Score Test for Homogeneity of Variances in Normal Distributions

In this study, we suggest a novel test statistic based on the Score statistic for evaluating the homogeneity of variances in normal distributions. In addition to the conventional chi-square approximation of the Score statistic, we introduce a parametric bootstrap technique known as the Computational Approach Test (CAT). Through a simulation study, we evaluate the proposed test’s CAT approach (referred to as CS) and assess its performance against established methods under varying group sizes and sample sizes. The results show that, regardless of the number of groups, the CAT approach of the Score test performs well when sample sizes and variances are directly proportional, even with a minimum sample size of three. Furthermore, when sample sizes and variances are inversely proportional, the proposed test significantly outperforms alternative methods. To demonstrate the application of the discussed methods, we provide two numerical examples.