## Technote (troubleshooting)

## Problem(Abstract)

What is the nature of the Levene test for homogeneity of variance, which appears in output for the EXAMINE, ONEWAY, and T-TEST

procedures? Why has this test replaced the traditional tests for variance homogeneity, such as S^2max/S^2min?

## Resolving the problem

The version of the Levene test implemented in ONEWAY and T-TEST, and in EXAMINE prior to Release 8.0 calculates the absolute value of each observation's difference from its group mean and then performs an analysis of variance on these absolute deviations. The Levene test is less sensitive than more traditional tests to nonnormality in the data. See:

Levene, H. (1960). Robust tests for equality of variances. In I. Olkin (Ed.). Contributions to Probability and Statistics. 278–292. Palo Alto: Stanford University. Press..

A worked example of the test is available in

Snedecor, G.W., & Cochran, W.G. (1980). Statistical Methods (7th Ed.) Ames IA: Iowa State University Press.

A history of the test and its variants is available in Volume 4 of the "Encyclopedia of Statistical Sciences".

The Levene test is available in EXAMINE by requesting "Spread vs level" in the Plots dialog of Explore or by adding the keyword SPREADLEVEL to the /PLOT subcommand of EXAMINE. In ONEWAY, request Levene plots by choosing "Homogeneity of variance test" from the Options dialog or adding the keyword HOMOGENEITY to the /STATISTICS subcommand. For the T-TEST for independent samples, the Levene test is printed as standard output.

Beginning with SPSS version 8.0, EXAMINE offers four different versions of the Levene test. In addition to the version in ONEWAY and T-TEST that uses absolute values of deviations from group means, versions using absolute values of deviations from group medians and from trimmed means are offered, and for the median, two different options for degrees of freedom are displayed.

## Historical Number

12715