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# Appendix B: Guidance on Sample Numbers

## Number of sampling points for hot spot detection

The method to calculate the number of sampling points required for hot spot detection is based on detecting circular hotspots with 95% confidence using a square grid sampling pattern. To detect hot spots of other shapes, at other confidence levels or by using other sampling patterns, consult the following reference materials:

• RO Gilbert (1987) Statistical Methods for Environmental Pollution Monitoring. Van Nostrand Reinhold, New York, NY.
• CC Ferguson (1992) The statistical basis for spatial sampling of contaminated land. Ground Engineering, 25(1), pp 34-8.

Equations used:

where:

G      =  distance between two sampling points (the grid size of the sampling pattern, in metres)

R      =  radius of the smallest hot spot that the sampling intends to detect, in metres

0.59 =  factor derived from 95% detection probability assuming circular hot spots (based on &#946 = 0.05 and
S = 1.0, see Figure 10.3 of Gilbert, 1987)

N      = number of sampling points needed

A      = size of the sampling area, in square metres.

Method

1. Determine the radius (R) of the hot spot that needs to be detected.
2. Calculate the grid size, G, from equation 1.
3. Determine the number of sampling points required, N, from equation 2.

Notes

The sampling points calculated are located in a plane, and do not take into account vertical contamination throughout the soil profile; ie, the sampling point is the lateral location at which a soil sample is collected. Where the contamination is located in different soil strata, the numbers of sampling points may need to be increased to reflect the different vertical distribution of contaminants.

Using the above equations, the minimum sampling points required for site characterisation based on detecting circular hot spots using a square grid sampling pattern at 95% confidence levelis provided in Table A1.

Table A1: Minimum sampling points required for detection of circular hot spots using a systematic sampling pattern at 95% confidence level

Diameter of the circular hot spot that can be detected with 95% confidence (m) Square grid size G (m) Area of site (ha)* Area of site (m2) Minimum number of sampling points recommended (N)
11.8 10.0 0.05 500 5
15.2 12.9 0.1 1000 6
19.9 16.9 0.2 2000 7
21.5 18.2 0.3 3000 9
22.5 19.1 0.4 4000 11
23.1 19.6 0.5 5000 13
23.6 20.0 0.6 6000 15
23.9 20.3 0.7 7000 17
24.2 20.5 0.8 8000 19
25.0 21.2 0.9 9000 20
25.7 21.8 1 10,000 21
28.9 24.5 1.5 15,000 25
30.5 25.8 2 20,000 30
31.5 26.7 2.5 25,000 35
32.4 27.5 3 30,000 40
32.9 27.9 3.5 35,000 45
33.4 28.3 4 40,000 50
34.6 29.3 4.5 45,000 52
35.6 30.2 5 50,000 55

* 1 ha = 10,000 m2

Number of sampling points needed for determining the average concentration of an analyte

The method to calculate the number of sampling points needed for determining the average concentration of a contaminant is below an acceptable limit. The method can be applied to sampling an area or a stockpile of soil, and for validation sampling. The method requires prior knowledge of the average concentration (µ) and standard deviation (s) of the contaminant that can be obtained from previous statistically designed studies, or from experience.

Equations used:

where:

&#948    = estimated standard deviation of the contaminant concentrations in the sampling area, in mg/kg
CH  = highest possible analyte concentration in the sample area
CL   = lowest probable analyte concentration in the sample area
n    = number of sampling points needed
6.2 = factor derived from 0.05 a risk and 0.2 &#946 risk (see Glossary for definitions)
Cs  = specified limit, in mg/kg
µ    = estimated average concentration in the sample area, in mg/kg.

Method

1. Estimate the average concentration of contaminant (µ) in the sampling area based on previous sampling results or by judgement. Note that µ should have a value less than the specified limit (Cs).
2. Estimate the standard deviation (s) in the sampling area based on previous sampling results, or using equation 3 where no data are available.
3. Establish the specified limit (Cs) of the contaminant, in mg/kg.
4. Calculate the number of samples needed using equation 4.

Notes

The method assumes the distribution of analyte concentrations for the sample mean has a normal distribution, and that the analyte concentrations do not exhibit any spatial structure. The data from previous investigations should be representative of the whole area under investigation, and characteristics of the samples used in previous designs should be similar to those planned for the current study.

## Number of sampling points needed for determining the degree of contamination

This method determines the number of samples needed if the objective of sampling is to show that:

• a site has no greater than a certain proportion of its area where concentrations exceed a specified limit
• a stockpile of soil has no greater than a certain proportion of its volume where concentrations exceed a specified limit.

Equation used:

where:

N = number of samples needed
P o = maximum allowable proportion of an area or a stockpile of soil that has concentrations exceeding a
specified limit
P 1 = expected proportion of an area or a stockpile of soil that has concentrations exceeding a specified
limit.

The equation is based on 0.05a risk and 0.2&#946 risk.

Method

1. Determine Po. The value of Po typically ranges from 0.05 (testing 95% of an area or a stockpile of soil is below an acceptable limit) to 0.25 (testing 75% of an area or a stockpile of soil is below an acceptable limit).
2. Determine P1. Note the value of P1 must be less than Po.
3. Calculate N from equation 5.

References

New South Wales Environment Protection Authority (1995) Contaminated Sites: Sampling design guidelines, New South Wales Environment Protection Authority, Sydney.

US EPA (1989) Methods for Evaluating the Attainment of Cleanup Standards. Volume 1: Soils and solid media. Chapter 6: Box 6.3 (EPA 230/02-89-042).Office of Policy, Planning and Evaluation, United States Environmental Protection Agency, Washington, DC.