Sensitivity and Robustness of Bartlett Test, Levene Test and ‎Randomization Test for The Analysis of Completely ‎Randomized Design

Abstract

This Monte Carlo simulation study evaluates the robustness and sensitivity of ‎the Bartlett test (B), the Levene test (L), and their randomization-based counterparts (RB and RL) for testing homogeneity of variances in a completely randomized design. The study took ‎into account normal and non-normal data (uniform, beta, lognormal, and gamma ‎distributions), three treatment groups (t = 2, 3, and 5), two significance levels (α = 0.01 and ‎‎0.05), two variance ratios (1 and 2), and seven sample sizes (n =30,60,90,120,150,300, ‎and 600). Type-I-error rates were assessed using Bradley’s criterion of robustness, with ‎power comparisons restricted to tests satisfying this condition. The randomization framework improved the performance of both test statistics by stabilizing small-sample performance and enhancing power without compromising Bradley’s criterion of robustness. ‎Bartlett test fails to maintain nominal type-I-error rates under non-normal data, exhibiting ‎strong sensitivity to non-normality. The Levene test had control of the type-I error rate, with ‎the randomization-based Levene test consistently maintaining robustness across all settings. In ‎terms of power, RL outperforms B, RB, and L across most conditions, while RB shows ‎improved performance over B but with some instability at small sample sizes. Hence, RL ‎should be used whenever data are suspected to deviate from normality in CRD.