My data analysis involves a comparison of baseline EEG power with immediately after the intervention and 30 min after the intervention EEG power. I did the data analysis using the Friedman test and then the pairwise comparison for the significant results using the Wilcoxon-signed rank test. I wonder whether I need to use the Bonferroni correction as I did multiple comparisons? My sample size is 15 and I found in the google that Bonferroni correction is not necessary for small sample size. How far is this valid and are there any reference to support this argument?
No-one seems to have noticed your question!
There is no reason why a correction for family-wise error rate is not necessary with small samples. Small samples is that they have low power, but that does not mean that we can cheerfully reject lots of null hypotheses as a result.
The important thing is to think of your hypothesis. First, your hypothesis says that your intervention changes the ECG power and second it says that this change endures for 30 minutes.
My first thought is to go with ordered logistic regression. Create a dataset with three observations for each of your sample : one for each condition. Create one dummy variable for immediately after the intervention (so it's 1 immediately afterwards and zero otherwise) and create another dummy for 30 minutes. The first dummy tests immediate treatment effect and the second tests the lasting effect.
You can use a post hoc test to see if the two intervention effects are significantly different.
Because you have three observations on each subject, you will need to use robust standard errors clustered by subject ID.
By now you've probably solved this. What did you decide??
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