Table 2. - Sample sizes for all alternatives in scenarios with equal sensitivity and specificity
Although the most dramatic effects of misclassification were observed when p 0 was near 0 or 1 (more than fourfold increase in sample size for p 0=0.01 with left-sided alternative and Se Sp  = 99%), even in the best case, that is when p 0=0.5, the increase in necessary sample size was 22% with Se =Sp =95%, and 9% with Se =Sp =98%.
For the two-sided alternatives, results differ depending on whether the assumed true proportion pa is smaller or greater than p 0. Increase of necessary sample size is greater than that for the respective one-sided alternative illustrated by the extreme sample size increase of more than 6400 individuals (from an initial 433) in case of the two-sided alternative withp a<p0 whenp 0=0.01 with Se =Sp =95%.
Our results showed that ignoring even small misclassification probabilities may result in considerable power loss. Here we studied the exact binomial test in detail, but results are similar for other tests for the binomial proportion. Our R function enables sample size calculation for any test given an R function for the test is available. Presumably similar tendencies could be observed in the comparison of two or more binomial samples, which will be investigated later.
Although not presented in the article, we performed the same calculations for several asymptotic methods as well (Agresti-Coull, Wald and Wilson) resulting in similar amount of sample size increase.