
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 (Case: Test Based on Medians) Response Variable: Y GroupID Variable: X H0: Homogeneous Variances Ha: Variances Are Not Homogeneous Summary Statistics: Total Number of Observations: 45 Number of Groups: 3 Levene Test Statistic Value: 10.88618 CDF of Test Statistic: 0.99984 PValue: 0.00016 Percent Points of the Reference Distribution  Percent Point Value  0.0 = 0.000 50.0 = 0.705 75.0 = 1.433 90.0 = 2.434 95.0 = 3.220 97.5 = 5.149 99.0 = 5.149 99.9 = 8.179 Conclusions (Upper 1Tailed Test)  Alpha CDF Critical Value Conclusion  10% 90% 2.434 Reject H0 5% 95% 3.220 Reject H0 2.5% 97.5% 5.149 Reject H0 1% 99% 5.149 Reject H0  
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Date created: 06/05/2001 