                                              1
                                                                              1
                                                                              3
                                                                              6
                                                                              1
                                                                              2
                                                                              1
                                                                              1
                                                                              3
                                                                             24
                                                                              3
                                                                              1
                                                                              3
                                                                              3
                                                                              3
                                                                              2
                                                                              3
                                                                              1
                                                                              2
                                                                              3
                                                                              6

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

                                       1
                                       2
                                       3
                                       4
                                       5
                                       6

                                   Declining
                                   Constant

"Input Version"
Dissolved Oxygen
                                      35%
                                      43%
                                      43%
                                      85%
                                     100%
                                       -
                                       -
                                       -
Water Clarity
                                      1.5
                                       3
                                       3
                                       4
                                       5
                                       -
                                       -
                                       -
Aquatic Grasses (acres)
                                    38,000
                                    80,000
                                    80,000
                                    130,000
                                    165,000
                                       -
                                       -
                                       -
Lake Condition
                                       2
                                       3
                                       3
                                       4
                                       5
                                       -
                                       -
                                       -
Annual Household Cost
                                      $0
                                      $0
                                      $40
                                      $60
                                     $180
                                     $250
                                     $370
                                     $500
"Endpoint Version"
Water Clarity
                                      1.5
                                       3
                                       3
                                       4
                                       5
                                       -
                                       -
                                       -
Blue Crab (millions)
                                      235
                                      250
                                      250
                                      280
                                      312
                                       -
                                       -
                                       -
Oysters (tons)
                                     2,800
                                     3,300
                                     3,300
                                     4,300
                                     5,250
                                       -
                                       -
                                       -
Lake Condition
                                       2
                                       3
                                       3
                                       4
                                       5
                                       -
                                       -
                                       -
Annual Household Cost
                                      $0
                                      $0
                                      $40
                                      $60
                                     $180
                                     $250
                                     $370
                                     $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 8 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
                                      864
                                     6341
                                     0.017
                                     0.010
Watershed
                                  13,442,787
                                      864
                                     15559
                                     0.017
                                     0.010
Other East Coast
                                  30,034,913
                                      576
                                     46563
                                     0.021
                                     0.012
Overall
                                  48,956,876
                                     2,304
                                     21248
                                     0.014
                                     0.008
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).

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
                                     1565
                                     1672
                                     1043
                                     1100
District of Columbia
                                      229
                                      244
                                      152
                                      162
Maryland
                                     1848
                                     1974
                                     1231
                                     1311
Virginia
                                     2619
                                     2798
                                     1745
                                     1857
Delaware
                                      120
                                      128
                                      80
                                      85
New York
                                     2556
                                     2731
                                     1703
                                     1813
Pennsylvania
                                     1753
                                     1873
                                     1168
                                     1243
West Virginia
                                      267
                                      285
                                      178
                                      189
Connecticut
                                      160
                                      171
                                      107
                                      113
Florida
                                      866
                                      925
                                      577
                                      614
Georgia
                                      418
                                      447
                                      279
                                      297
Maine
                                      65
                                      69
                                      43
                                      46
Massachusetts
                                      297
                                      318
                                      198
                                      211
New Hampshire
                                      61
                                      65
                                      40
                                      43
New Jersey
                                      335
                                      358
                                      223
                                      238
North Carolina
                                      437
                                      467
                                      291
                                      310
Ohio
                                      537
                                      574
                                      358
                                      381
Rhode Island
                                      48
                                      52
                                      32
                                      34
South Carolina
                                      210
                                      225
                                      140
                                      149
Vermont
                                      30
                                      32
                                      20
                                      32
Total:
                                     12522
                                     13379
                                     8343
                                     8880

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.