Levene's test

The Levene test referred to in the statistics a significance test, which tests for equality of variances ( homoscedasticity ) of two or more populations ( groups).

Similar to the Bartlett test checks the Levene test of the null hypothesis that all group variances are equal. The alternative hypothesis is therefore that at least one pair of groups having unequal variances ( heteroscedasticity ):

The significance value of the test is below a predetermined level, the differences in the variances of the sample over random ( significant) and the null hypothesis are of equal variances can be rejected.

Example

The chart above shows the distribution of net income by gender and month of birth. The issue of car :: leveneTest in R:

• The Levene test by gender yields a p- value less than and is therefore highly significant:

Levene 's Test for Homogeneity of Variance          Df F value Pr ( > F) group 1 106.09 < 2.2e - 16 ***        2404 --- Signif. codes: 0 ' ***' 0.001 '**' 0.01 '*' 0.05 0.1 '' 1 '.'

• The Levene test after birth month yields a p-value and is not significant at a given Signifkanzniveau of 5 %:

Levene 's Test for Homogeneity of Variance          Df F value Pr ( > F) group 11 1.6621 0.076.        2384 --- Signif. codes: 0 ' ***' 0.001 '**' 0.01 '*' 0.05 0.1 '' 1 '.' test statistic

(And ) the sampling variables and

With the number of groups ( samples), the number of observations in Group and the sample mean value of the group. Then the test statistic

Distributed with the total number of observations

The sample mean of all groups and the sample mean value across.

The test statistic is identical with respect to the test statistic of the one-factor ANOVA ( test for equality of group means ). By the transformation of the group of mean values

Robust estimators of group variances. Although the normal distribution assumption for the ANOVA does not apply, however, which often have a right-skewed distribution for the ANOVA can be applied.