I am working on a research study to complete my BSc in Psychology. I conducted an positive psychology intervention study but uptake was poor, only 3 participants. The intervention is the IV and I have 4 DVs. The data does not meet all the assumptions of normality to conduct a MANOVA which was what I had in mind if I had more participants. How do I analyze this data?
You can't. Not really, except as an exercise demonstrating that you know how. If you really want to run significance tests, just do As Stephen Edwards suggests, a series of Wilcoxon signed-rank tests could be used. These are equivalent to one-sample t-tests, but for rank-ordered data (which is how to get around the issue of violating assumptions of normality). But with N = 3 it is virtually impossible to obtain significant results. Only do it if that's a requirement of the assignment.
If you want to develop any kind of principled argument about your intervention's effectiveness, calculate the effect size - how big a difference there was, in standard deviation units. But be very, very cautious in discussing any inferences, because you cannot be confident that the results will generalize.
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