Statistical tests when each variable in a sample is a percentage I am performing a temperature preference test in mice. Mice are placed into a chamber with one half of a chamber having a cold floor and the other half having a warm floor. Mice spend a specific total time in the chamber (3 min) and can select the cold or warm part of the chamber. I calculate the time (in percent of the total time) spent on each side for each subject (each mouse). The results look like this:
Mouse   Warm%   Cold%
    1     85%     15%
    2     80%     20%
    3     87%     13%
    4     84%     16%



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*How do I calculate the confidence interval for the mean cold time percentage of the population from which this group of mice was selected?

*If I perform the same test with a second group of mice which received some experimental treatment, which statistical test to use to check for a difference between two groups of mice?
 A: It depends a bit on how you calculated those percentages, but I will guess at some simple method. If your 85%, for example, means "looked at the mouse 20 times; 17 times it was in the warm" then it's the mean of a binomial (Bernoulli) variable with possible values 0 and 1. Score 0 = cold, 1 = warm, mean 0.85 or 85%. 
Note that there is really one percentage being estimated here, as the two sum to 100 by definition. 
However, there is a big reservation. Those so-many observations may not be independent. Suppose a mouse prefers warm, so it chooses warm, but then it gets too hot and moves to the cooler bit; or vice versa. You can only treat them as independent if you are confident that your set-up is equivalent to the same number of experiments in which each mouse was observed once and heating and cooling effects don't operate. 
For more complicated set-ups, you would probably be best off recasting this as a logit model. That wouldn't solve any dependence problems unless you build those into the model. 
