An Improvement to the Aligned Rank Statistic for Two-factor Analysis of Variance

We modify the nonparametric method of Brunner, Dette and Munk (1997) by applying their method to the aligned ranks of the data. We compare this new approach to three other rank tests: the F-test applied to the ranks of the date, the approximate F-test of Brunner, Dette and Munk (1997) applied to the ranks of the data, and the F-test applied to the aligned ranks of the data. We also compare the new test to parametric F-test and to the approximate F-test using the modified Box-type adjustment of Brunner, Dette and Munk (1997). In addition, we show that using the Box-type adjustment alleviates the problem of Type I error rate inflation seen previously for the aligned rank test, without a noticeable loss of power, as long as sample sizes are moderate (n = 7)