A Comparison of Type I Error Rates of Alpha-Max with Established Multiple Comparison Procedures.Report as inadecuate

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J. Barnette and J. McLean (1996) proposed a method of controlling Type I error in pairwise multiple comparisons after a significant omnibus F test. This procedure, called Alpha-Max, is based on a sequential cumulative probability accounting procedure in line with Bonferroni inequality. A missing element in the discussion of Alpha-Max was the empirical determination of actual probabilities of Type I errors. This paper compares the Type I error rates of Alpha-Max with other commonly used multiple comparison procedures: (1) Fisher's Least Significant Difference (LSD); (2) Dunn-Bonferroni; (3) Tukey's Honestly Significant Difference (HSD); (4) the Student Newman Keuls (SNK) procedure; and (5) the Scheffe approach. Monte Carlo procedures were used to generate 10,000 replications with varied alpha of 0.05 and 0.01; 3, 4, and 5 groups; and 5 sample sizes. Actual Type I error rates were determined for the greatest difference and for total number of Type I errors. Results indicate that in virtually every situation LSD and Alpha-Max had significantly higher probability of Type I errors than the other four methods. SNK and HSD had higher than nominal alpha probabilities for committing Type I errors, with SNK having a lower level than HSD. Dunn-Bonferroni had a level slightly lower than the nominal level, while the Scheffe had a level much lower than the nominal level. Varying sample size had little practical significance. While Alpha-Max did not provide for acceptable experiment-wise control of Type I error, it may provide an alternative for control of Type I error in the planned, nonorthogonal situation or in situations where assumptions of analysis of variance are violated. (Contains 25 tables and 4 references.) (Author/SLD)

Descriptors: Analysis of Variance, Comparative Analysis, Monte Carlo Methods, Probability, Sample Size, Simulation

Author: Barnette, J. Jackson; McLean, James E.

Source: https://eric.ed.gov/?q=a&ft=on&ff1=dtySince_1992&pg=8788&id=ED415284

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