What type of data analysis should I carry out?

Question

In my experiment I have two groups each with 30 participants (experimental group and a control group) The experimental group consists of autistic individuals and the control consists of neurotypical controls. There will be two sessions one week apart where they will complete an emotion recognition task (with six different emotions). In one of the sessions they will receive actual transcranial direct current stimulation and in the other session they will receive sham stimulation. It will be counterbalanced which of these sessions they will do first.

I need to write a planned data analysis section for a report I am doing. The planned data analysis needs to answer my two research questions:

• Whether the stimulation effects the experimental group more than the control group.
• If there is a difference between each emotion on the emotion recognition task.

I was thinking of doing a 6x2x2 (emotion type, group, stimulation type) ANOVA but am struggling on how I would interpret this. I need help on what interactions to look for and what post-hoc tests to run

Answer 1

A critical statistical issue here is thow to handle your outcome measure. Unless it's a continuous measure, ANOVA would not be a good choice. For example, if you are marking recognitions as either "right" or "wrong," then you would want to use a generalized linear multiple regression model, e.g. logistic regression, to evaluate your results. If you are interested in which incorrect choices tend to be made, you could consider a multinomial output model with the "correct" emotion for each case as a predictor; that might require a lot of data, however.

As an ANOVA model can be represented as a multiple regression model with continuous outcomes, the logic with a generalized model like logistic regression can be similar to ANOVA. There are similar tests for things like significance of interactions, based on model log-likelihood comparisons rather than variance-based ANOVA F-tests, often called "anova" tests even if they might not technically be considered such.

The "interactions to look for" are more a matter of what questions you are trying to answer than of statistics per se. For example, when you ask:

If there is a difference between each emotion on the emotion recognition task.

do you care about potential differences between neurotypical and autistic Groups in terms of the between-emotions comparisons? If so, there needs to be an Emotion:Group interaction term.

Do you care about differences of the between-emotions comparisons with respect to stimulation versus not? Then there needs to be an Emotion:Stimulation interaction. Do you care about whether the Emotion:Stimulation interaction depends on the neurotypical/autistic Group? Then you need the 3-way Emotion:Stimulation:Group interaction.

Do you suspect that there might be a learning component, such that results of the second session would differ for an individual even if the Stimulation were the same? Then your model would have to include a marker for the actual session, too.

Finally, I caution against your using the term "post-hoc tests" in this context. That term is generally used for tests specified after you see the initial results. What you are doing now is to pre-specify critical hypotheses of interest without seeing the data, the best practice and a very wise choice.