ERIC Number: ED427043
Record Type: Non-Journal
Publication Date: 1998-Nov-4
Reference Count: N/A
The Tukey Honestly Significant Difference Procedure and Its Control of the Type I Error-Rate.
Barnette, J. Jackson; McLean, James E.
Tukey's Honestly Significant Difference (HSD) procedure (J. Tukey, 1953) is probably the most recommended and used procedure for controlling Type I error rate when making multiple pairwise comparisons as follow-ups to a significant omnibus F test. This study compared observed Type I errors with nominal alphas of 0.01, 0.05, and 0.10 compared for various sample sizes and numbers of groups. 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). Means and standard deviations of observed Type I error rates and percentages of observed Type I errors falling below, within, and above the 0.95 confidence intervals were determined for total number of Type I errors. The results indicate that HSD is conservative relative to experimentwise Type I error control across all alpha levels, sample sizes, and number of groups. However, when per-experiment (total Type I errors) is of interest, HSD was liberal at alpha of 0.10 and 0.05, but was very conservative when alpha was 0.01. Results also point out the differences inherent in selection of a Type I error mode of control. Differences between per-experiment and experimentwise Type I error control was mostly a function of the number of groups being compared. As the number of groups increased, the difference between per-experiment and experimentwise error proportions increased. However, sample size was also a significant predictor; as sample size increased, the difference decreased. (Contains 9 tables and 14 references.) (Author/SLD)
Publication Type: Reports - Research; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A