New statistical hypothesis tests with respect to membership grades of fuzzy set(s) using analysis of variance in Latin Square Design for finding the effect of factors of classification of a population are proposed. The decision rules to be taken about the null hypothesis based on the F-test statistic value which is defined on the grades of the membership function of the fuzzy set(s) for each individual observation of the random sample or samples, are given. The proposed technique is demonstrated with numerical examples for understanding. © Research India Publications.