ERIC Number: ED427044
Record Type: Non-Journal
Publication Date: 1998-Nov-5
Reference Count: N/A
Protected versus Unprotected Multiple Comparison Procedures.
Barnette, J. Jackson; McLean, James E.
Conventional wisdom suggests the omnibus F-test needs to be significant before conducting post-hoc pairwise multiple comparisons. However, there is little empirical evidence supporting this practice. Protected tests are conducted only after a significant omnibus F-test while unprotected tests are conducted without regard to the significance of the omnibus F-test. Monte Carlo methods were used to generate replications expected to provide 0.95 confidence intervals of +/- 0.001 around the nominal alphas of 0.10, 0.05, and 0.01 for 42 combinations of "n" (5, 10, 15, 20, 30, 60, and 100) and numbers of groups (3, 4, 5, 6, 8, and 10). Unprotected and protected tests were conducted using the Dunn-Bonferroni, Dunn-Sidak, Holm, and Tukey's Honestly Significant Differences (HSD) procedures. Means and standard deviations of observed per-experiment Type I errors rates and percentages of observed per-experiment Type I error falling below, within, and above the 0.95 confidence intervals were determined for total number of Type I errors. Differences in observed Type I errors for sample size and number of groups was minimal. However, there were differences in Type I error control among the four multiple comparison procedures and when the tests were conducted as protected or unprotected. The Dunn-Bonferroni had the best control of Type I error as an unprotected test with 96.0% of the observed Type I errors falling within the 0.95 confidence interval while 87.3% of the observed Type I errors fell below the 0.95 confidence interval when used as a protected test, thus being very conservative. As unprotected tests, the Dunn-Sidak and Holm tended to be liberal, but were conservative as protected tests. The HSD was liberal in both situations, but much more so as an unprotected test. These results, combined with the ease of using the Dunn-Bonferroni, suggest this method may provide the most accurate and easiest control of per-experiment Type I error when used in an unprotected mode. (Contains 4 tables and 13 references.) (Author/SLD)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A