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I am investigating animal behavioural states using Markov Chains, and want to test differences in the transition probabilities between my control and impact groups. However, I’m worried about small sample sizes and choosing the correct test for comparing proportions.

I have five possible behavioural states for a ‘control’ and ‘impact’ context. So, say that I have a sample size of 230 for a particular preceding behaviour in a control context, which consists of 143, 3, 44, 22, and 18 transitions for each of the five succeeding behaviours (i.e. probabilities of 0.62, 0.01, 0.19, 0.10, 0.08 respectively). I wish to compare this with the corresponding impact context, which has a sample size of only 31 consisting of 25, 1, 4, 1 and 0 transitions (i.e. 0.81, 0.03, 0.13, 0.03 and 0 probabilities respectively).

So I will be comparing 0.62 (n = 230) with 0.81 (n = 31), then 0.01 (n = 230) with 0.03 (n = 31), etc.

In the literature, previous studies have used a Z-Test for proportions on the behaviour-transition probability matrix (each control transition was compared to its impact counterpart). But these studies give no mention of their sample sizes. I’ve read a real mixed-bunch of opinions regarding applying the Yates’ continuity correction for small sample sizes…

So my questions are:

  1. Can I apply a Z-Test to these data? Or are the sample sizes too small for any kind of proportion comparison at all?
  2. I generally use R for stats, but am also a bit confused about the prop.test() - is this a Z-Test? Some people seem to say 'yes, essentially', but then the output contains an X-squared value...
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