A new approach in synchronized permutation tests forbalanced IXJ designs

IXJ factorial designs are experiments in which the effects of various combinations of two factors and their levels on the response variable are examined. The most important advantage of this design, which is widely used in engineering, health sciences, zootechnical and agricultural research, is that it can predict both the main effects and interactions of the factors that are thought to affect the studied feature with the least error. Two-way ANOVA (Analysis of Variance) methodology is one of the important models in experiment design theory used in many research areas. In cases where the assumptions for two-way ANOVA are not provided, permutation tests that are not affected by the assumptions can be applied as a non-parametric method. Synchronized permutation tests provide three uncorrelated exact tests for two main effects and interaction effects in factorial designs. In this study, the square form of the test statistics for the effect of the main factors and the interaction effect of the synchronized permutation test was replaced with the absolute value function and for balanced IxJ factorial designs, Synchronized permutation test with tests statistics containing square form, synchronized permutation test with tests statistics containing absolute value function and two-way ANOVA in cases where error terms are not normally distributed and normally distributed were compared in terms of Type I error rates and power of the test. At the same time, permutation procedures were examined in the synchronized permutation tests and a random selection permutation procedure was proposed as an alternative to constrained synchronized permutations (CSPs ) for cases where the number of replication is greater than 7 and this method was compared to the constrained synchronized permutations in terms of power and type I error rates of the synchronized permutation tests.