Rank tests for the Latin square design

A rank test for Latin square data is derived. Forms are given for when there are no ties, for when ties occur and mid-ranks are used, and for when ties occur in general. These adjustments are akin to those for the Kruskal-Wallis, Friedman, and Durbin tests. Since substantial block effects may affect ranking, alignment is recommended. The ANOVA F test on the ranks, the rank transform test, is a competitor test. We designate this test, where the data are aligned before ranking, the FART test. The proposed test, implemented as a permutation test, is designated the permutation aligned RL test: the PARL. We also give an approximation to the sampling distribution using the χ2 distribution, and call this test the CARL. An indicative simulation study assuming the usual parametric model and testing the null hypothesis that the treatment parameter is zero shows that the CARL, PARL, FART, and the F test on the raw data all control their type I errors well and have comparable powers.