Critical Points in Multiple Comparisons

Abstract

Analysis of variance (ANOVA) is a statistical method for comparing the population means of more than two groups. When a statistically significant difference across those population means has been found, a multiple comparison method can be used to look for specific differences between pairs of groups. This article presents the priciple of a single-step procedure for multiple comparisons of the Bonferroni, Scheffe and Turkey method. The Bonferroni method is the most effective for comparing some pairwise comparisons while the most acceptable for testing all pairwise comparisons is Turkey method. Considering only the p-values obtained from the multiple comparisons is inadequate for interpretation of results. The confidence intervals for each population mean being compared and the confidence intervals for a difference between population means of the pairwises should be used to summarize the findings together with the scientifically meaningful in order to make a practical information for decisions to put the findings into practice.