Although the optimal choice depends on the underlying distribution, the definition based on the median is recommended as the choice that provides good robustness against many types of non-normal data while retaining good statistical power. Levene's test is equivalent to a 1-way between-groups analysis of variance (ANOVA) with the dependent variable being the absolute value of the difference between a score and the mean of the group to which the score belongs (shown below as Z i j = | Y i j − Y ¯ i ⋅ |, above). 2 Comparison with the Brown–Forsythe test.Levene's test may also be used as a main test for answering a stand-alone question of whether two sub-samples in a given population have equal or different variances. Welch's t-test, or unequal variances t-test is a more conservative test.
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When Levene's test shows significance, one should switch to more generalized tests that is free from homoscedasticity assumptions (sometimes even non-parametric tests). Levene's test is often used before a comparison of means. Some of the procedures typically assuming homoscedasticity, for which one can use Levene's tests, include analysis of variance and t-tests. Thus, the null hypothesis of equal variances is rejected and it is concluded that there is a difference between the variances in the population. If the resulting p-value of Levene's test is less than some significance level (typically 0.05), the obtained differences in sample variances are unlikely to have occurred based on random sampling from a population with equal variances. It tests the null hypothesis that the population variances are equal (called homogeneity of variance or homoscedasticity). Some common statistical procedures assume that variances of the populations from which different samples are drawn are equal. 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.
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