Can I know how to perform comparison between 2 groups (intervention vs control) for a parameter which obtained at 0, 3 and 6 months (3 readings) and the data is abnormally distributed?
Hello Ehab,
The basic design is that of a one-between (group: 2 levels) and one-within (occasion: 3 levels: 0, 3, 6 mo.) subjects anova. Some would call it a mixed anova; others a split-plot anova; others a repeated measures anova (recognizing the occasions factor).
In this design, the issue of normality applies to within-group scores on a single occasion (e.g., Group 1 at 3 months). Why? Because the normality assumption applies to the errors/residuals from the overall model and the two specified IVs are group and occasion. So, if you're checking normality, be sure to evaluate it in this way.
That said, if you are convinced that non-normality is a legitimate issue for your data set, you could:
1. Try transforming the DV score so as to have the data conform better to the normality assumption;
2. Use an exact/resampling/bootstrap method to evaluate the relevant effects (main effect of group; main effect of occasion; and group x occasion interaction);
(though more statistics packages are offering this as an option, here's a link that will give you some ideas about how to execute this: https://rpubs.com/howelb/39050)
3. Pray for robustness and run the ordinary anova.
Good luck with your work!
David Morse Was joking with choice #3. There is a third choice, however. You could write your ANOVA model as a regression model and run a robust regression to get your parameter estimates. The pure regression approach is covered in Venables and Ripley, pp 271-282 with robust regression pp 158ff and in Wilcox, search for split plot. These links should be helpful: https://b-ok.cc/book/466042/d5d065 and https://b-ok.cc/book/2085546/2b5c75 and http://sgpwe.izt.uam.mx/files/users/uami/gma/R_for_dummies.pdf
I would suggest that the approaches given by Wilcox might be more straightforward. I have attached a brief paper on robust methods that I wrote some years ago as an intro to the topic. Best wishes, David Booth
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