Pairwise Multiple Comparison Procedures Research Articles

Pairwise Multiple Comparisons in the Unequal Variance Case

Abstract Four pairwise multiple comparison procedures for the case in which the variances in the groups are unequal were compared by computer simulation: the GH procedure based on the Studentized range and the Welch formula for approximate degrees of freedom (df), the C procedure based on a weighted average of two Studentized range points, the T2 procedure based on Student's t, and the T3 procedure based on the Studentized maximum modulus. The results indicate that C, T2, and T3 have the desirable property of being conservative, whereas GH sometimes is not. Of the three conservative procedures, T3 always has shorter confidence interval length than T2, whereas C has shorter length than T3 for large df, but longer length for small df.

Evaluation of Cluster Analysis for Comparing Treatment Means1

AbstractUnivariate cluster analysis of treatment means is considered as an alternative to the least significant difference for those experiments where pairwise multiple comparisons are applicable. Although cluster analysis procedures produce distinct, non‐overlapping groupings of the treatments, little previous study has been made of their statistical behavior. The objective of the present research was to examine statistical properties of four clustering algorithms in terms of their power and Type I and III error rates for several patterns of homogeneity among treatment means. The Scott‐Knott (SK) divisive procedure and three agglomerative procedures based on single linkage (SL), complete linkage (CL), and unweighted pair group averages (UPG), respectively, were compared to the least significant difference (FLSD) when a preliminary F test of overall treatment effects is performed.Results of simulation studies indicate that the overlapping nature of the groupings of treatments obtained with the FLSD provides considerable protection against Type I and Type III errors. Both types of errors occurred with higher frequencies for all four clustering algorithms than for the FLSD. Furthermore, comparisonwise Type I error rates for the FLSD are determined by the researcher's choice of significance level, while the rates for cluster analysis are dependent on both the significance level and the degree of precision of the experiment. Consequently, researchers should contemplate with caution any possible adoption of cluster analysis as a replacement for a pairwise multiple comparison procedure such as the FLSD.

Choosing the most powerful pairwise multiple comparison procedure in multivariate analysis of variance.

Choosing the most powerful pairwise multiple comparison procedure in multivariate analysis of variance.

Choosing the most powerful pairwise multiple comparison procedure in multivariate analysis of variance.

Choosing the most powerful pairwise multiple comparison procedure in multivariate analysis of variance.

A Monte Carlo study of nonparametric multiple-comparison tests for a two-way layout

A Monte Carlo study of two overall tests, the Friedman and Doksum, and five nonparametric multiple-comparison tests, the McDonald-Thompson, Nemenyi, Wilcoxon, Rhyne-Steel, and sign test, was done to determine the tests’ Type I error rates in a two-way layout with k = 3, 5, and 7 treatments and n = 8, 11, and 15 blocks. It was found that (1) the Friedman test was superior to the Doksum test as an overall test, and (2) the Wilcoxon signed-ranks test, when protected by a significant Friedman test, was the best pairwise multiple-comparison procedure. In a second Monte Carlo study, a modified sign test, termed the stepped-down sign test, was found to be superior to the Wilcoxon test as a protected test; it is recommended for pairwise comparisons in a two-way layout.

Pairwise Multiple Comparison Procedures with Unequal N’s and/or Variances: A Monte Carlo Study

Three different methods for testing all pairs of yȳk, - yȳk’ were contrasted under varying sample size (n) and variance conditions. With unequal n’s of six and up, only the Behrens-Fisher statistic provided satisfactory control of both the familywise rate of Type I errors and Type I error rate on each contrast. Satisfactory control with unequal n’s of three and up is dubious even with this statistic.

Pairwise Multiple Comparison Procedures with Unequal N's and/or Variances: A Monte Carlo Study

Pairwise Multiple Comparison Procedures with Unequal N's and/or Variances: A Monte Carlo Study

An Evaluation of Ten Pairwise Multiple Comparison Procedures by Monte Carlo Methods

An Evaluation of Ten Pairwise Multiple Comparison Procedures by Monte Carlo Methods

An Evaluation of Ten Pairwise Multiple Comparison Procedures by Monte Carlo Methods

Abstract Computer simulation techniques were used to study the Type I and Type III error rates and the correct decision rates for ten pairwise multiple comparison procedures. Results indicated that Scheffé's test, Tukey's test, and the Student-Newman-Keuls test are less appropriate than either the least significant difference with the restriction that the analysis of variance F value be significant at α = .05, two Bayesian modifications of the least significant difference, or Duncan's multiple range test. Because of its ease of application, many researchers may prefer the restricted least significant difference.