A A Comparison of the Efficiency of Resampling-Based Test Statistics for Randomized Complete Block Designs under Log-Normal Distributed Data

Abstract

This study aimed to evaluate the performance of resampling-based test statistics for the randomized complete block design. The tests considered were the bootstrap F-test and the permutation F-test, and they were compared with two traditional methods: the F-test and the Friedman test. The experiments were conducted under log-normal distributed data. The design included three treatments, and the numbers of blocks considered were 3, 5, 7, and 10. The significance level was set at 0.05. The results showed that the F-test, the Friedman test, and the permutation F-test controlled the Type I error in all scenarios, while the bootstrap F-test controlled the Type I error only when there were at least five blocks. For statistical power, the F-test had the highest power when there were three blocks. However, when the number of blocks increased, the bootstrap F-test provided the highest power in most cases.