I'm attempting an analysis on sampling rates and window sizes of accelerometer for human activity recognition (HAR). I'm looking for a good test for statistical significance. My data can't fulfill the sphericity assumption for the repeated measures two way ANOVA. As for the Friedman test, I have replicated 10-fold data which means it's not "unreplicated block data". Are there any alternatives I should look at? Or perhaps some way to adjust the dataset to fulfill the requirements of either test?
Thanks.
I don't think you are going to find a non-parametric test that can do what you need to do.
1: I don't entirely understand the sphericity assumption for repeated measures, but does it help to add an autocorrelation structure to the model? Both SAS PROC MIXED and nlme package in R allow for adding autocorrelation structures.
2: Have you tried transforming the dependent variable?
3: Are there any other effects you can add to the model?
The Greenhouse Geisser correction proposed by Sofia is a widely used method to correct the df for violation of sphericity. On the other hand, you could use a MANOVA approach to analyse repeated measurements, since MANOVA does not have sphericity assumptions. You could check Tabachnick & Fidell - Using Multivariate Statistics.
These methods are somehow old. Now linear mixed effects models offer a wider range of error/random effect correlation patterns and fits data very well. I suggest it.
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