Sorry for the verbose background to this question:
Occasionally in investigations of animal behaviour, an experimenter is interested in the amount of time that a subject spends in different, pre-defined zones in a test apparatus. I've often seen this sort of data analyzed using ANOVA; however, I have never been entirely convinced of the validity of such analyses, given that ANOVA assumes the observations are independent, and they never actually are independent in these analyses (since more time spent in one zone means that less is spent in other zones!).
D. R. Smith, C. D. Striplin, A. M. Geller, R. B. Mailman, J. Drago, C. P. Lawler, M. Gallagher, Behavioural assessment of mice lacking D1A dopamine receptors, Neuroscience, Volume 86, Issue 1, 21 May 1998, Pages 135-146
In the above article, they reduce the degrees of freedom by 1 in order to compensate for the non-independence. However, I am not sure how such a manipulation can actually ameliorate this violation of ANOVA assumptions.
Perhaps a chi-squared procedure might be more appropriate? What would you do to analyze data like this (preference for zones, based on time spent in zones)?