How to test mean differences in proportions that are dependent

Question

I have an experimental setup where I have allowed groups consisting of about 50 animals to select between two environmental conditions. I.e. animals had the possibility to move between the two environmental conditions, and the number of animals found in each environmental condition counted after a given time. The results from the experiments is as follows:

|-----------|----------|----------|
|  Envir 1  |  Envir 2 |   Total  |
|-----------|----------|----------|
|    36     |    18    |     54   |
|    33     |    16    |     49   |
|    30     |    22    |     52   |
|    34     |    16    |     50   |
|    30     |    17    |     47   |
|    31     |    17    |     48   |
|-----------|----------|----------|

I want to test whether there is a higher proportion of animals in one environment compared to the other. I thought this would be strait forward through some two-sample test, however here are some problems in that my data is slightly unbalanced (not exactly 50 animals in each experiment), my data is likely non-normally distributed (meaning a need for non-parametric test) and also that the results are dependent (number of animals in one environment also determines the number of animals in the other). I see that binomial tests are useful to determine if proportions differ, but have only seen examples on this when you have one observation. I have six repetitions of the experiment (not the same animals). If anyone have a suggestion for an appropriate statistical test for this data I would really appreciate it.

KenT

Answer 1

I can think of a number of reasonable seeming analyses:

1. Exact stratified logistic regression with environment as a factor and repeated experiment as a stratum.
   2. Generalized linear mixed effects model (random effects logistic regression) with environment as a factor and a random effect for the repeated experiment.

Either should give you an odds ratio.