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I am doing an anova in matlab and to check for homogeneity of residual variances I want to perform a Levene's test. Matlab offers this handy function vartestn to do that. In the documentation there are two types of Levene's test:

  1. 'LeveneQuadratic': Levene’s test computed by performing ANOVA on the squared deviations of the data values from their group means.
  2. 'LeveneAbsolute': Levene’s test computed by performing ANOVA on the absolute deviations of the data values from their group means.

The quadratic version shows no significance (p = 0.14), while the absolute version rejects H0 of equal variances with a p value of 0.04.

I'm not sure what to make of this, the best way would be to thoroughly understand what the difference is between these two versions, but I am failing to get an intuition what effect squared and absolute deviations would have on the test results.

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