1. 1 of 86 The EPA 7-Step DQO Process Step 7 - Optimize Sample Design (70 minutes) Presenter: Sebastian Tindall Day 2 DQO Training Course Module 7

2. 2 of 86 Terminal Course Objective To be able to use the output from the previous DQO Process steps to select sampling and analysis designs and understand design alternatives presented to you for a specific project

3. 3 of 86 Step Objective: Identify the most resource effective data collection and analysis design that satisfies the DQOs specified in the preceding 6 steps Step 7: Optimize Sample Design Step 4: Specify Boundaries Step 2: Identify Decisions Step 3: Identify Inputs Step 1: State the Problem Step 5: Define Decision Rules Step 6 : Specify Error Tolerances Step 7 : Optimize Sample Design

4. 4 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs

5. 5 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs The outputs should provide information on the context of, requirements for, and constraints on data collection design. Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

6. 6 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Based on the DQO outputs from Steps 1-6, for each decision rule develop one or more sample designs to be considered and evaluated in Step 7.

7. 7 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs For each option, pay close attention to the Step 4 outputs defining the population to be represented with the data: Sample collection method Sample mass size Sample particle size Etc.

8. 8 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Remember: Sampling Uncertainty is decreased when sampling density is increased. Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

9. 9 of 86 Types of Designs n Simple Random Statistical Methods for Environmental Pollution Monitoring, Richard O. Gilbert, 1987 n Systematic Grid with random start n Geometric Probability or “Hot Spot” Sampling n Stratified Random –Stratified Simple Random –Stratified Systematic Grid with random start

10. 10 of 86 Simple Random n Definition- choice of sampling location or time is random n Assumptions –Every portion of the population has equal chance of being sampled n Limitation-may not cover area

11. 11 of 86 Simple Random n To generate a simple random design: –Either grid the site - set up equal lateral triangles or equal side rectangles and number each grid, use a random number generator to pick the grids from which to collect samples –Randomly select x, y, z coordinates, go to the random coordinates and collect samples

12. 12 of 86 Example - Simple Random Using Coordinates

13. 13 of 86 Systematic Grid, Random Start n Definition-taking measurements at locations or times according to spatial or temporal pattern (e.g., equidistant intervals along a line or grid pattern) n Assumptions –Good for estimating means, totals and patterns of contamination –Improved coverage of area

14. 14 of 86 Systematic Grid, Random Start (cont.) n Limitations –Biased results can occur if assumed pattern of contamination does not match the actual pattern of contamination –Inaccurate if have serial correlation n NPDES outfall –Periodic recurring release; time dependent n Groundwater: –seasonal recurrence; water-level dependence

15. 15 of 86 Remember: Start at random location Move in a pre-selected pattern across the site, making measurements at each point Systematic Grid, Random Start (cont.)

16. 16 of 86 Geometric Probability or Hot- Spot Sampling n Uses squares, triangles, or rectangles to determine whether hot spots exist n Finds hot spot, but may not estimate the mean with adequate confidence

17. 17 of 86 n Number of samples is calculated based on probability of finding hot area or geometric probability Geometric Probability or Hot- Spot Sampling (cont.) n Assumptions –Target hot spot has circular or elliptical shape –Samples are taken on square, rectangular or triangular grid –Definition of what concentration/activity defines hot spot is unambiguous

18. 18 of 86 n Limitations –Not appropriate for hot spots that are not elliptical Geometric Probability or Hot- Spot Sampling (cont.) –Not appropriate if cannot define what is hot or the likely size of hot spot

19. 19 of 86 Example Grid for Hot-Spot Sampling

20. 20 of 86 n In order to use this approach the decision makers MUST –Define the size of the hot spot they wish to find –Provide rationale for specifying that size. –Define what constitutes HOT (e.g., what concentration is HOT) –Define the effect of that HOT spot on achieving the release criteria Geometric Probability or Hot- Spot Sampling (cont.)

