Tests for Homogeneity of Variance

Introduction

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. If the variances are not homogeneous, they are said to be heterogeneous. If this is the case, we say that the underlying populations, or random variables, are heteroscedastic (sometimes spelled as heteroskedastic).

In this entry we will initially discuss the case when we compare variances of two populations, and subsequently will extend to k populations.

Comparison of Two Population Variances

The standard F-test is used to test whether two populations have the same variance. The test statistic for testing the hypothesis if σ ₁ ² = σ ₂ ² where σ ₁ ² and σ ₂ ² are the variances of two populations, is

$$F = \frac{{s}_{1}^{\;2}} {{s}_{2}^{\;2}},$$

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