Nothing
# target calculates the T1E rate for a certain alternative, level and
# variance ratio and substracts the target T1E rate.
# Used in levelSceptical to calculate the controlled level for
# replication success
target <- function(alphalevel, alternative = alternative, c = c, targetT1E){
myT1E <- T1EpSceptical(alternative = alternative, level = alphalevel, c = c,
type = "nominal")
myT1E - targetT1E
}
.levelSceptical_ <- function(level,
c = NA,
alternative = c("one.sided", "two.sided"),
type = c("golden", "nominal", "controlled")){
stopifnot(is.numeric(level),
length(level) >= 1,
is.finite(level),
0 < level, level < 1,
!is.null(alternative))
targetT1E <- level^2 # because we only consider one and two sided
alternative <- match.arg(alternative)
stopifnot(!is.null(type))
type <- match.arg(type)
if (type == "nominal") {
res <- level
# } else if (type == "liberal") {
# res <- pIntrinsic(p = level, alternative = alternative, type = "Held")
} else if (type == "controlled") {
mylower <- sqrt(targetT1E)
if (alternative=="one.sided") {
myupper <- 0.5
} else if (alternative=="two.sided") {
myupper <- 1-.Machine$double.eps^0.25
}
result <- stats::uniroot(target, lower = mylower, upper = myupper,
alternative = alternative, c = c,
targetT1E = targetT1E)
res <- result$root
} else if (type == "golden") {
res <- pIntrinsic(p = level, alternative = alternative, type = "Matthews")
}
return(res)
}
#' Computes the replication success level
#'
#' The replication success level is computed based on the specified
#' alternative and recalibration type.
#' @param level Threshold for the calibrated sceptical p-value.
#' Default is 0.025.
#' @param c The variance ratio. Only required when \code{type = } "controlled".
#' @param alternative Specifies if \code{level} is "one.sided" (default) or
#' "two.sided". If "one-sided",
#' then a one-sided replication success level is computed.
#' @param type Type of recalibration. Can be either "golden" (default), "nominal" (no recalibration),
#' or "controlled". "golden" ensures that for an original study just significant at
#' the specified \code{level}, replication success is only possible for
#' replication effect estimates larger than the original one.
#' "controlled" ensures exact overall Type-I error control at level \code{level}^2.
#' @return Replication success levels
#' @details \code{levelSceptical} is the vectorized version of
#' the internal function \code{.levelSceptical_}.
#' \code{\link[base]{Vectorize}} is used to vectorize the function.
#' @references
#' Held, L. (2020). A new standard for the analysis and design of
#' replication studies (with discussion). \emph{Journal of the Royal
#' Statistical Society: Series A (Statistics in Society)}, \bold{183},
#' 431-448. \doi{10.1111/rssa.12493}
#'
#' Held, L. (2020). The harmonic mean chi-squared test to substantiate
#' scientific findings. \emph{Journal of the Royal Statistical
#' Society: Series C (Applied Statistics)}, \bold{69}, 697-708.
#' \doi{10.1111/rssc.12410}
#'
#' Held, L., Micheloud, C., Pawel, S. (2022). The assessment of replication
#' success based on relative effect size.
#' \emph{The Annals of Applied Statistics}, \bold{16}, 706-720.
#' \doi{10.1214/21-AOAS1502}
#'
#' Micheloud, C., Balabdaoui, F., Held, L. (2023). Assessing replicability
#' with the sceptical p-value: Type-I error control and
#' sample size planning. \emph{Statistica Neerlandica}. \doi{10.1111/stan.12312}
#'
#' @author Leonhard Held
#' @examples
#' levelSceptical(level = 0.025, alternative = "one.sided", type = "nominal")
#' levelSceptical(
#' level = 0.025,
#' alternative = "one.sided",
#' type = "controlled",
#' c = 1
#' )
#' levelSceptical(level = 0.025, alternative = "one.sided", type = "golden")
#' @export
levelSceptical <- Vectorize(.levelSceptical_)
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