Comparison of p values for Levene mean test and Levene median test? I am doing Levene's mean test and Levene's median test (Brown-Forsythe).
I want to compare the p-values of these two tests to see which is better. 
I get large p-values for both tests which are 0.562 (Levene mean) and 0.611 (Levene median) for normal distribution.


*

*Which test shows the better type I error rate? 

*does  Levene's mean test perform best when the data follows a normal distribution? 

 A: NIST & Wikipedia both cite Brown & Forsythe's 1974 paper in saying that the version of Levene's test using the median performs better for skewed distributions.
You can't infer that the test performed well or badly from the p-value you get unless you know whether the samples did in fact come from populations with unequal variances, & then you'd have to repeat many times to find the distribution of the p-value.  Which is just what Brown & Forsythe did to justify their claim.
A: The Conover test, A.K.A., the squared ranks test is the only nonparametric equivalent that I know about of a test of difference of dispersion of data that works under non-normal conditions. That is, the Levene's test is somewhat sensitive to non-normal conditions.
The Brown-Forsythe test statistic is the F statistic resulting from an ordinary one-way analysis of variance on the absolute deviations from the median. This may reasonably be expected to be related to variance for symmetric distributions like the Cauchy density function (which statement concerns the pdf, not the random values, as the Cauchy moments do not exist). However, it is likely more powerful just to use the Conover test for non-normal conditions.
