A modified F-test for hypothesis testing in large-scale data

Nowadays, performing simultaneous hypothesis testing under small sample sizes in large-scale features has received unprecedented attention in practice. Traditional approaches are not appropriate for this purpose. Instead, a novel approach which is based on the null statistic is used in the literature. The null statistic approach, using the permutation samples of all features, permits the more accurate estimation of the [Formula: see text]-value for a target feature. However, the known methods, working based on the null statistic, cannot be applied to features with three or more levels. In the present study, an attempt is made to introduce a new permutation test statistic which can be modified to the null statistic approach when features have three or more levels. The robustness of the proposed test statistic and its performance in estimating the [Formula: see text]-value are demonstrated through conducting simulation studies and the analysis of two real datasets.