#' @title Compute effect size from Standardized Regression Coefficient
#' @name esc_beta
#'
#' @description Compute effect size from Standardized Regression Coefficient.
#'
#' @param beta The standardized beta coefficient.
#' @param sdy The standard deviation of the dependent variable.
#' @param grp1n Treatment group sample size.
#' @param grp2n Control group sample size.
#' @param es.type Type of effect size that should be returned.
#' \describe{
#' \item{\code{"d"}}{returns standardized mean difference effect size \code{d}}
#' \item{\code{"f"}}{returns effect size Cohen's \code{f}}
#' \item{\code{"g"}}{returns adjusted standardized mean difference effect size Hedges' \code{g}}
#' \item{\code{"or"}}{returns effect size as odds ratio}
#' \item{\code{"cox.or"}}{returns effect size as Cox-odds ratio (see \code{\link{convert_d2or}} for details)}
#' \item{\code{"logit"}}{returns effect size as log odds}
#' \item{\code{"cox.log"}}{returns effect size as Cox-log odds (see \code{\link{convert_d2logit}} for details)}
#' \item{\code{"r"}}{returns correlation effect size \code{r}}
#' \item{\code{"eta"}}{returns effect size eta squared}
#' }
#' @param study Optional string with the study name. Using \code{\link{combine_esc}} or
#' \code{as.data.frame} on \code{esc}-objects will add this as column
#' in the returned data frame.
#'
#' @return The effect size \code{es}, the standard error \code{se}, the variance
#' of the effect size \code{var}, the lower and upper confidence limits
#' \code{ci.lo} and \code{ci.hi}, the weight factor \code{w} and the
#' total sample size \code{totaln}.
#'
#' @note If \code{es.type = "r"}, Fisher's transformation for the effect size
#' \code{r} and their confidence intervals are also returned.
#'
#' @references Lipsey MW, Wilson DB. 2001. Practical meta-analysis. Thousand Oaks, Calif: Sage Publications
#' \cr \cr
#' Wilson DB. 2016. Formulas Used by the "Practical Meta-Analysis Effect Size Calculator". Unpublished manuscript: George Mason University
#'
#' @examples
#' esc_beta(.7, 3, 100, 150)
#' esc_beta(.7, 3, 100, 150, es.type = "cox.log")
#'
#' @export
esc_beta <- function(beta, sdy, grp1n, grp2n,
es.type = c("d", "g", "or", "logit", "r", "f", "eta", "cox.or", "cox.log"),
study = NULL) {
# match arguments
es.type <- match.arg(es.type)
totaln <- grp1n + grp2n
sdx <- sqrt(abs((grp1n - (grp1n ^ 2 / totaln)) / (totaln - 1)))
b <- beta * (sdy / sdx)
sdpooled <- sqrt(abs(((sdy ^ 2 * (totaln - 1)) - (b ^ 2 * ((grp1n * grp2n) / (grp1n + grp2n)))) / (totaln - 2)))
es <- b / sdpooled
v <- esc.vd(es, grp1n, grp2n)
# return effect size
esc_generic(
es = es,
v = v,
es.type = es.type,
grp1n = grp1n,
grp2n = grp2n,
info = "standardized regression coefficient",
study = study
)
}
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