An overview of homogeneity of variance tests on various conditions based on type 1 error rate and power of a test

Abstract

In most statistical analyses, the data variance used is assumed to be homogeneous, but not all cases follow the assumption. Therefore, the homogeneity of variance assumption testing should be carried out prior to performing the main analysis. There are various statistical tests of variance homogeneity that exist and to obtain the best statistical test in the testing of variance equality, this study makes a comparison of statistical tests against assumptions met, assumptions violated and the existence of outlier. The comparison is based on the Type 1 Error rate and the power of the statistical test. For normal distribution, the comparison is between parametric statistical tests such as the Fisher test, the Bartlett test, the Levene test, the Brown-Forsythe test, and the Cochran C test. While for chi-squared distribution and outlier data, the comparison is between parametric and nonparametric statistical tests. The nonparametric statistical tests used are the Mood test, the Ansari-Bradley test, and the Fligner-Killeen test. The data used is the result of a normal and Chi-squared Monte Carlo simulation. The results showed that almost all the parametric statistical tests can control Type 1 Errors well in almost all situations. For the Chi-squared distribution only the Brown-Forsythe parametric statistical test was found to be robust. But most of the robust tests on non-normal data are nonparametric statistical tests. While for normal data with heterogeneous variance, the power of the test of all parametric statistical tests is seen to increase and exceed 0.80 as the size effect increases. On non-normal distributions, the power of the test is smaller than normal, but the value will increase as the size effect increases. The case was different for the Fisher test, the Bartlett test, and the Cochran C test, which was tested against data with 10% outlier in one group. The power of the test for the 1:2 variance ratio is seen as large, but the value is decreasing as the size effect increases. Thus, it can be concluded that none of the statistical tests were found to be robust and suitable for use in all the conditions set.