My team made some experiments how animals choose their location in different environmental conditions (to check the hypothesis of ideal free distribution). The animals were placed in the experimental settings, which was composed of linearly connected chambers (1st was connected with 2nd, 2nd with 3rd, 3rd with 4th etc). The output of each experiment was the distribution of animals in the chambers, which can be seen as a vector. For example, if there were 20 animals in the settings of 5 chambers, the distributions in 3 repetitions of the experiment may look like:
$[14, 6, 0, 0, 0], [10, 2, 5, 2, 1], [7, 7, 4, 2, 0]$
There is also theoretical prediction how those animals should distribute themselves. Let's say that for the above example of 20 animals it looks like this:
$[10, 5, 3, 2, 0]$
The question is: how to compare those experimental and theoretical distributions, most preferably using some statistical test? The additional problem is that those 20 animals were put together, so flocking or aversion behaviour almost for sure took place (actually, this is one of the things we want to test and what the theoretical distribution takes into account). Hence, the distribution of 20 animals in each single experiment is not independent. In one of the similar studies authors use G-test, but I doubt if it is appropriate, because of the mentioned violation of independence assumption.