WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Development of the Robust Test for Testing the Homogeneity of Variances and Its Applications
Authors: ,
Abstract: The objective of this study is to develop a robust Levene’s test for testing the homogeneity of the variances of k datasets $$( k=3 )$$ by reformulating the test in the form of a two-stage regression framework in the absolute different scenario and the squared different scenario. The resultant test statistics comprise $$L_{AB}^{OLS}, L_{AB}^{LAD}, L_{AB}^{S}, L_{SQ}^{OLS}, L_{SQ}^{LAD},$$ and $$L_{SQ}^{S}$$ Simulations of the test statistics draw on a Monte Carlo technique and are repeated 1,000 times constituting three patterns of data distribution: a normal distribution, a logistic distribution, and a lognormal distribution. The differences between the ratios of variances are determined using a non-centrality parameter value. The research results show that the Levene’s test statistic performs better in the absolute different scenario than in the squared different scenario. Additionally, the test statistic $$L_{AB}^{S}$$, one of the test statistics in the absolute different scenario used to carry out the parameter estimation of the regression model in Stage 1 using the S-estimation method and of the regression model in Stage 2 using the OLS method, is the most efficient in all situations. Simulations of the six test statistics and their applications to actual data lead to comparable results. Based on the findings, it can be concluded that $$L_{AB}^{S}$$ is a highly efficient test statistic that is robust to logistically, and lognormally distributed data.
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Keywords: Robust Levene’s test, homogeneity of variances, ordinary least squares, least absolute deviation, S-estimation method, heavy-tailed distribution
Pages: 90-113
DOI: 10.37394/23206.2025.24.12