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In statistics, Levene's test is an inferential statistic used to assess the equality of variances for a variable calculated for two or more groups. [1] This test is used because some common statistical procedures assume that variances of the populations from which different samples are drawn are equal. Levene's test assesses this assumption.
Violation of this assumption can be conceptualised as a correlation existing between the variances and the means of dependent variables. This violation is often called 'heteroscedasticity' [4] and can be tested for using Levene's test. [5]
In order to understand this, it is necessary to understand the test used to evaluate differences between groups, the F-test. The F-test is computed by dividing the explained variance between groups (e.g., medical recovery differences) by the unexplained variance within the groups. Thus,
The null hypothesis of this chi-squared test is homoscedasticity, and the alternative hypothesis would indicate heteroscedasticity. Since the Breusch–Pagan test is sensitive to departures from normality or small sample sizes, the Koenker–Bassett or 'generalized Breusch–Pagan' test is commonly used instead.
In statistics, Bartlett's test, named after Maurice Stevenson Bartlett, [1] is used to test homoscedasticity, that is, if multiple samples are from populations with equal variances. [2] Some statistical tests, such as the analysis of variance , assume that variances are equal across groups or samples, which can be checked with Bartlett's test.
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.Notionally, any F-test can be regarded as a comparison of two variances, but the specific case being discussed in this article is that of two populations, where the test statistic used is the ratio of two sample variances. [1]
The squared ranks test is arguably a test of significance of difference of data dispersion not variance per se. This becomes important, for example, when the Levene's test fails to satisfy the rather generous conditions for normality associated with that test and is a default alternative under those conditions for certain statistical software ...
An f-test pdf with d1 and d2 = 10, at a significance level of 0.05. (Red shaded region indicates the critical region) An F-test is a statistical test that compares variances. It's used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different.