Suppose I have performed a study wherein I compare a novel intervention (N) against the standard intervention (S). Participants are assigned to N or S randomly, and the study is performed. There are two outcome variables, A and B.
With only two outcome variables, is it appropriate and/or necessary to apply a Bonferroni correction to my analysis? If N shows statistically significant improvement in both outcomes, but S does not, can I reject the null hypothesis that N has a more significant effect than S?
In other words, could the Bonferroni correction possibly lead to a false-negative when the number of comparisons is only 2? And is there a way to detect whether Bonferroni correction is leading to a false negative?