Table 3.

The Maximum Value Test (after CLR 7).

A9.Values that exceed Soil Guideline Values will invariably warrant some further consideration even when the mean value test has been passed. The problem of acceptance or rejection of maximum values that exceed Soil Guideline Values is not straightforward. This is because there is a need to balance the primary goal of health protection with the recognition that contaminants in soil often have high sampling and analytical variability. This is especially so for contaminants occurring at low concentrations.
A10.In forming a view on whether extra sampling and analysis may be required, a useful question to ask is whether the maximum value in a set of measurements is likely to have come from the same population as the other measurements, or whether it is a statistical outlier
A11.To make progress with this question it is necessary to assume the form of the underlying distribution; the vast bulk of the relevant literature on outliers relates to an underlying Normal distribution. In the context of chemical analyses of contaminated soils, it is common practice to work with the logarithms of the measured values. This log-transformation usually results in a more or less symmetric distribution which, while not strictly Normal, is usually close enough to allow Normal statistics to be used with some confidence.
A12.Thus the raw measurements x1, x2,.....,xn are first log-transformed (y1=log x1 etc); and the sample mean ybarand unbiased sample standard deviation Syare then calculated from the log transformed values.
A13.An appropriate test is then: T=(ymax − ybar)/Sy If the value of Tis smaller than some critical value, the maximum value may be accepted (at the prescribed level of confidence) as a member of the underlying population from which the other measurements were drawn. If Tis greater than the critical value the maximum value is treated as an outlier, which may indicate a localized area of contamination. Of course, the outlier might instead be the result of a measurement or recording error; but in any event it flags up the need for further investigation. A worked example is given in Annex 2 [of CLR 7].