Why Most Published Research Findings Are False for a demonstration of how the probability of a significant result reflecting a true relationship can in fact be very low when the prior probability of the relationship being true is small. I.e. if the number of true relationships vs non-relationships in some study area is very low, a significant finding is most likely false. Using a more permissive approach to p value interpretation with exploratory research compounds this problem; if anything I think one should do the opposite (lower alpha values for exploratory research).
I don't really know what the best analysis method would be for your study. What is the actual purpose of the study? What are you trying to achieve by looking at these group differences?