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#' Power simulations for cluster-randomized trials: proportion of F-test rejections
#'
#' This function can be called by some of the clusterPower functions to
#' calculate the proportion of F-test rejections and produce exact confidence intervals.
#'
#' @author Alexandria C. Sakrejda (\email{acbro0@@umass.edu} and Ken Kleinman (\email{ken.kleinman@@gmail.com})
#'
#' @param nsim A scalar; the number of simulations chosen by the user.
#' @param alpha A numeric; the user-selected alpha cutoff.
#' @param sig.LRT A logical vector indicating whether or not the model was significant.
#'
#' @return A dataframe
#' \describe{
#' \item{Ftest}{Exact confidence intervals produced using \code{binom.test()}}
#' }
#'
#' @noRd
prop_H0_rejection <- function(alpha = alpha,
nsim = nsim,
sig.LRT = sig.LRT) {
# Proportion of times P(>F)
LRT.holder.abbrev <- sum(sig.LRT)
f.test <- binom.test(p = 0.05, n = length(sig.LRT), x = LRT.holder.abbrev)
Power = f.test$estimate
Lower.95.CI = f.test$conf.int[1]
Upper.95.CI = f.test$conf.int[2]
Beta <- 1 - Power
Alpha <- alpha
Ftest <- data.frame(Power, Lower.95.CI, Upper.95.CI, Alpha, Beta)
num.returned <- data.frame("Converged" = length(sig.LRT),
"Requested" = nsim)
Ftest <- cbind(Ftest, num.returned)
return(Ftest)
}
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