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A Comparison of Distribution Tests and Relevant Point and Interval Estimators

JORDFORSK, Centre for Soil and Environ. Res., 1432 Ås, Norway.

^* Corresponding author (ketil.haarstad{at}jordforsk.nlh.no).

ABSTRACT

This is a study of samples from natural, terrestrial environments, with coefficients of variation ranging from 4 to 211%. To select estimators, physical and chemical sample distributions are separated into three categories: normal (N), lognormal (LN), and nonparametric (NP) distributions. The type of distribution is given by (i) the Lilliefors procedure of the Kolmogorov-Smirnov test (KST), (ii) the Shapiro-Wilk test (SWT), or (iii) the Skewness test (ST). For 46 samples, 14 (30%) were NP, 14 (30%) were LN, and 18 (39%) were N, based on test (i). Test (ii) gave 14 (30%) NP, 19 (41%) LN, and 13 (28%) N. Only 29 of the 46 samples could be tested by Method (iii) due to the limit on minimum sample size of 25:11 (38%) were NP, 9 (31%) LN, and 9 N. The KST and SWT disagreed in 35% of the samples, whereas KST and ST disagreed in 24% of the samples. The SWT disagreed with ST results in 10% of the samples, when categorizing the distributions at a significance level of 5%. The ratio between the selected point estimator and the mean varied from 13 to 249%, with mean values of 73% for NP and 112% for LN. The ratio between the selected interval estimator and the range varied from 2 to 71%. It is not possible to characterize one of the distribution tests as superior to the others based on the results from this study.