Exact Type 1 Error Rates for Robustness of Student's t Test with Unequal Variances

Philip H. Ramsey

Journal of Educational and Behavioral Statistics, 1980, vol. 5, issue 4, 337-349

Abstract: It is noted that disagreements have arisen in the literature about the robustness of the t test in normal populations with unequal variances. Hsu's procedure is applied to determine exact Type I error rates for t . Employing fairly liberal but objective standards for assessing robustness, it is shown that the t test is not always robust to the assumption of equal population variances even when sample sizes are equal. Several guidelines are suggested including the point that to apply t at α = .05 without regard for unequal variances would require equal sample sizes of at least 15 by one of the standards considered. In many cases, especially those with unequal N 's, an alternative such as Welch's procedure is recommended.

Keywords: Homogeneous Variances assumption; Heterogeneous variances; Assumption failure; Type I errers; Robustness; t test (search for similar items in EconPapers)
Date: 1980
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:5:y:1980:i:4:p:337-349

DOI: 10.3102/10769986005004337

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