Homogeneity of variance

Our third assumption is that the variance in the DV needs to be the same at each level of the IV. If we fail to meet the assumption, we say we have heterogeneity. It might help you to remember that the prefix homo means same and hetero means different.

We can test this assumption in two ways.

Visualize the distribution of data across groups

First, we can look at the data points across groups. This can be done by choosing a plot in the Descriptives analysis and adding your IV to the “Split By” box. Then select Box Plot, Violin, Data (Jittered) under Plots.

For example, here’s an example of data that violates the assumption of homogeneity of variance (gender by mile time) because the variance in scores for females (1) is a lot wider than the variance in scores for males (0):

Examine the variances across groups

Similarly, in the Exploration –> Descriptives under Statistics you can ask for Variance after splitting the DV by the IV. The variance for Gender == 0 (male) is 6796.20 whereas the variance for Gender == 1 (female) is 15401.55. Clearly, there is much greater variability for females than males for time it takes to run the mile.

Levene’s test

When we perform inferential statistics that have the assumption of homogeneity of variance, in jamovi there will be a check box to check the assumption. It will perform Levene’s test.

However, you may be testing the assumption prior to running your analysis (or learning about inferential statistics just yet). In that case, to perform Levene’s test, go to Analyses then ANOVA then One-way ANOVA. Move your continuous variable to the Dependent Variables box and move your nominal variable to the Grouping Variable box. Check the box “homogeneity test.” Only report the results of Levene’s test; ignore the one-way ANOVA results!

Here’s the result of Levene’s test for the effect of gender on mile duration:

Levene’s	F	df1	df2	p
MileMinDur	41.33	1	381	<.001

Like the other tests above, a non-significant Levene’s test means we meet the assumption of homogeneity of variance. However, if Levene’s test is statistically significant, then we fail to meet the assumption of homogeneity of variance and have heterogeneity of variance. In this case, our test is statistically significant so, in combination with our plot above, we say we violated this assumption.