A Comparison of Distribution Tests and Relevant Point and Interval Estimators
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.Please view the pdf by using the Full Text (PDF) link under 'View' to the left.
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