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Statistical Treatment of Soil Chemical Concentration Data

Statistics Dep., The Ohio State Univ., Columbus, OH 43210;

S. E. Nokes^* and S. R. Workman

Biosystems and Agric. Eng. Dep., Univ. of Kentucky, Lexington KY 40546-0276.

^* Corresponding author (snokes{at}bae.uky.edu).

ABSTRACT

Soil chemical field data typically do not satisfy the required statistical assumptions, and this renders statistical tests based on normal theory either invalid or not particularly powerful. The objective of this study was to compare the t-test and two nonparametric tests (Wilcoxon signed rank and the Sign test) for a theoretical data set and 3 yr of soil atrazine (2-chloro-4-ethylamino-6-isopropylamino-s-triazine) concentration field data, to demonstrate how the sample distribution affects the statistical analysis. The theoretical data set was contructed to emulate a soil chemical data set in which a minimum detection limit resulted in multiple zeros within the data. These data were non-normal, and the normal-theory tests were not valid. The converse was also demonstrated. The performance of the nonparametric tests was evaluated when the data were from a normal distribution. The Wilcoxon signed rank test performed well on normal data, although there were some data for which the t-test was more powerful. Actual soil atrazine concentration data from 78 sampling events were analyzed both with the paired t-test, Sign test, and Wilcoxon signed rank test. Thirty-three percent of the events were not from normal distributions, and 15% of these resulted in different decisions regarding the null hypothesis if the paired t-test was used instead of the Wilcoxon signed rank test. Of the 66% of data sets that were from normal distributions, 5.7% of these resulted in different decisions regarding the null hypothesis if the Wilcoxon signed rank test was used instead of the t-test. It is recommended that all soil chemical data sets be tested for normality. If the data are not normally distributed, the appropriate nonparametric test should be used rather than attempting to transform the data to normality. Several other nonparametric tests are presented.