Comparison of effect size methods

Effect size provides a more scientific approach to the size of an intervention rather than statistical significance. There are three different aspects of effect size. The first aspect is the type of information of interest; The second aspect is the functionalization of the effect size through the equation linking statistics or parameters to the effect size, and the third aspect is the value of the effect size. There are three standard effect size estimators, namely Cohen d, Glass delta and Hedge g, under the assumption of normal distribution of two independent groups. Effect size estimators Cohen d, Glass delta, and Hedge g are consistent and asymptotic as long as the assumption of normality is present. Non-parametric effect size measures have been proposed for two independent groups in cases where the populations are not normally distributed. These effect size measures are Cliff delta, Glass Rank Biserial Correlation Coefficient, and Vargha and Delanay A (VDA). In this study, Cohen d, Hedge g, Glass delta, Cliff delta, VDA and Rank-Biserial Correlation Coefficient effect size methods were explained and reference intervals were evaluated with simulation study. For non-parametric effect size methods, the performances and reference intervals of the methods were evaluated at varying skewness and kurtosis values. A new effect size approach called the Meta Fuzzy Effect Size Function (MBEBF) has been proposed by combining the parametric and non-parametric effect size methods used for two independent groups, which are independent of the assumptions. According to the results obtained from the simulation study, the reference values of the parametric and non-parametric effect size methods differed according to the literature. The MBEBF effect size approach proposed in this thesis study showed the best performance with the lowest mean absolute percentage error according to the methods evaluated.