Lack of homogeneity of Variance in two-way ANOVA


I am currently analyzing my data in SPSS. Since I am testing the effect of two independent variables on a dependent one, I was planning on using a two-way independent ANOVA. (I have a between subjects design).

1. Experimental condition (2 levels)
2. Personality grouping (3 levels)

Score on a test (continuous variable)

Levene's test for homogeneity of variance came out significant and I am not quite sure what to do. I know that Welch's test and Brown-Forsythe test can be used, however I only know how to use them in SPSS for a one-way ANOVA. Can I use them for a two-way ANOVA? If yes, where do I find them? If no, is there any other solution to this issue?


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You are correct, the p-values from the regular ANOVA F-test are not accurate if variances are different between the groups.


A typical approach taken by practitioners in social sciences (if the programming skills are limited) is to use the ANOVA p-values conservatively. We say that something is statistically significant only if the p-value is of the order 0.001, not 0.01. Of course, this is quite wasteful and approximate but may be sufficient for some people if the data set is large.


Use R, Matlab or any other programming language to program the ANOVA F-test yourself and get the relevant standard errors and p-values using bootstrap. Bootstrap always works... Sadly, SPSS is not good for any customized programming but there is a bootstrapping feature there. To the best of my knowledge, you can use that feature if you rewrite your ANOVA model as a linear regression model (always possible).
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An Anova is perfectly acceptable methodological approach in controlled psychology style experiments or quasi experiments.

That being said, if you are analyzing observational data or something where you do not have strong control over potential nuisance then an ANOVA is probably inappropriate and would not get past a reviewer.

A few comments on boot strapping. Depending on sample size, it might not be needed, further, depending on where you are submitting, it can lower the "readability" of your manuscript without gaining a whole lot in terms of precision of your estimates.

Finally, there is no need to rewrite anova as a linear regression because an anova is a linear regression.
I also want to comment that depending on the issues with homogeneity, you might not even worry about it. ANOVA is usually pretty robust towards a bit of homogeneity. Further, levene's test is a glorified "spitballing" test. If you are looking at your residuals and see that condition 1 all has their responses clustered together while condition two has them all over the place, then yes, then there is something going on that is probably not related to your treatment. Honestly, if levene's is not that off, then your estimates are likely to be unbiased.

Remember when you are looking at these things. It is a diagnostic. It can tell you if there is a nuisance variable, data not keyed in correctly, or any number of problems.