21. 21 of 86 Stratified Random n Definition-divide population into strata and collect samples in each strata randomly n Attributes –Provides excellent coverage of area –Need process knowledge to create strata –Yields more precise estimate of mean –Typically more efficient then simple random n Limitations –Need process knowledge

22. 22 of 86 Example - Stratified Simple Random Strata 1 Strata 2

23. 23 of 86 Sampling Approaches n Sampling Approach 1 –Simple Random –Traditional fixed laboratory analyses n Sampling Approach 2 –Systematic Grid –Field analytical measurements –Computer simulations –Dynamic work plan

24. 24 of 86 Approach 1 Sample Design CS Plan View Former Pad Location Runoff Zone 050100150 ft 0153046 m Buffer Zone

25. 25 of 86 Design Approaches Approach 1 Collect samples using Simple Random design. Use predominantly fixed traditional laboratory analyses and specify the method specific details at the beginning of DQO and do not change measurement objectives as more information is obtained

26. 26 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs 1. Statistical Method/Sample Size Formula 2. Cost Function Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

27. 27 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs 1. Statistical Method/Sample Size Formula Define suggested method(s) for testing the statistical hypothesis and define sample size formula(e) that corresponds to the method(s).

28. 28 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Perform a preliminary DQA: Generate frequency distribution histogram(s) for each population Select one or more statistical methods that will address the PSQs List the assumptions for choosing these statistical methods List the appropriate formula for calculating the number of samples, n

29. 29 of 86 Histogram CS

30. 30 of 86 3 Approaches for Calculating n n Normal approach n Skewed approach n FAM/DWP approach –Badly skewed or for all distributions use computer simulation approach e.g., Monte Carlo

31. 31 of 86 How Many Samples do I Need? Begin With the Decision in Mind Optimal Sampling Design Alternative Sample Designs , , ,  Correct Equation for n (Statistical Method) Population Frequency Distribution Contaminant Concentrations in the Spatial Distribution of the Population The end Data field onsite methods traditional laboratory

32. 32 of 86 Logic to Assess Distribution and Calculate Number of Samples

33. 33 of 86 Normal Approach Due to using only five samples for initial distribution assessment, one cannot infer a ‘normal’ frequency distribution Reject the ‘Normal’ Approach and Examine ‘Non-Normal’ or ‘Skewed’ Approach CS

34. 34 of 86 Logic to Assess Distribution and Calculate Number of Samples

35. 35 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Using the formulae appropriate to these methods, calculate the number of samples required, varying ,  for a given . Repeat the same process using new  s. Review all of calculated sample sizes and along with their corresponding levels of , , and . Select those sample sizes that have acceptable levels of , , and  associated with them. Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

36. 36 of 86 Pb, U, TPH (DRO/GRO) n Because there were multiple COPCs with varied standard deviations, action limits and LBGRs, separate tables for varying alpha, beta, and (LBGR) delta were calculated n For the U, Pb, and TPH, the largest number of samples for a given alpha, beta and delta are presented in the following table CS

37. 37 of 86 Pb, U, TPH Based on Non-Parametric Test CS

38. 38 of 86 Aroclor 1260- Non-Parametric Test n For PCBs, the Aroclor 1260 has the greatest variance and using the standard deviation results in a wide gray region n The following table presents the variation of alpha, beta and deltas for Aroclor 1260 CS

39. 39 of 86 Aroclor 1260- Non-Parametric Test CS

40. 40 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs 2. Cost Function For each selected sample size, develop a cost function that relates the number of samples to the total cost of sampling and analysis.

41. 41 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs In order to develop the cost function, the aggregate unit cost per sample must be determined. This is the cost of collecting one sample and conducting all the required analyses for a given decision rule.

