Contributed by Marc Salmon
The following table shows the estimated number of analytical samples required to estimate the arithmetic mean at a 95% confidence level, based on the maximum probable error (MPE) method for various MPEs and relative standard deviations (RSDs). The estimates were developed using ProUCL statistical software[1].
As described in Background, as the variability of the sample data is required to determine n using this method, either existing site data, data from similar studies, or from a small-scale scoping study should be used as an estimate of the sample standard deviation. As a general guide, for media that is not expected to be contaminated, RSDs of < 50% would be expected, and for those that are impacted, RSDs of > 70% would be expected; noting that in media that is homogenously impacted, lower RSDs will occur.
Once an RSD is determined and the desired level of precision selected (MPE 35% – 50%), the number of samples is simply determined from Table 1 as the intersect of those values. The RSD and MSD for the sample data are shown in the Basic Stats and UCLs outputs, under Other.
Example
Consider an accessible soil land use and lead sourced from former lead painted structures, which is distributed from “top-down” paint flakes and some leaching and downward migration. The action level in soil is 300 mg/kg. The relevant estimates are:
Reference to Table 1 shows for surface soils, with an RSD of 80% and an MPE of 75%, 7 samples are estimated. For deeper soils, with an RSD of 40% and an MPE of 35%, 7 samples are also estimated.
In the surface soils, based on a higher RSD, the MPE is raised, and with a maximum that exceeds the action level, the surface soils have not been sufficiently characterised to confirm land use suitability. This is reflected in the 95% UCL, which is above the action level and much greater than the mean, i.e. a large MOE.
In the deeper soils, based on a lower RSD, the MPE is reasonably low, and with a maximum that is ~ 10% of the action level, the deeper soils appear to be relatively well characterised. This is reflected in the small 95% UCL, which is close to the mean, i.e. a small MOE.
In this case, either the decision area of surface soils could be remediated, or using the same MPE as for the deeper soils (35%), at the RSD for surface soils (80%), 22 samples in total could be collected; that is an additional 15 samples would be needed. This may result in a 95% UCL that is below 300 mg/kg, and may avoid the need for remediation; or in a lesser amount of remediation being required.
However, as distribution of contaminants is essentially random at any specific location, the resultant 95% UCL may remain above the action level. In which case, the decision area was likely under-sampled and insufficiently representative data had been obtained in the first sampling event. It is also likely that the more representative data will result in better decisions and less remediation cost, and therefore still be advantageous for the stakeholders.