
LEVENE TESTName:
The assumption of homogeneous variances arises in other contexts in addition to analysis of variance. Levene's test can be applied in these cases as well. The Levene test is an alternative to the Bartlett test. Although it is more commonly used, the Bartlett test is known to be sensitive to departures from normality. The Levene test is less sensitive to nonnormality than the Bartlett test. The Levene test is defined as:
where <y> is a response variable; <tag> is a factor identifier variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the median based Levene test.
where <y> is a response variable; <tag> is a factor identifier variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the median based Levene test.
where <y> is a response variable; <tag> is a factor identifier variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the mean based Levene test.
where <y> is a response variable; <tag> is a factor identifier variable; and where the <SUBSET/EXCEPT/FOR qualification> is optional. This syntax computes the trimmed mean based Levene test. It trims the lowest 10% and the highest 10% of the data.
LEVENE TEST Y1 GROUP SUBSET GROUP > 2 MEDIAN LEVENE TEST Y1 GROUP MEAN LEVENE TEST Y1 GROUP TRIMMED MEAN LEVENE TEST Y1 GROUP
READ VANGEL32.DAT Y X BATCH . LEVENE TEST Y X STATUS PARAMETERS Dataplot generated the following output: ************************** ** LEVENE TEST Y X ** ************************** LEVENE FTEST FOR SHIFT IN VARIATION (ASSUMPTION: NORMALITY) 1. STATISTICS NUMBER OF OBSERVATIONS = 45 NUMBER OF GROUPS = 3 LEVENE F TEST STATISTIC = 10.88619 FOR LEVENE TEST STATISTIC 0 % POINT = 0. 50 % POINT = 0.7047137 75 % POINT = 1.433075 90 % POINT = 2.433564 95 % POINT = 3.219942 99 % POINT = 5.149141 99.9 % POINT = 8.179383 99.98448 % Point: 10.88619 3. CONCLUSION (AT THE 5% LEVEL): THERE IS A SHIFT IN VARIATION. THUS: NOT HOMOGENOUS WITH RESPECT TO VARIATION. PARAMETER INFINITY HAS THE VALUE: 0.3402823E+39 PARAMETER PI HAS THE VALUE: 0.3141593E+01 PARAMETER STATVAL HAS THE VALUE: 0.1088619E+02 PARAMETER STATCDF HAS THE VALUE: 0.9998448E+00 PARAMETER CUTOFF0 HAS THE VALUE: 0.0000000E+00 PARAMETER CUTOFF50 HAS THE VALUE: 0.7047137E+00 PARAMETER CUTOFF75 HAS THE VALUE: 0.1433075E+01 PARAMETER CUTOFF90 HAS THE VALUE: 0.2433564E+01 PARAMETER CUTOFF95 HAS THE VALUE: 0.3219942E+01 PARAMETER CUTOFF99 HAS THE VALUE: 0.0000000E+00 PARAMETER CUTOF999 HAS THE VALUE: 0.0000000E+00
Date created: 6/5/2001 