Choosing a Two-Sample Location Test

Type I error rate and power for the t test, Wilcoxon-Mann-Whitney (U) test, van der Waerden Normal Scores (NS) test, and Welch-Aspin-Satterthwaite (W) test were compared for two independent random samples drawn from nonnormal distributions. Data with varying degrees of skewness (S) and kurtosis (K)...

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Bibliographic Details
Published in:The Journal of experimental education 1994-07, Vol.62 (4), p.343-360
Main Author: Penfield, Douglas A.
Format: Article
Language:English
Subjects:
Kurtosis
Measurement, Statistics, and Research Design
Monte Carlo Methods
Nonparametric Statistics
Power (Statistics)
Range errors
Sample Size
Sampling
Sampling distributions
Sampling errors
Selection
Simulation
Skewed distribution
Statistical Analysis
Statistical discrepancies
Statistical Distributions
Statistics
T Test
T tests
Test ranges
Test Use
Type I Errors
Variance
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Summary:Type I error rate and power for the t test, Wilcoxon-Mann-Whitney (U) test, van der Waerden Normal Scores (NS) test, and Welch-Aspin-Satterthwaite (W) test were compared for two independent random samples drawn from nonnormal distributions. Data with varying degrees of skewness (S) and kurtosis (K) were generated using Fleishman's (1978) power function. Five sample size combinations were used with both equal and unequal variances. For nonnormal data with equal variances, the power of the U test exceeded the power of the t test regardless of sample size. When the sample sizes were equal but the variances were unequal, the t test proved to be the most powerful test. When variances and sample sizes were unequal, the W test became the test of choice because it was the only test that maintained its nominal Type I error rate.
ISSN:0022-0973
1940-0683
DOI:10.1080/00220973.1994.9944139