Comparison of Familywise Error Rate of Multiple Comparison Methods for a Randomized Complete Block Design under Negative Skewed Distribution

Abstract

The purpose of this research is to study the efficiency of five multiple comparison tests; Fisher’s Least Significant Difference, Duncan’s Multiple Range Test, Newman-Keuls test, Tukey’s honestly significant difference test and Scheffe’s test. The population distribution of this study is a negatively skewed distribution. The numbers of treatments and blocks are 3, 4 and 5. Monte Carlo simulation is performed with repeated 10,000 times. The results demonstrate that the Tukey’s honestly shows significant difference test and Newman-Keuls test can control the familywise error rate (FWER) for all cases, whereas Duncan’s Multiple Range Test, Fisher’s Least Significant Difference and Scheffe’s test fail to control FWER. Duncan’s Multiple Range test is the most liberal test while Scheffe’s test is the most conservative test.