Rank analogues of the likelihood ratio test for an ordered alternative in a two-way layout

Summary Distribution-free tests for no treatment effect against the simple order alternative in a two-way layout with equal number of observations per cell are considered. The nonparametric test statistics are constructed by the rank analogues of the likelihood ratio test statistic assuming normality (i) based on within-block rankings and (ii) based on combined rankings of all the observations after alignment within each block. The exact distributions are given and large sample properties are investigated. The asymptotic power of the test (i) as the number of observations per eell tends to infinity can be satisfied enough, and in the case that the number of blocks tends to infinity, the asymptotic power of the test (ii) is almost higher than that of the test (i). Also these rank tests are compared with linear rank tests and it is shown that these proposed tests are robust by a table.