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Tests for Equality of Variances

Tests for equality of variances have several uses.  One use is to check the assumption of constant variance of residuals when performing Regression, ANOVA, or using DOE methods.

These tests are used to test if k samples are from populations with equal variances. Equal variances across samples is called homoscedasticity or homogeneity of variances. (Wikipedia)  The condition of unequal variances is called heteroscedasticity.

These tests are a formal test of hypotheses:
  • H0:  σ12=σ22==σn2
  • H1: above is not true for at least one σi2

Two common methods are Bartlett's Test and Levene's Test. The Brown–Forsythe test may also be used.

Bartlett's Test

Very sensitive to the assumption of normality.  If the validity of this assumption is in doubt, Bartlett's test should not be used.  (Montgomery)

Levene's Test

The Levene test is less sensitive than the Bartlett test to departures from normality. If you have strong evidence that your data do in fact come from a normal, or nearly normal, distribution, then Bartlett's test has better performance. (NIST)

The modified Levene test uses the absolute deviation of the observations yij in each treatment from the treatment median.  (Montgomery)

Brown–Forsythe Test

Similar to Levene's test, but is based on the median instead of the mean.

The Brown and Forsyth test statistic is the F statistic resulting from an ordinary one-way analysis of variance on the absolute deviations from the median.  (Wikipedia)