he Effect of Selection of Samples for Homogeneity on Type I Error Rate

by Donald W. Zimmerman .

Abstract: Abstract:The Type I error probability of the two-sample Student t test is known to deviate from the statistical significance level when variances are unequal and, at the same time, sample sizes are unequal. The present simulation study indicates that, for various sample sizes and ratios of population standard deviations, the conditional probability of a Type I error, under the condition that the ratio of sample standard deviations falls in a narrow interval close to 1.00, is larger than the unconditional probability of a Type I error. This result emphasizes that it is essential to distinguish between homogeneity of population variances and homogeneity of sample variances. If population variances are heterogeneous and sample sizes are unequal, a Student t test will be invalid, whether or not sample variances of treatment groups happen to be equal. Accordingly, it is not possible for researchers to protect the significance level of the test by explicit selection of homogeneous samples.

Key Words: significance test, Student t test, Welch t test, separate-variances t test, significance level, Type I error, homogeneity of variance, conditional probability

Donald W. Zimmerman, donzimmer@midmaine.com

Editor: Richard Graf , rgraf@sunstroke.sdsu.edu

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