42. 42 of 86 AUSCA$ = USC$ +  USA$ i Where (here): USC$ = Unit Sample Collection Cost USA$ = Unit Sample Analysis Cost AUSCA$ = Aggregate Unit Sample Collection and Analysis Cost j = Number of analytical methods planned Aggregate Unit Sampling and Analysis Cost i=1 j

43. 43 of 86 CS Approach 1 Sampling Design (cont.) Surface Soils S&A Costs

44. 44 of 86 CS Approach 1 Sampling Design (cont) Sub-surface Soils S&A Costs

45. 45 of 86 CS Approach 1 Sampling Design (cont.) Surface Soils

46. 46 of 86 CS Approach 1 Sampling Design (cont.) Sub-surface Soils

47. 47 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Merge the selected sample size outputs with the Aggregate Unit Sample Collection and Analysis cost output. This results in a table that shows the product of each selected sample size and the AUSCA$. This table is used to present the project managers and decision makers with a range of analytical costs and the resulting uncertainties. From the table, select the optimal sample size that meets the project budget and uncertainty requirements.

48. 48 of 86 SHOW EXCEL File

49. 49 of 86 Approach 1 Based Sampling Design n Design for Pb, U, TPH –Alpha = 0.05; Beta = 0.2; Delta = total error –The decision makers agreed on collection of 9 surface samples for Pb, U and TPH (GRO & DRO) from each of the two surface strata, for a total of 18 samples using a stratified random design –For the sub-surface, 9 borings/probes will be made in each of the two subsurface stratum at random locations; one sample will be collected at a random depth down to 10 feet from each boring, to assess migration through the vadose zone, for a total of 18 samples n Design for PCBs –Alpha = 0.05; Beta = 0.20; Delta = 0.50 (50% of the AL) –The decision makers agreed on collection of 24 surface samples from each of the two surface strata; total of 48 samples using a stratified random design –For the sub-surface, 24 borings/probes will be collected from each of the two subsurface stratum at random locations, collected at a random depth down to 10 feet for a total of 48 samples CS

50. 50 of 86 Approach 1 Sample Locations (Surface Strata) CS Plan View Former Pad Location Runoff Zone 050100150 ft 0153046 m Buffer Zone

51. 51 of 86 CS Approach 1 Sampling Design (cont.)

52. 52 of 86 Remediation Costs* CS *Does not include layback area

53. 53 of 86 Approach 1 Based Sampling Design n Compare Approach 1 costs versus remediation costs –Approach 1 S&A costs $11,700 (Pb, U, TPH) + $21,600 (PCBs) = $33,300 –Remediation costs Cost to remediate surface soil under footprint of pad and buffer area: $204,200 Cost to remediate subsurface soil under footprint of pad and buffer area: $3,881,400 CS

54. 54 of 86 Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs If no sample design meets the error tolerances within the budget: relax one or more of the constraints or request more funding, etc.

55. 55 of 86 Design Approaches Approach 2: Dynamic Work Plan (DWP) & Field Analytical Methods (FAMs) n Use DWP to allow more field decisions to meet the measurement objectives and allow the objectives to be refined in the field using DWP n Manage uncertainty by increasing sample density by using field analytical measurements

56. 56 of 86 Approach 2 Sampling Design n Phase 1: Pb, U, TPH, PCBs –Perform field analysis of the four strata on-site using XRF (Pb & U), on-site GC (TPH), and Immunoassay (PCBs) methods. Take into account the chance of false positives at the low detection levels –This will produce a worse-case distributions that will be used to calculate the number of confirmatory samples for laboratory analysis for the surface and below grade strata CS

57. 57 of 86 n Phase 1: Pb, U, TPH, PCBs –Provide detailed SOPs for performance of FAMs: XRF, GC, & Immunoassay analysis –Divide both surface strata into triangular grids –Use systematic sampling, w/random start (RS), to locate sample points; sample in center of each grid n Pad & Run-off zone n CSM expects contamination more likely here 10 ft equilateral triangle: 43.35 ft 2 Pad + Run-off zone = 12,272 ft 2 n 283 sample points n Buffer area: n Also 283 sample points n CSM expects contamination less likely here n Thus, grid triangle has larger area Approach 2 Sampling Design (cont.) CS

