I have ran multiple mixed ANOVA's on results I obtained during a recent study. I understand how to conduct a mixed ANOVA but I'm having trouble with satisfying certain assumptions of this test.
Two of the assumptions of Mixed ANOVAs are:
1) No significant outliers - outliers are more than 2/3 SD from the mean.
2) Equality of Covariance Matrices - p value should be non significant to accept the null hypothesis that the observed covariance matrices of the dependent variable are equal across groups.
1) When I check for normality using the Shapiro-Wilk test, I have some data that isnt normally disributed due to outliers than I dont want to remove. All the outliers are values well above or below the mean but only some our classed as extreme in SPSS (*). What should I do with this data for the mixed ANOVA? Should the data all be transformed? I have read that the data only has to be approximately normal!? Is the ANOVA I have already ran therefore incorrect?
2) With the equality of covariance matrices, some of my Levene's test values are significant (p < 0.05). However to accept the null hypothesis stated above we would like p > 0.05. What do I do in this instance?
Thank you in advance for your kind help. Statistics is far from my area of expertise unfortunately!!
1) For non-normal distributed data you can try to use log transformation first before you throw it into model
2) The assumption of equal covariance is the limitation of repeated ANOVA. Another disadvantage is the way to handle missing data. If you miss one repeated measure for one subject, that subject will be excluded from analysis. You can try to use mixed model analysis in SPSS. Repeated ANOVA can be viewed as special case of mixed model. In mixed model analysis you can choose different covariance structure that fits your data, such as unstructured structure or auto-regressive. And it uses all available data to run the analysis.
1) the normality assumptions are about the residuals of your model. In a repeated measures model these don't have the same distribution as the raw scores - so I'd always look at the residual plots. Also what matters more than anything is influence of extreme values rather than whether there are extreme values - so I'd save Cook distance from the output and look out for very large values of this statistic. These points are the ones that are influencing your parameter estimates.
2) transformations can be helpful but I'd need to know what the data are before suggesting how to handle this. The log transformation is sometimes appropriate for positively scored data with no upper bound (e.g., waiting times).
3) Mixed ANOVA assumes multisample sphericity. This doesn't require equality of covariance matrices between groups (though multisample sphericity is always true if there is equality of covariance matrices). Using a multilevel/linear mixed model is one option - but it requires that you model the covariance matrices correctly (but an unconstrained model would often be sensible). However, you don't mention the number of levels on each factor. If this is 2 on each repeated factor sphericity is not an issue.
My sincere apologies for the delayed response Thom! Thank you so much for your help. I will follow your advice for the normality assumptions, that's great and I only have 2 levels, so sphericity isn't actually an issue. Thank you!
Is there an alternative option if the data is not normally distributed, if normal distrubution assumption is voilated?
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