I run an experiment where subject had to recognize an emotion from various musical stimuli (which were composed with a certain emotional intent). There were 4 levels of emotional_intent, subjects results of a forced choice task were either 1 for correct, and 0 for wrong. There were 2 groups of participants, musicians and non-musicians. So the dependent variable is binary, the within subject factor is emotional_intent with 4 levels, and the between subject factor is musical_expertise. My goal is to understand wether there are differences in the recognition 1) between groups overall, 2) between emotions, 3) between groups within each emotional_intent level.
What is the best way to analyze the data? I considered these options:
Chi square: I compare the number of correct and wrong answers for the groups, and for the emotions, and for the interaction of these two factors. That seems simple, but what are the disadvantages here?
Use a mixed effect model and use post hoc test on the factors and interaction term Here I got a problem because being the answers either 0 or 1, the data are clearly not normally distributed. So the use of the anova on the fitted model resulting from the mixed effect would break the normality assumption. Am I correct, or can I still use the mixed effect model?
This is what I would use in R:
fit <- lmer(correct ~ emotional_intent* musical_expertise + (1|subject), data=scrd) anova(fit) # Post hoc of the interaction term emmeans(fit, pairwise~emotional_intent*musical_expertise, adjust = "tukey")
- Use a binomial logistic regression followed by an ANOVA: Here I could do an ANOVA on a model fitted using a binomial logistic regression, and then I can compute the post hoc tests on that model:
model <- glm(correct ~emotional_intent * musical_expertise,family=binomial(link='logit'),data=scrd) anova(model, test="Chisq") # Post hoc of the interaction term emmeans(model, pairwise~emotional_intent*musical_expertise, adjust = "tukey")
- I calculate the percentage of correct answers for each subject, then I compute a two-way ANOVA with repeated measures and the usual post-hoc tests. Here data are normally distributed, and assumptions are not violated. However, using the method at step 2, I get that there is actually statistical significance in the interaction term and in the related pairwise comparisons of the posthoc test.
Which method is more correct to use and why? Are there other methods?