Homogeneity of Variance

An Example

One study looked at the processes underlying obsessive-compulsive disorder by inducing a negative mood, a positive mood, or no mood in people and then asking them to imagine they were going on holiday and to generate as many things as they could that they should check before they went away. The data are in Table 1.

Three different groups participated in this experiment, each group representing a level of the independent variable, mood: negative mood, positive mood, and no mood induced. Homogeneity of variance would mean that the variances of scores on the dependent variable (in this case the number of items people generated that needed to be checked) would be approximately the same in the three different mood conditions. For participants in a negative induced mood, the variance of the number of items generated was 36.27 (see Table 1), but the variances for the positive-mood and no-mood-induced groups were 8.89 and 5.57, respectively.

Testing Homogeneity of Variance

To see whether variances are roughly equal across different levels of a variable, we compare the ratio of the largest and smallest variance. This variance ratio should be less than 2 if homogeneity is to be assumed. In this example, the largest variance is 36.27 and the smallest is 5.57; the variance ratio is 36.27/5.57 = 6.51, and because this value is greater than 2, homogeneity of variance cannot be assumed.

Homogeneity of variance can also be tested with Levene's test, which tests the null hypothesis that the difference between the variances is zero. If Levene's test is significant at p ≤ .05, then the variances are significantly different, and homogeneity of variances cannot be assumed. Figure 1 shows the SPSS output for Levene's test for the data in our example; because the significance of the test statistic is less than the conventional level of significance of .05, homogeneity of variance cannot be assumed.

It has been noted that the power of Levene's test to detect differences in variances across levels of a variable depends on the amount of data collected: With large samples, small differences in variances will give rise to a significant Levene's test; conversely, in small samples, relatively large differences between variances may remain undetected.

Figure 1 Test of Homogeneity of Variancea