ANOVA methodology is one of the important models in the experimental design theory. Synchronized permutation provides exact solution in factorial designs within a nonparametric framework. Synchronized permutation tests have quadratic form test statistics. In this paper we studied synchronized permutation tests with absolute value form in the test statistics for main factors and interaction for IXJ balanced factorial designs in case of nonnormal distributed error terms. Then we investigate the behavior of synchronized permutation tests with absolute value form and quadratic form in the test statistics in a comparative simulation study with the parametric ANOVA is reported in 3X2 design when error terms normal and non-normal distributed.