Standard errors for proportions

So far we have considered standard errors associated with means and differences between means. When dealing with binary data and proportions different formulas apply. 

In Section 2.2.4 we let r denote a proportion in the sample, and 0 the corresponding proportion in the population. For a single proportion r the standard error formula is (1 — r)/n where n is the number of subjects in the sample. 

For the difference between two proportions, for example if we are looking at the difference — t2 between the cure rate in the active group (group 1) and the cure rate in the placebo group (group 2), the standard error formula is /rl (1 — r jn - - r2 (1 — rj)ln2 where i and are the numbers of subjects in groups 1 and 2 respectively. 

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