# Do I need a Bonferroni correction on a 2x2 chi-squared analysis?

I'm really hoping someone here can help.

I have performed a chi-square test of independence, looking at men/women and early/late drop out from therapy. I have a p-value of 0.047. Do I need to do any post hoc testing on this? Men drop out almost 50:50 early:late whereas women drop out almost 25:75 early:late. Do I need post hoc testing for this and a Bonferroni correction, or is the answer simply:

The frequency of retention rates was compared across gender, finding a significant interaction (X2 (1) = 3.94, p = 0.047), indicating that females were more likely to be retained past the third CBT session than men.

Any help would be greatly appreciated.

You are answering the research question by one single hypothesis test, so no need to think about multiple testing.

Your statement is okay. Maybe you could say something like:

x of xy (50%) men had an early drop out, while for female patients, the drop-out rate was y out of yz (25%). This difference is statistically significant at the 5% level (Chi-squared test-statistic ....., p value 0.047).

If the sample size is not too large, I actually would go for Fisher's exact test, especially since the result is close to non-significance.

• Hi Michael, Thank you for the quick response. That's really helpful! I hadn't considered Fisher's exact test could be used for this purpose! I will go and check this out now! Thanks again, it's really confusing because some texts on-line say things like for chi-square of more than 2 x 2 and sometimes even for 2 x 2 you might want to do post hoc testing. When would you need to do post hoc testing on a 2x2 - is that a thing? Oct 6, 2019 at 18:27
• Hi Michael, sorry, one more question, would I look at the fishers exact score for 2 sided or 1 sided? Thank you. Oct 6, 2019 at 18:35
• Just to be sure: You are in a 2x2 scenario, right? The Fisher's exact test would be two-sided (there, "sided" is meant regarding the odds ratio, which is 1 without association). Oct 6, 2019 at 19:02
• Yeah, I think so! I have Gender = male/female and Dropout = early/late? Oct 6, 2019 at 19:10
• Sounds like 2x2! Oct 6, 2019 at 19:17