Because the techniques involved make assumptions about the statistical nature of the observed data values it may be necessary to transform these values prior to analysis, in order to achieve a closer approximation to Normality. Frequently this is performed via a log or Box-Cox transform (see subsection 1.5.2.7 for a range of data transformation functions). In Figure 6‑38 we show a series of transformations of 301 Radon level measurements made in part of South-West Ireland. These graphs and the associated test statistics were generated using the Minitab package. Three very large-valued outliers were removed from the original dataset prior to distribution analysis.

The raw data plotted in Figure 6‑38A is clearly non-Normal, diverging substantially from the straight line which indicates a Normal distribution. In this case simple Log transformation of the data improves the fit to Normal but still diverges, even when corrections are made for background radiation (Figure 6‑38C). In each of these three cases the Anderson-Darling test of fit to Normal fails, whereas for the Box-Cox transform (Figure 6‑38D) with optimised parameter, k, the test passes and in this instance analysis proceeded using this specific transform. The Anderson-Darling test is a variation on the Kolmogorov-Smirnov test, again based on the cumulative distribution function, but is more sensitive to the tails of the distribution.