The EPA 7-Step DQO Process

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

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

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

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

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

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

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

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

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

11. Simple Random • 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. Example - Simple Random Using Coordinates

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

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

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

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

17. Geometric Probability or Hot-Spot Sampling (cont.) • Number of samples is calculated based on probability of finding hot area or geometric probability • 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. Geometric Probability or Hot-Spot Sampling (cont.) • Limitations • Not appropriate for hot spots that are not elliptical • Not appropriate if cannot define what is hot or the likely size of hot spot

19. Example Grid for Hot-Spot Sampling

20. Geometric Probability or Hot-Spot Sampling (cont.) • 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

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

22. Strata 1 Strata 2 Example - Stratified SimpleRandom

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

24. CS Plan View Former Pad Location Buffer Zone 0 50 100 150 ft 0 15 30 46 m Runoff Zone Approach 1 Sample Design

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

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

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

29. CS Histogram

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

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

32. Logic to Assess Distribution and Calculate Number of Samples

33. CS 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

34. Logic to Assess Distribution and Calculate Number of Samples

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

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

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

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

39. CS Aroclor 1260- Non-Parametric Test

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

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

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

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

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

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

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

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

48. SHOW EXCEL File

49. CS Approach 1 Based Sampling Design • 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 • 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

50. CS Plan View Former Pad Location Buffer Zone 0 50 100 150 ft 0 15 30 46 m Runoff Zone Approach 1 Sample Locations(Surface Strata)