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I am looking at a $\chi^2$ (crosstabs) test looking at interactions between types of dyads in an animal group. My categories are Male-Male, Male-Female, and Female-Female dyads in the rows and "Were Seen to Interact" and "Were Never Seen to Interact".
The matrix looks something like:

21   7  
85   19  
77   1

There is a very significant p value. My question is, when running the post hoc tests, is it appropriate to compare each category to the sum of the other two (i.e. Male-Male, vs Male-Female+Female-Female) when looking for which category is driving the difference, or should I compare the categories to each other (Male-Male vs Male-Female, then Male-Male vs Female-Female)?

I'm looking for an answer to the question of whether one of the types of dyads are more likely to fail to interact. I think the statement "There are more Males-Female dyads that were never seen to interact than would be expected by chance" would be easier to comprehend than if I had to write out the comparisons of the three pairs. I just don't know if it's allowable.

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Your chi-square test tells you that you have an interaction in your effects so the probability of subject interactions is dependent upon your dyad. Therefore, you're just checking to see which of those it's dependent upon and you can test. But you don't really need a test here... it's kinda obvious with the last row showing a 77:1 effect while the others are about or 3 or 4:1. If you want to do binomial test comparisons among the 3 perhaps just lower your alpha a little and don't try to conclude that the first two dyads are the same. You might also want to report a confidence interval for each individual dyad.

Another issue you have here is not one of post-hoc testing but one of the chi-square statistic being believed unreliable when the expected in a cell is less than 5 (for the male-male). However, this is probably not a problem.

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  • $\begingroup$ Is there another way you would suggest arranging the data? One that would suit another test that wouldn't have a problem with there being only 1 F-F dyad that was never seen to interact? I have data on individual dyads not just for whether or not they interact, but also who 'won' the interaction and how many times. $\endgroup$ – Rafe Sep 5 '11 at 19:02
  • $\begingroup$ the 1 FF isn't the problem... it's that there's an expected value too low. Always calculate your expected values or get your stats software to give them to you. I edited the answer and added that I don't think it's really much of an issue. $\endgroup$ – John Sep 5 '11 at 20:26
  • $\begingroup$ Not everyone agrees about the expected value > 5 criterion, see Frank Harrell's post and the cited paper. $\endgroup$ – caracal Sep 5 '11 at 21:21

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