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Say I have a large population of people who are randomly divided into a treatment group and a control group. Individuals from both groups regularly undergo event "x," which sometimes results in complication "y." For each individual one can calculate the fraction of "x" events that were complicated "y." What is the best way to determine whether the treatment has any effect on the frequency of y complicating x?

Related question: how would I calculate the minimum detectable difference with an alpha 0.05 and power 0.80? A bit more information: there are 75 people in the treatment group and 25 people in the control group. Each person has about 75 events. The rate of y complicating x is about 0.30 in the treatment group and 0.20 in the control group.

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Formula for power given here: Power for experimental design (this is like the third time I linked this answer in the past week!)

For estimation of the effect of a randomly allocated treatment on a proportion, perhaps use a beta regression?

Alternatively, proportion data can be modeled using binomial glm's, but logit, probit and cloglog are probably bad models for your data.

OR if there isn't much variability in the proportions (both proportions are far from zero and 1), you could get away with a standard gaussian regression.

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