How Many Samples do I Need? Part 3

1. DQO Training Course Day 1 Module 6 How Many Samples do I Need?Part 3 Presenter: Sebastian Tindall (50 minutes)(5 minute “stretch” break)

2. Sampling for Environmental Activities Chuck RamseyEnviroStat, Inc.PO Box 636Fort Collins, CO 80522970-689-5700970-229-9977 fax chuck@envirostat.org www.envirostat.org

3. Seven Major Sampling Errors • Fundamental Error - FE • Grouping and Segregation Error - GSE • Materialization Error - ME • Delimination Error - DE • Extraction Error - EE • Preparation Error - PE • Trends - CE2 • Cycles - CE3

4. Ramsey’s “Rules” • All measurements are an average • With discreet sampling, an average is a random variable • With discreet sampling, SD is an artifact of the sample collection process • Heterogeneity is the rule • Multi-increment sampling can drive a skewed distribution towards normal • FE2 • proportional to particle size • inversely proportional to mass • Lab data are suspect (error can be large)

5. Ramsey’s “Rules” (cont.) • Good sampling technique is critical • Typical sample sizes will underestimate the mean • Quality control (QC) is important • NO boiler plate; (e.g., PARCC) • QC must be problem specific • Maximize the use of onsite analysis to guide planning & decisions • DQOs are the most important component of the process

6. Ramsey’s “Rules” (cont.) • One measurement is a crap shoot: • Tremendous heterogeneity (variability) between: • Particles within a sample • Aliquots of a sample • Duplicate samples • Never take ONE grab sample to base a decision • Always collect X increments and use AT LEAST one multi-increment sample to make the decision

7. Multi-Increment Sampling is the Way to Go Next following slides show “How to” perform multi-increment sampling

8. Multi-Increment Sampling n = m * k 100 = 1 * 100 100 = 2 * 50 100 = 4 * 25 100 = 5 * 20 100 = 10 * 10 n = number of samples required k = increments m= samples analyzed

9. n = m * k Collect “n” samples Group into “k” increments k = 3 k = 3 Remember; we want the AVERAGE over the Decision Unit Combine “k” into “m” multi- increments m = 2 FAM/Laboratory

10. Comparison of Discrete vs. Multi-Increment Remember: (In discreet sampling) • An average is a random variable; • The SD is an artifact of the sample collection process.

11. Average Exposure • In discreet sampling, the sample mean is a random variable. • In discreet sampling, the 95% UCL is a random variable. • In discreet sampling, the sample standard deviation is an artifact of sample collection process. • n (# samples) is NOT proportional to the size of the population (e.g. area, mass, or volume).

12. A A A A B B B A B B A B B A A Average depends on locations sampled Average A = 16 ppm Average B = 221 ppm Average from discrete sampling is a random variable

13. Hot Spots x • 1,000,000 g at site • 100,000 g > AL • Take 10 samples • 1> AL • Remove that 1 • Re-sample = clean • Wrong! • If 100,000 >AL • Minus 1 • Still 99,999>AL AL= action level

14. Hot Spots Simply Means: “I want to look at units (e.g. Mass, volume) that are becoming smaller and smaller and smaller and smaller and smaller and smaller and smaller” $ $ $ $ $ $ $ $$

15. Effects of Grinding a Soil Walsh, Marianne E.; Ramsey, Charles A.; Jenkins, Thomas F., The Effect of Particle Size Reduction by Grinding on Subsampling Variance for Explosives Residues in Soil, Chemosphere 49 (2002) 1267-1273.

16. Additional Population Considerations • Sample support - “physical size, shape and orientation of the material that is extracted from the sampling unit that is actually available to be measured or observed, and therefore, to represent the sampling unit.” • Assure enough sample for analyses • Specify how the sample support will be processed and sub-sampled for analysis. EPA Guidance on Choosing a Sampling Design for Environmental Data Collection, EPA QA/G-5S, December 2002, EPA/240/R-02/005

17. Sub-Sampling • The DQO must define what represents the population in terms of laboratory sample size: • Typical laboratory sample sizes that are digested or extracted: metals - 1g, volatiles - 5g, semi-volatiles - 30 g • The 1g or 30g sample analyzed by the lab is supposed to represent a larger area/mass (e.g., acre). Does it?