58. 58 of 86 n Phase 1: Pb, U, TPH, PCBs –Sub-surface strata: Pad & Run-off zone n Use Direct Push Technology (DPT) to collect n Push at all surface sample points > ALs n Minimum sample locations: 40 (+ 10 >ALs) = ~50 n Collect sub-surface samples every 3 feet n 50 X 3 = 150 sub-surface samples in this strata n Use systematic sampling, w/random start (RS), to locate sample points –Buffer area n CSM expects contamination less likely here n Thus, fewer sample points n Same >ALs rationale as above n 50 X 3 = 150 sub-surface samples in Buffer area n Use systematic sampling, w/RS, to locate sample points Approach 2 Sampling Design (cont.) CS

59. 59 of 86 Stratified Systematic Grid with Random Start (Surface Strata) CS Not to scale Squares will be adjusted according to Step 7 design N Footprint of Concrete Pad (Stratum 1) Runoff Zone (Stratum 1) Buffer Zone (Stratum 2)

60. 60 of 86 n Phase 2: Pb, U, TPH, PCBs –Evaluate the FAM results and construct FDs for each COPC –Using Monte Carlo method, evaluate the alpha, beta and delta and resulting n based on the XRF, on-site GC, and Immunoassay data and select a value (worst case) for n to confirm the FAM data, using traditional laboratory analysis for each of the four strata –For this Case Study, we will assume that number came out to be 9 per strata or 36 confirmatory lab samples CS Approach 2 Sampling Design (cont.)

61. 61 of 86 CS Approach 2 Sampling Design (cont.) Surface Soils SC&SA Costs

62. 62 of 86 CS Approach 2 Sampling Design (cont) Sub-surface Soils SC&SA Costs

63. 63 of 86 CS Approach 2 Sampling Design (cont.)

64. 64 of 86 CS Approach 2 Sampling Design (cont.)

65. 65 of 86 n Evaluate costs of Approach 2 vs. remediation costs –Sampling and analysis (S&A) costs $127,798 –Original budget for S&A $45,000 –Remediation cost Cost to remediate surface soil under footprint of pad and buffer area: $204,200 Cost to remediate subsurface soil under footprint of pad and buffer area: $3,881,400 CS Approach 2 Sampling Design (cont.)

66. 66 of 86 CS Remediation Costs: Surface - $204,200 Sub-surface - $3,881,400 Approach 2 Sampling Design (cont.)

67. 67 of 86 A Visual Decision Strategy

68. 68 of 86 Approach 2b Sampling & Lab Analyses Remember: Sampling Uncertainty is decreased when sampling density is increased n n = m * k n Select k of specified Mass/diameter 3 –FE²  22.5 * d³ / M (to control sampling error) n Prepare m multi-increment samples for lab analysis n Perform lab analyses on m samples

69. 69 of 86 n = m * k k = 3 m = 2 Laboratory Collect “n” samples Group into “k” Combine “k” into “m” composites Remember; we want the AVERAGE over the Decision Unit Approach 2b Sampling & Lab Analyses

70. 70 of 86 Approach 2b Sampling Design n Phase 2b: Pb, U, TPH, PCBs –Let n = 283 (for each Surface strata); n = 150 (for each Sub- surface strata) –Select appropriate values for m and k, based on cost and managing uncertainty n k = 3 (Surface); k = 3 (Sub-surface); add $5 to SC cost n m = 94 (each Surface strata); Total = 188 Surface samples n m = 50 (each Sub-surface strata); Total = 100 Sub-surface samples –Perform field analysis of the four strata on-site using XRF (Pb & U), on-site GC (TPH), and Immunoassay (PCBs) methods. –Again, this will produce worse-case distributions that will be used to evaluate  and  errors and to calculate the number of confirmatory samples for laboratory analysis for the surface and below grade strata; Still assume 36 total CS

71. 71 of 86 Stratified Systematic Grid with Random Start (Surface Strata) CS Not to scale Squares will be adjusted according to Step 7 design N Footprint of Concrete Pad (Stratum 1) Runoff Zone (Stratum 1) Buffer Zone (Stratum 2)

72. 72 of 86 CS Approach 2b Sampling Design (cont.)

