I have a set of 9 different factor levels from my independent variable to be compared against each other. Here are the results of the different assumption tests in R. I'm just going through my methodology in the hope that someone can guide me to the right conclusion.
- The Shapiro-Wilk test is significant and shows that the my dependent variable is not normally distributed. I read somewhere that the assumption of normality doesn't always have to be met if the size of the dataset is substantial as it will almost always deviate from normality when it's the case.
- Mauchly's test for sphericity is significant, therefore the assumption of sphericity has been violated. My Greenhouse-Geiser correction confirmed it, but it's p-value is significant, which indicates that the levels of my independent variable significantly affects the dependent variable.
Where do I go from here?
The example I'm basing my methodology on in a textbook goes on to use these methods on the same dataset every time (though that dataset is different than mine)
- Repeated measures ANOVA
- A multilevel approach
- Robust test
Based on what I know, I think I have to go for a robust method given the assumptions above, but I have no idea if this is the right call.