A Monte Carlo method was used to find power functions of the t test and the Mann-Whitney U test under violation of assumptions of normality and homogeneity of variance. These functions showed that the t test was always more powerful than the U test, for differences of any magnitude between population means, even when population distributions did not satisfy parametric assumptions. The difference in power in favor of the t test which characterized nearly normal distributions with equal variances was about the same for distributions far from normal. The difference was proportionally greater for distributions having unequal variances than for those having equal variances.
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References
1.
GibbonsJ. D.Nonparametric statistical inference. New York: McGraw-Hill, 1971.
2.
HuberP. J.Robust statistics: a review. Annals of Mathematical Statistics, 1972, 43, 1041–1067.
3.
SiegelS.Nonparametric statistics. New York: McGraw-Hill, 1956.
4.
WalshJ. E.A handbook of nonparametric statistics. 2 vols.New York: Van Nostrand, 1962.
5.
WeinbergG. H.SchumakerJ. A., & OltmanD.Statistics: an intuitive approach. Monterey, CA: Brooks-Cole, 1981.
