AN INVESTIGATION OF THE EFFECTIVENESS OF STUDENT’S t-TEST UNDER HETEROGENEITY OF VARIANCE

Within the field of psychology, few tests have been as thoroughly investigated as Student’s t-test. One area of criticism is the use of the test when the assumption for heterogeneity of variance between two samples is violated, such as when sample sizes and observed sample variances are unequal. The current study proposes a Monte Carlo analysis to observe a broad range of conditions in efforts to identify the resulting fluctuations in the proportion obtained significant results for two conditions: no mean difference (ðœ‡ô€¬µ = ðœ‡ô€¬¶) compared to the set level of alpha, and small-to-moderate mean differences (ðœ‡ô€¬µ ≠ðœ‡ô€¬¶) compared to the expected power. For each condition, population standard deviations and sample sizes will be changed incrementally. Results indicate that outside of conditions with extreme differences in population standard deviations and relative sample sizes will produce results comparable to conditions with homogenous sampling conditions at roughly the same rate. As differences between population means are increased, researchers also need not be concerned with massive losses to statistical power. Future directions for researchers are discussed further.