Efficiency Evaluation of Statistical Tests for Homogeneity of Variances under Normal, Beta, and Weibull Distributional Frameworks

This research endeavor aims to evaluate six test statistics relevant to assessing of homogeneity of variance (HOV): Bartlett’s (BL), Levene’s (LV), modified Levene’s (LVM), Klotz’s (KL), Layard’s (LY), and Samiuddin’s (SMD). Simulated datasets were generated under the frameworks of normal, Beta, and Weibull distributions, encompassing both three and four groups, while incorporating variations in sample sizes that were both equal and unequal. Each experimental condition was replicated 5,000 times to ensure the precision of statistical outcomes. In the context of the normal distribution, the BL, LY, and SMD statistics exhibited strong control over Type I error rates, with the BL and LY statistics achieving the highest statistical power among the tests classified as acceptable. Whereas the LV and LVM statistics demonstrated competence in error control, they were characterized by reduced power; conversely, the SMD statistic exhibited significantly low power. In contrast, the KL statistic consistently yielded inflated error rates, rendering it inappropriate for practical application. In the realm of the Beta distribution, the KL, LVM, and LY statistics emerged as the most proficient performers, adeptly preserving Type I error rates. The KL statistic, notwithstanding its mediocre performance under normal distribution conditions, demonstrated the greatest resilience within this specific context. The LVM statistic maintained a conservative approach; the LY statistic exhibited precision yet was somewhat less robust when faced with skewed data, the LV statistic demonstrated moderate effectiveness, the BL statistic was excessively cautious, and the SMD statistic was classified as unreliable. In relation to the Weibull distribution, the LY, SMD, KL, and LVM statistics consistently controlled the Type I error rates. The BL statistic performed satisfactorily but exhibited a slight inclination towards inflation of Type I error rates, whereas the LV statistic was assessed as unreliable. The BL statistic attained the highest statistical power, albeit with correspondingly elevated Type I error rates. The LVM and LY statistics demonstrated considerable power across diverse scenarios, with the LY statistic being preferentially utilized for small to medium sample sizes and the LVM statistic for larger sample sizes. The SMD and KL statistics consistently ranked lowest in terms of empirical power.