Robustness of theF-Test to Errors of Both Kinds and the Correlation Between the Numerator and Denominator of theF-Ratio

In this study of robustness the insensitivity of the F-test between means to its underlying assumptions (normally distributed populations with equal variances) is investigated. Using two nonnormal distributions (exponential and lognormal), it is found that the test is fairly insensitive for moderate and equal sample size (n = 32) when the variances are equal. Further, for small samples (n < 32), the test is conservative with respect to Type I error. It is also conservative with respect to Type II error for a large range of φ (noncentrality), depending on the size of the sample and α. When the within cell error variances are heterogenous, the test continues to be conservative for the upper values of φ and slightly biased toward larger Type II errors for smaller values of φ depending on the size of α. Analysis of the correlation between the numerator and denominator of F under the null hypothesis indicates that the robustness feature is largely due to this correlation. Analytic proofs under the non-null hypothesis were not possible, but some empirical results are presented.