Non parametric tests based on the alignment of observations for replicated Latin squares

Non parametric tests for a replicated Latin square design that test for both general and increasing alternatives are presented. The tests are based on aligning the observations and allowing existing well-known tests for randomized complete block designs to be utilized. We also present two theorems that show how the asymptotic distribution properties of the test statistics hold when alignment coefficients are estimated. Simulation studies on datasets generated from several design variations (including error terms that follow a contaminated normal distribution) show that the proposed methods maintain their significance levels under the null hypothesis, with ordered alternative tests outperforming the general alternative counterparts in terms of power when the treatment effects are indeed ordered.