Hello everyone,
we conducted a 3-way mixed ANOVA and got significant results for the main factors and the two-way interactions. However, the box test of equality of covariance matrices is significant as well. In his book "Discovering statistics using IBM SPSS statistics : and sex and drugs and rock 'n' roll", Andy Fields proposes to employ "robust methods" in that case, which is only possible using R packages (however, he doesn't precise what one would need to do exactly). Others say that often, mixed ANOVAs are done anyway and the violation of assumptions is reported in the discussion part (https://statistikguru.de/spss/mixed-anova/varianzgleichheit-ueberpruefen.html).
I am not sure how to interpret my results. Do you have any suggestions what to do?
Thank you in advance!
Hannah Bauer
Hannah Bauer What is your total sample size? Do you have (roughly) an equal number of participants in each cell?
ANOVA is fairly robust to violation of equality of variance assumption with a sufficient sample size and comparable group sizes
@Blaine Tomkins if I understand your robustness comment it's not.really true. It can be handled by robust regression. For an example see the attached teaching unit main. example. Best wishes David Booth
David Eugene Booth While I agree the simplest solution is just not use ANOVA, I also think the equality of variance assumption is bogus given that it's almost certain to be false in practice
Are any of these differences in covariance of substantive interest. Also, and Blaine Tomkins asks, what is your sample size as "statistical significance" is a function of the sample size and how discrepant the covariance matrices are is more important that a p-value. That said, robust methods exist so using them might be easier than justifying not using them.
Hello Hannah Bauer. Given that your discipline appears to be psychology, and given that you are reading Andy Field's book and looking at a website with spss in the address, I'll guess that you might be using SPSS as your primary stats package. If so, have you considered using the MIXED command rather than GLM? MIXED has options for allowing/modeling heterogeneity of variance. Take a look at the examples on these two UCLA pages.
- https://stats.oarc.ucla.edu/spss/seminars/repeated-measures/
- https://stats.oarc.ucla.edu/spss/library/comp_repeat_spss/
HTH.
Dear Bruce, GLM allows you to model everything directly in most modern stat packages. I would suggest R, SAS or something similar. I did mine in VAX BASIC all those years ago. Best wishes, David see attached
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