How to use analysis of variance correctly——the multiple comparisons among the multiple means

Abstract

The purpose of the paper was to introduce the multiple comparison method among multiple means and the SAS implementation. The multiple comparison approaches could be subdivided into the pairwise comparisons， the comparisons of all treatment groups with a control group， the comparisons of the mean of each treatment group with the average of all groups， the approximate and simulation-based approach， the multi-stage testing and Bayesian method. Except for the Bayesian approach， the difference between other multiple comparison methods lied in the types of error that were controlled. Error types could be roughly divided into the following three categories， the comparisonwise error rate， the experimentwise error rate and the maximum experimentwise error rate. The multiple comparison methods constructed based on the control of different error rates were not all the same in the strength of inference to draw conclusions. This paper used the SAS software to analyze the examples and explained the output results.

Keywords

• analysis of variance
• multiple comparisons
• comparisonwise error rate
• experimentwise error rate
• range distribution