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It is my understanding is that a Levene's test is simply looking at to see whether there are any differences between the differences of the mean. Here is some data:

participant group mean  group.mean  abs.mean.diff
1             a   200     300           100    
2             a   300     300             0
3             a   400     300           100
4             b   600     650            50
5             b   700     650            50
6             b   650     650             0

The Levene's test is taking the absolute mean difference (right most column) for each participant, then see whether there is a statistical difference (with an one-anova) between the absolute mean difference when treating group as a factor. My question is if the Levene's test is essentially a one-way anova on the absolute mean difference, can I run a Levene's test on a 2-by-2 anova where I treat group as a between subject variable and condition as a within subject variable?

participant group  condition mean  group.mean  abs.mean.diff
1             a        x      200     250           50    
2             a        x      300     250           50
3             a        y      400     500          100
4             a        y      600     500          100
5             b        x      700     675           25
6             b        x      650     675           25
7             b        y      200     150           50
8             b        y      100     150           50
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You can run Levene's test, but do not run Levene's test. See Zimmerman (2004) below. It is essentially a harmful waste of time. When you use an alternative test after Levene's test, the nominal error rate of that test is altered. Using a Welch-type adjustment has been shown to be close in power to its classic parametric equivalent under homogeneity of variance, and more powerful under heterogeneity of variance. So it might as well be used by default.

Here are a couple of things you can do. If you have a balanced design (equal sample sizes in your cells), then you should be fine, and can get away with running your two-way ANOVA. If you do not have a balanced design, what is the ratio of the smallest variance to your largest variance. This is cell-level variance. If it is high (above 10), then you have a problem.

You should just go ahead and apply the Welch-James procedure, especially if your data are normal. See the article below by Vallejo, Fernández and Livacic-Rojas (2010).


Zimmerman, D. W. (2004). A note on preliminary tests of equality of variances. British Journal of Mathematical and Statistical Psychology, 57(1), 173–181. https://doi.org/10.1348/000711004849222

Vallejo, G., Fernández, M. P., & Livacic-Rojas, P. E. (2010). Analysis of unbalanced factorial designs with heteroscedastic data. Journal of Statistical Computation and Simulation, 80(1), 75–88. https://doi.org/10.1080/00949650802482386

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