We investigated the statistical rationale for pooling the data by performing one-way ANOVAs for each metal to test the null hypothesis that there is no effect of soil type on the average concentration of each metal. If this hypothesis is verified then there is purely statistical justification for pooling the data across soil types. Two ANOVA assumptions were tested prior to one way analysis for each metal: (1) that the sample data were distributed normally in each soil type class and (2) that the sample variances from each soil type class were not significantly different. This homogeneity of variance assumption could be equally, or more important than the results of the ANOVA because it would indicate that the samples from each soil type were drawn from a single population with a single variance. Thus, if the sample variances were equal among soil types it would be more intuitive to derive a UTL based on data from all soil types in part because the UTL is a direct function of the standard deviation. The two ANOVA assumptions were investigated by performing Shapiro Wilk tests for normality on all soil type/metal combinations (n=72 tests), and performing Hartley�s Fmax test on the variances among soil types for each metal (n=4 tests). Table C.1 contains the matrix of normality tests and Table C.2 contains the results of the Hartley�s Fmax tests, which were only performed on the metals that met the normality assumption.
If the data among soil types for each metal were distributed normally and their variances were equal, ANOVA assumptions were met, and the one-way ANOVA was performed to test the null hypothesis of no effect of soil type on the mean metal concentration. If the ANOVA assumptions could not be verified then Kruskal Wall is tests, the non parametric analog to ANOVA, were performed. The Kruskal Wallis test assesses whether the samples are distributed equally among soil types, but this test is not as informative as the ANOVA because it does not analyze between-groups error; i.e., that there is a significant amount of variation in the data due specifically to the different soil types, and if so, which of those soil types are the source of this variation. Therefore, results from the Kruskal Wallis test should be interpreted with caution. These results are presented in Table C.3.
For five metals (Cr, Cu, Pb, Ni, and Zn) the normality assumption was verified and in four of these the homogeneity of variance assumption was verified (See matrix of normality test results and the Hartley�s Fmax test results in Tables C.1-C.2). Parametric ANOVA tests were performed on these five metals and the non-parametric analog was performed on the remaining metals. All Kruskal Wallis tests indicated that the sample data were distributed differently among the soil types (Table C.3). Three of five one-way ANOVAs (Cr, Pb, and Zn) showed a significant effect of soil type on mean levels of metals in the soil (Table C.3). For these three metals, post hoc tests using Tukey�s Least Significant Difference (LSD) tests showed that Brackett-Tarrant soils (BtE) had consistently lower levels of metals than the other soil types (Tables C.4-C.6). Of the 25 combinations of soil types that exhibited significant differences in mean concentration 17, or 68%, of these involved BtE, and in 16 of these 17 cases BtE was significantly lower. Since mean metals concentration in the Brackett-Tarrant soils were consistently lower than the other soil types, these data suggest that this particular soil type was the main source of variation in mean metals concentration. Moreover, a two way ANOVA of the effect of soil type and metal on variation in soil concentrations showed that the interaction effect was non-significant (p=0.1626) indicating that for each of the five metals the pattern of deviation in mean metal concentration was equal with respect to soil type, with levels of all five metals in BtE apparently lower than the other soil types (Table C.7). These results motivated the following analysis repeating the same procedure detailed above but in the absence of the Brackett-Tarrant soil data.
One way ANOVAs were run again looking for the effect of soil type without BtE on mean soil concentration of each of the metals. When BtE was dropped from the analysis of variance the effect of soil type disappeared for lead (p=0.0914) and zinc (p=0.435) and was only marginally significant for chromium (p=0.043) (see Table C.9). When it was dropped from the Kruskal Wallis analysis the effect for Barium (p=0.295) disappeared, but the effect for Arsenic (p=0.0065), Mercury (p=0.001),and Cadmium (p=0.001) remained (see Table C.9). Removal of BtE does not seem to change the story for Arsenic, Mercury, and Cadmium because the differences among the soil types remained significant. Despite the lingering significant effects the magnitude of each effect was lower than when BtE was included in the analysis, indicating that the influence of soil type on the distribution of the metals data was somewhat lessened in the absence of BtE. Therefore, UTL calculations were performed for the data excluding and including BtE for the purpose of comparison. If these two sets (no BtE & with BtE) of metals data do not differ appreciably in their respective UTLs this could allow one to make the argument to pool the data with the knowledge that one soil type may have lower values of metals concentrations but this difference is insignificant with respect to the soil UTLs (See Figure C.8).