σ 2 is variance, x i is a set constituent, μ is the sample mean, and N is the total number of set constituents. You may think this formula is very similar to the SD formula. That is because variance is SD squared, hence being denoted as σ 2. In the previous section, the SD was ±2.96 units. Should we want to obtain the variance, we just x: A linear model or an ANOVA object. method: Name of the method (underlying test) that should be performed to check the homogeneity of variances. May either be "levene" for Levene's Test for Homogeneity of Variance, "bartlett" for the Bartlett test (assuming normal distributed samples or groups), "fligner" for the Fligner-Killeen test (rank-based, non-parametric test), or "auto". Bartlett’s test is used to test if k samples are from populations with equal variances. Equal variances across populations are called homoscedasticity or homogeneity of variances. Some statistical tests, for example, the ANOVA test, assume that variances are equal across groups or samples. The Bartlett test can be used to verify that assumption.
10.8: Homogeneity of Variance. Before wrapping up the coverage of independent samples t-tests, there is one other important topic to cover. Using the pooled variance to calculate the test statistic relies on an assumption known as homogeneity of variance. In statistics, an assumption is some characteristic that we assume is true about our data
Homogeneity of variance ( homoscedasticity) is an important assumption shared by many parametric statistical methods. This assumption requires that the variance within each population be equal for all populations (two or more, depending on the method). For example, this assumption is used in the two-sample t -test and ANOVA.
An F -test ( Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal. The one-tailed version only tests in one direction, that is the variance from the first population
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    • how to test homogeneity of variance