In human research, we define our universe and estimate the effect size we expect to observe, then we can draw the a sample of a given size.
How is sample size determined for experiments in the animal research field?
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Determining sample size for an animal experiment is no different than in research with human subjects. What you need to know is the effect size, the significance level and the power (which is the probability that the test detects a significant effect assuming that there is one). The tricky part is getting the effect size (for an interesting discussion have a look at this thread). The other two things are chosen by you as the experimenter. An overview paper on power analysis was written by Cohen (1992).
Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155. PDF