A comparison of the F-test, Friedman’s test, and several aligned rank tests for the analysis of randomized complete blocks

Several tests for randomized complete block designs are compared, including the F-test, Friedman’s test, and a few aligned rank tests. An additive model was used in this simulation study with random errors that were generated independently from one of nine distributions. These distributions included the uniform, normal, double exponential, and six skewed distributions from the generalized lambda family. The simulations showed that Friedman’s test has low power compared with the aligned rank tests if the number of treatments does not exceed six. A new aligned rank F-test is proposed that maintains its significance level and has relatively high power. The simulations also showed that the proposed aligned rank test has higher power than the F-test for the double exponential and the skewed distributions if there is a large number of experimental units. If the number of experimental units exceeds 30, the proposed aligned rank test is recommended for skewed or long-tailed distributions. If the number of experimental units does not exceed 30, the normal theory F-test is recommended.