Evaluation of Statistical Methods for Determining Differences between Samples from Lognormal Populations
1993
Parkin, T. B.
Soil variables often exhibit frequency distributions that are positively skewed. When this situation exists, the assumption of normality associated with analysis-of-variance procedures is violated, and two common recommendations are given: (i) perform a normalizing transformation, or (ii) apply nonparametric statistical methods. Information regarding the relative efficacy of these two procedures with regard to power to detect differences between batches of samples is lacking. This study evaluates five statistical procedures for detecting differences between samples drawn from Iognormal populations. The tests evaluated were (i) two-tailed t-test on untransformed data, (ii) twotailed t-test on natural log-transformed data, (iii) nonparametric Mann- Whitney test, (iv) median confidence interval overlap method, and (v) a mean confidence interval overlap method. The tests were evaluated with regard to Type I error rate by comparing batches of samples drawn from the same Iognormal population. Also, the power of the statistical tests to detect differences between two batches of samples drawn from different Iognormal populations was evaluated over a range of population variances and sample sizes (n = 4 to 100). It was found that three of the tests (Tests 2, 3, and 4) were sensitive to sample differences when the underlying populations differed with regard to their medians. The other two tests (Tests 1 and 5) were sensitive to differences in population means. Test 2 is recommended when the median is the location parameter of interest; however, Test 5 should be used to detect differences in means. Contribution from the USDA-ARS, National Soil Tilth Laboratory.
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