73. 73 of 86 CS Approach 2b Sampling Design (cont.)

74. 74 of 86 n Evaluate costs of Approach 2b vs. remediation costs –Sampling and analysis (S&A) costs $75,034 –Original budget for S&A $45,000 –Remediation cost Cost to remediate surface soil under footprint of pad and buffer area: $204,200 Cost to remediate subsurface soil under footprint of pad and buffer area: $3,881,400 CS Approach 2b Sampling Design (cont.)

75. 75 of 86 CS Remediation Costs: Surface - $204,200 Sub-surface - $3,881,400 Approach 2b Sampling Design (cont.)

76. 76 of 86 CS Approach 2b Was Selected Most Cost-Effective and Best Management of Uncertainty

77. 77 of 86 n Measure both gasoline & diesel range fractions (GRO/DRO) n Ship & process all samples in one batch to decrease cost. n QC defined per SW 846 [1 MS/MSD, 1 method blank, 1 equipment blank (if equipment is reused), 1 trip blank for GRO only]. n Cool GRO/DRO to 4°C, +/- 2°C. n QAP written and approved before implementation. CS QC and Analysis Details Used in All Approaches

78. 78 of 86 Steps 1- 6 Step 7 Optimal Design Iterative Process

79. 79 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Justification for a judgmental sampling design Timeframe Qualitative consequences of an inadequate sampling design (low, moderate, severe) Re-sampling access after decision has been made (accessible or inaccessible) Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

80. 80 of 86 WARNING!! If a judgmental design is selected in lieu of a statistical design the following disclaimer must be stated in the DQO Summary Report: “Results from a judgmental sampling design can only be used to make decisions about the locations from which the samples were taken and cannot be generalized or extrapolated to any other facility or population, and error analysis cannot be performed on the resulting data. Thus, using judgmental designs prohibits any assessment of uncertainty in the decisions.”

81. 81 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs The output is the most resource-effective design for the study that is expected to achieve the DQOs. Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

82. 82 of 86 Data Quality Assessment Guidance for Data Quality Assessment, EPA QA/G9, 2000 Step 1: Review DQOs and Sampling Design n Step 2: Conduct Preliminary Data Review n Step 3: Select the Statistical Test n Step 4: Verify the Assumptions of the Test n Step 5: Draw Conclusions From the Data

83. 83 of 86 need Statistical Support: To succeed in a systematic planning process for environmental decision making, you need Statistical Support: qualified statisticians environmental data collection designsstatistical data quality assessments One or more qualified statisticians, experienced in environmental data collection designs and statistical data quality assessments of such designs. Summary

84. 84 of 86 Summary (cont.) n Going through the 7-Step DQO Process will ensure a defensible and cost effective sampling program n In order for the 7-Step DQO Process to be effective: –Senior management MUST provide support –Inputs must be based on comprehensive scoping and maximum participation/contributions by decision makers –Sample design must be based on the severity of the consequences of decision error –Uncertainty must be identified and quantified

85. 85 of 86 Information INActions Information OUT From Previous Step To Next Step Select the optimal sample size that satisfies the DQOs for each data collection design option For each design option, select needed mathematical expressions Check if number of samples exceeds project resource constraints Decision Error Tolerances Gray Region Review DQO outputs from Steps 1-6 to be sure they are internally consistent Step 7- Optimize Sample Design Develop alternative sample designs Optimal Sample Design Go back to Steps 1- 6 and revisit decisions. Yes No

86. 86 of 86 End of Module 7 Thank you