How Many Samples do I Need? Part 3

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How Many Samples do I Need?Part 3

Presenter: Sebastian Tindall

(50 minutes)(5 minute “stretch” break)

DQO Training CourseDay 1

Module 6

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Sampling for

Environmental ActivitiesChuck Ramsey

EnviroStat, Inc.PO Box 636

Fort Collins, CO 80522970-689-5700

970-229-9977 fax

[email protected]

www.envirostat.org

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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

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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)

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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

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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

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Multi-Increment Sampling is the Way to Go

Next following slides show “How to”

perform multi-increment sampling

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Multi-Increment Sampling

n = m * k

100 = 1 * 100100 = 2 * 50100 = 4 * 25100 = 5 * 20100 = 10 * 10

n = number of samples requiredk = incrementsm= samples analyzed

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n = m * k

k = 3k = 3

m = 2

FAM/Laboratory

Collect “n” samples

Group into “k”increments

Combine “k”into “m”multi-increments

Remember;we want the

AVERAGEover theDecision Unit

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Comparison of Discrete vs. Multi-Increment

n Avg SD n m k Avg SD5 34.2 51.4 250 5 50 68.9 145.85 48.0 40.7 250 5 50 72.4 153.95 9.6 12.9 250 5 50 74.6 150.35 291.8 331.0 250 5 50 66.5 157.1

Discrete Multi-Increment

Remember: (In discreet sampling)

1. An average is a random variable;

2. The SD is an artifact of the sample collection process.

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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).

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Average A = 16 ppmAverage B = 221 ppmAverage from discrete sampling is a random variable

AB

A

B

A

A

A

A

B

B

B

B

BA

A

Average depends on locations sampled

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Hot Spots

• 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

x

AL= action level

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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”

$ $ $ $ $ $ $ $ $

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Effects of Grinding a Soil

Rep2-g NotGround

50-g NotGround 2-g Ground 50-g Ground

1 0.39 0.25 2.33 2.032 0.48 1.81 2.25 2.043 0.37 0.37 2.22 2.004 0.41 1.48 2.28 2.035 28.61 7.93 2.15 1.976 0.48 0.56 2.15 2.007 0.45 0.35 2.15 1.908 0.68 0.75 2.17 2.029 0.77 0.56 2.00 1.97

10 1.08 0.35 1.98 1.9811 0.77 0.62 2.10 1.9012 0.47 5.62 1.96 1.91

mean 2.91 1.72 2.15 1.98std dev 8.09 2.46 0.12 0.05R S D 278% 143% 5.50% 2.57%

Walsh, Marianne E.; Ramsey, Charles A.; Jenkins, Thomas F., The Effect ofParticle Size Reduction by Grinding on Subsampling Variance for ExplosivesResidues in Soil, Chemosphere 49 (2002) 1267-1273.

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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

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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?

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Fundamental Error

FE = fundamental errorM = mass of sample (g)d = maximum particle size <5% oversize (cm)

M

dFE

32 5.22 ~

EPA/600/R-92/128, July 1992

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Fundamental Error

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

MdFE

32

5.22 ~

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Fundamental Error

Solve forparticle size

Solve for

mass of sample

OR

dFEM 3

2

5.22

)(

2

3

5.22FE

dM

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Constant Particle SizeSample Mass Approx. FE (%)1 gm 42%2 gm 30%10 gm 13%30 gm 8%

Particle Size - 2mm

9217 gm 20%4097 gm 30%

Particle Size - 2.54 cm

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Examples of FE, Mass, Particle Size

Mass Particle SizeFE~20%

Particle SizeFE~30%

1g 0.12mm 0.16mm

2g 0.16mm 0.20mm

10g 0.26mm 0.35mm

30g 0.38mm 0.50mm

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Examples of FE, Mass, Particle Size

May not work well or at all with some media

•Clay

•Water

•Air

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Multi-Increment Sampling is the Way to Go

x x x x xx x x x x

exposure unit = decision unit [DU] (1)

calc d & FE & mass

(2,3,4)

10 scoops(5)

Samples & QC

(6)

Lab(7)

Grind(9)

Re-Calculate particle size

(8)

Sub sample mass for lab

analysis(10)

Analyze entire sub

sample(11)

Average concentration

for DU(12,13)

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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.

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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.

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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.

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Example (cont)

Check particle size representatives

FE percent = 120%

Compliments of EnviroStat, Inc.

EPA/600/R-92/128, July 1992

44.11

)4.0)(5.22(18 332

S

mFE m

dfS

22 FESFE FE = = 1.2

FE percent = 1.2 * 100

44.1

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Example (cont)

What mass is required to reduce FE to 15%?

But lab can analyze 10 grams at the most

gM S 6415.

4).5.22(2

3

Compliments of EnviroStat, Inc.

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Example (cont)

To what particle size does the sample need to be reduced to achieve FE of 15%?

mmC

MFEd

mmC

MFEd

S

S

15.22

)1(15.

2.25.22

)10(15.

3

2

3

2

3

2

3

2

Compliments of EnviroStat, Inc.

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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

%2115.15. 2222

12 FEFETE

Compliments of EnviroStat, Inc.

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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.

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Multi-increment Sampling

Saves money Results are more defensible Does not excite the public Faster

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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

Key Points

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Due to inherent heterogeneity, collecting representative sample is difficult

Managing Uncertainty 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

Key Points (cont.)

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Managing Uncertainty 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

Key Points (cont.)

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How Many Samples do I Need?

REMEMBER:

HETEROGENEITY

IS THE RULE!

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SummaryUse 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

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End of Module 6Thank you

Questions?

We will now take a

Second Afternoon 5-minute “Stretch” Break.

Please be back in 5 minutes