I have been using the mann whitney and kruskal wallis test as the scores are not normally distributed. I have compared two different groups in the study. This serves as non-parametric research. However, I have also conducted ANOVA repeated measures and ANCOVA repeated measures in order to identify the effect in within the sessions. Can I refer to parametric test basd on the absolute scores values although the scores are not normally distributed?
Dear Nan,
It is possible to use parametric tests even when their normality assumption is not met. This is sometimes called robust use. The particular conditions under which they can still be used depend upon the individual test and have been established by running simulations.
For example, I believe the robust use of ANOVA requires equal group sizes and at least 40 degrees of freedom and a non-significant kurtosis (i.e. its absolute value should be less than twice its standard error).
If the robust exceptions or the parametric assumptions are borderline, there is no reason why you should not run both the parametric and the nonparametric tests.
For your anova and ancova, you don't need the data to be normally distributed. You need the residuals to be normally distributed, along with the other model assumptions. If these assumptions aren't reasonably met, I wouldn't keep the model.
Sometimes building a better model will improve the behavior of the residuals (for example, adding the repeated measure and co-variate effects,as you have done).
Thank you respected researchers who hv helped me with constructive feedbacks, I really appreciate this.
Dear Nan,
I would ensure I had no outliers (outliers can negatively affect normality of distribution), and would also try normalization procedures before residing to non-parametric tests.
Happy researching
Respected researchers,
How if my degree of freedom is lower then 40? Can I still stick to the ANOVA and ANCOVA?
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