18. Fundamental Error FE = fundamental error M = mass of sample (g) d = maximum particle size <5% oversize (cm) 3 d 2 = FE 22 . 5 ~ M EPA/600/R-92/128, July 1992

19. Fundamental Error 3 d 2 FE = 22 . 5 22.5= ~ clfg • c - mineralogical factor  - density factor (for soil ~ 2.5) • l - liberation factor (between 0 -1) • f - shape factor (for soil ~0.5) • g - granulometric factor ~0.25 ~ M

20. 2 M ( FE ) = d 3 22 . 5 3 d = M 22 . 5 2 FE Fundamental Error Solve for particle size OR Solve for mass of sample

21. Constant Particle Size 9217 gm 20% 4097 gm 30% Particle Size - 2.54 cm

22. Examples of FE, Mass, Particle Size

23. Examples of FE, Mass, Particle Size May not work well or at all with some media • Clay • Water • Air

24. Multi-Increment Sampling is the Way to Go exposure unit = decision unit [DU] (1) Lab(7) Samples & QC (6) calc d & FE & mass(2,3,4) 10 scoops(5) Re-Calculate particle size(8) Average concentration for DU(12,13) Sub sample mass for lab analysis(10) Analyze entire sub sample(11) Grind(9)

25. Multi-Increment Sampling is the Way to Go 1. Agree on exposure unit or decision unit. 2. Select or measure a reasonable maximum sample particle size. 3. Select the FE. 4. Calculate the mass of sample needed based on the FE and particle size. 5. Using a square scoop large enough to capture the maximum particle size, collect enough sample increments (k) to equal the mass calculated in #4 and place in a jar, combining increments into one “sample” (m). 6. Repeat within a given decision unit to obtain a duplicate (or triplicate) to generate the QC. 7. Deliver the sample and QC sample(s) to the lab.

26. Multi-Increment Sampling is the Way to Go, continued 8. Calculate the particle size of sample needed based on the desired FE and the mass that the lab normally uses for a given analysis. 9. Lab must grind entire mass of field sample (& QC) to the agreed upon maximum analytical particle size in #8. 10. Lab must perform one-dimensional sub-sampling of entire mass [spread entire ground sample on flat surface in thin layer, then systematically or randomly collect sufficient small mass sub-sampling increments to equal the mass the laboratory requires for an analysis; do likewise for each QC sample]. 11. Combine sub-sampling increments into the “sample”, then digest/extract/analyze the sample and QC samples. 12. Calculate the concentration from sample. 13. Concentration represents average concentration or activity per decision unit.

27. Example • Soil like material • Largest particle about 4 mm • Action limit is 500 ppm • Analytical aliquot is one gram • Is this acceptable? Compliments of EnviroStat, Inc.

28. Example (cont) Check particle size representatives FE = = 1.2 FEpercent = 1.2 * 100 FEpercent = 120% EPA/600/R-92/128, July 1992 Compliments of EnviroStat, Inc.

29. Example (cont) What mass is required to reduce FE to 15%? But lab can analyze 10 grams at the most Compliments of EnviroStat, Inc.

30. Example (cont) To what particle size does the sample need to be reduced to achieve FE of 15%? Compliments of EnviroStat, Inc.

31. Example (cont) What is the FE to take 64 grams and grind it to 0.1 cm and take one gram? Ignoring all the other errors Compliments of EnviroStat, Inc.

32. Example (cont) • Option 1 • take at least 64 grams and grind to 0.1 cm • analyze one gram • Option 2 • take at least 64 grams and grind to 0.22 cm • analyze 10 grams • Other options • investigate/estimate sampling factors (clfg) Compliments of EnviroStat, Inc.

33. Multi-increment Sampling • Saves money • Results are more defensible • Does not excite the public • Faster

34. Key Points • All measurements are an average • In discreet sampling, the average is a random variable • In discreet sampling, the SD is an artifact of the sample collection process • Heterogeneity is the rule • Multi-increment sampling can save your butt! • Multi-increment sampling can get you defensible data within your sampling & analyses budget

35. Key Points (cont.) • Due to inherent heterogeneity, collecting representative sample is difficult • TRIAD approach and “Ramsey’s Rules” advocate • using cheaper, real-time, on-site methods • increasing sample density or coverage • Controlling laboratory analysis quality does not control all error • Errors occur in each step of the collection and analysis process

36. Key Points (cont.) • TRIAD approach encourages use of DWP to provide flexibility to obtain sufficient sample density • Larger the “mass”, the lower the sampling error • Smaller the “particle”, the lower the sampling error • Proper sub-sampling is critical • Sample design must assess the normal, skewed, and badly skewed distributions • For badly skewed computer simulations are needed • Multi-increment samples drive the distribution to normal

37. How Many Samples do I Need? REMEMBER: HETEROGENEITY IS THE RULE!

38. Summary Use Classical Statistical sampling approach: • Almost certain to fail Use Other Statistical sampling approaches: • Bayesian • Geo-statistics • Kriging Use Multi-Increment sampling approach: • Can use classical statistics • Cheaper • Faster • More defensible  MASSIVE DATA Required

39. End of Module 6 Thank you Questions? We will now take a Second Afternoon 5-minute “Stretch” Break. Please be back in 5 minutes