The effects of the Penry Wellfield on well-water quality

Ohio Journal of Science, The, Dec, 2007 by Keith O. Mann

Water-Quality Trends

Although the independent variables of geography (measured either from west-to-east or as distance-from-well TW-5) and well depth cannot be used as predictors of water chemistry, general geographic trends in water quality may exist within the study area. In order to address this possibility, ANOVA was conducted for each water quality parameter with respect to geography during each sampling round (Table 7). In this portion of the analyses, the Bonferroni Correction, based on the Bonferroni Inequality, was used to help guard against the accumulation of Type-I errors (a false rejection of the null hypothesis) when conducting multiple comparisons. The Bonferroni Inequality

p [greater than or equal to] [(1-[alpha]).sup.K] Equation 3

P = probability

[alpha] = level of significance

K = number of simultaneous comparisons

reveals that as the number of simultaneous comparisons rises, the probability of committing a Type-I error increases dramatically, if one uses the same confidence interval for each test as used for the entire study. For example, if 20 simultaneous t-tests are conducted (K = 20), using [alpha] = 0.05, the Bonferroni Inequality indicates that the probability of committing a Typed error would not be 5%, but would inflate to 64%: clearly an unacceptable level. The Bonferroni Correction,

[[alpha].sub.i] = [[alpha].sub.s/K, Equation 4

adjusts the confidence interval to reduce the chance of committing a systematic increase of Type-I errors when performing multiple-comparison statistical tests. The Bonferroni Correction enables the researcher to determine the level of significance ([[alpha].sub.i])for a given number of individual tests (K), once the study-wide level of significance ([[alpha].sub.s]) has been chosen. For this study, using [[alpha].sub.s] = 0.05 and performing seven individual comparisons (K= 7) for each round, the Bonferroni Correction indicates that [[alpha].sub.c], should be set at 0.007. Of the 63 slopes tested for significance, four significant trends during the entire study were identified: pH showed a significant trend only during sampling round 8 (declining along the flow path), specific conductance experienced a significant trend only during the last sampling round, and hardness displayed a positive trend (increasing along flow path) during both the first (see also Fig. 3) and last sampling round. Interestingly, the slope (both significant and non-significant) of 30 of the 63 comparisons were in fact opposite to what one would expect given the flow-paths of the study area. Clearly no significant trends persisted during any study phase and thus no strong and well-defined general trend of water quality exists within the study area either during non-pumping or pumping conditions. Such few and sporadic findings of significance may simply result from random chance (with four of 63, 6%, comparisons documenting significant findings).

Among Phase Analyses

Since no spatial or temporal trends appear to exist within each study phase, the data of each study phase can now be pooled and water-quality differences among the study phases can be explored. Although the independent variables could not be used to predict water quality within each of the three study phases, comparisons of the water-quality parameters among the study phases may reveal effects of pumping on water chemistry. Both parametric and nonparametric methods were used to explore this possibility. Parametric testing began by first applying ANOVA and if it exposed significant differences, multiple t-tests were then applied. When appropriate, the non-parametric Kruskal-Wallis Test was used, followed by the Wilcoxon Rank Sums Tests for pair-wise comparisons.