I have a sample composed by 14 Patients and 13 Healthy control. In total, there are two independent (between) variables (named Sex and Diagnosis) and a dependent (within) variable (composed by 6 emotion).
A non-parametric ANOVA (Kruskal Wallis test) was performed to analyze the effect of the “emotion” variable when controlling for “sex” and “diagnosis” variables.
I think that it is not appropriate performing a Repeated measure anova due to the sample sizes (considering also the two variables between: diagnosis and sex).
Moreover data the data are not normally distributed.
Is it the correct way?
Moreover, Where interactions are significant, can I go into details with a post-hoc analysis (Bonferroni)?
It's not clear how the dependent variable is measured. Was each participant measured multiple times on a single emotion scale? Or was each participant measured multiple times on six different emotions? In other words, is there one dependent variable or six?
Hello Martina,
Some general observations to your query:
1. Sample size isn't the determining issue for whether or not to use parametric tests, nor is it the determining issue for whether repeated measures anova is justified.
2. Any concerns about normality need to be applied to model errors/residuals (for the observed data after fitting it to your chosen model), not the original scores treated as a single batch.
3. Even if normality is demonstrated to be a problem, you can always opt for bootstrap/resampling estimates of effects, which permit you to ignore distributional assumptions. This is available in many statistical software packages.
4. The key issue for class of test is the strength of scores on the DV(s). If ordinal, stay away from the parametric tests. The rank analog to repeated measures anova is the aligned ranks anova (https://rcompanion.org/handbook/F_16.html). If interval, stay with the parametric tests.
5. With a sample size as modest as yours, a multivariate test (two-between, zero within, 6 DVs) won't have much statistical power. The repeated measures approach would offer better power; additionally, it would allow a direct test of group by measure interaction.
Good luck with your work.
I think that, since the "emotions" are repeated measures, the correct non-parametric test would be the 'Friedman two-way analysis of varaince by ranks'. In attachment an R script for such a test (including the Friedman aligned ranks test). (It takes the example of Winer, 'Statistical Principles in Experimental Design', p. 626).
The 3-way non-parametric analyses I mentioned are for a Within X Within X Between design, and not for a Within X Between X Between design as yours. You have 2 Between factors: Sex and Diagnosis. You could run 6 non-parametric test, the ARTool (see: http://depts.washington.edu/acelab/proj/art/index.html) But, is this really necessary to use non-parametric tests. Check the histograms. Do they all look very much not normally distributed (for example right or left skewed)? In attachment an R script for your design including non-parametric and robust (Wicoxon) tests.
The dependent variables are sex and diagnosis. Both the variables are qualitative variables. I presume, you must have developed a composite emotions score. I think you can categorized the emotion score into 2 or 3 categories. Then tabulate score vs sex (patient and Normal) on one hand and score vs diagnosis (Patient and Normal) on the other hand. Now, calculate either Chi-square and Odds ratio. If OR comes Out to be significant then conclude that emotion and sex are related. Similarly, conclude that emotion and diagnosis are significantly related on the other hand. Non- significant result will rules out any association between emotional score and sex or emotional score and diagnosis. Since, Chi-square is a non-parametric test, you are not violating any assumptions In carrying out the test. However, small sample size may become a problem in analysis of the data.
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