Ensemble of effect size methods based on meta fuzzy functions

Abstract

Many methods are used in the literature to determine the effect size (ES) for two independent groups. Many of these methods yield consistent results under the assumptions of normality of data and homogeneity of variances. However, not every dataset can provide these assumptions. In order to overcome the limitations mentioned, this study proposes the use of meta fuzzy effect size functions (MFESF). The MFESF weights six ES methods (Cohen's d, Hedge's g, and Glass' delta, Cliff's delta, Vargha and Delaney A and Glass' rank-biserial correlation) used for two independent groups according to their performances and provides better outcomes, regardless of assumptions. The MFESF method uses the fuzzy c-means (FCM) clustering algorithm to combine the selected ES methods. In this study, MFESF is evaluated by using generated datasets based on normal and non-normal distribution for six reference values. In addition, the performance of MFESF is evaluated by using real datasets with normal and non-normal distributions. As a result, the MFESF performed the best with the lowest mean absolute percentage error (MAPE) compared to the individual ES methods for all datasets.