#' Obtain Cohen's *d* from one-way F tests
#'
#' This function converts F statistics from one-way tests to Cohen's *d*.
#'
#' The formula that is used is the following (see e.g. Thalheimer & Cook,
#' 2002):
#'
#' \deqn{d= \sqrt{F (\frac{n_1 + n_2}{n_1 n_2})
#' (\frac{n_1 + n_2}{n_1 + n_2 - 2})}}
#'
#' @param F1 A numerical vector with one or more *F* values.
#' @param n1,n2 A numerical vector with the sample sizes of the two groups
#' formed by the dichotomous variable. Note that the *n*th element of these
#' vectors must correspond to the *n*th elements of the `F1` vector.
#' @param df2 A numerical vector with one or more values of degrees of freedom
#' 2.
#' @param sign Numerical vector to indicate the sign of the d-values
#' (\code{+1} or \code{-1}).
#' @param bias_correct Logical to indicate if the *d*-values should be
#' bias-corrected. Can also be a vector.
#' @param stopOnErrors On which errors to stop (see the manual page for [escalc::opts()] for more details).
#'
#' @return A data frame with in the first column, Cohen's `d` values, and
#' in the second column, the corresponding variances.
#'
#' @references Thalheimer, W., & Cook, S. (2002, August). *How to calculate
#' effect sizes from published research articles: A simplified methodology.*
#' @references Borenstein, M., Hedges, L. V., Higgins, J. P. T., & Rothstein,
#' H. R. (2009). *Introduction to Meta-Analysis*. Chichester, UK: John Wiley
#' & Sons.
#'
#' @examples
#' escalc::d_from_F_oneway(F1 = 2.828427,
#' n1 = 126,
#' n2 = 89,
#' sign = +1);
#' escalc::d_from_F_oneway
#'
#' @export
d_from_F_oneway <- function(F1,
n1,
n2,
df2,
sign,
bias_correct = FALSE,
stopOnErrors = opts$get(stopOnErrors)) {
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
###
### Argument checking
###
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
###--------------------------------------------------------------- F1, n1, n2
### Argument-checking - Check presence
###--------------------------------------------------------------- F1, n1, n2
if (missing(F1)) {
stop(.errmsg(missing='F1',
callingFunction = .curfnfinder()))
}
if (missing(n1) & missing(df2)) {
stop(.errmsg(missing='n1',
callingFunction = .curfnfinder()))
}
if (missing(n2) & missing(df2)) {
stop(.errmsg(missing='n2',
callingFunction = .curfnfinder()))
}
if (missing(n1) | missing(n2)) {
n1 <- (df2+2)/2
n2 <- (df2+2)/2
}
###--------------------------------------------------------------- t, n1 & n2
### Argument checking: lengths
###--------------------------------------------------------------- t, n1 & n2
#if (!missing(n1) && !missing(n2)) {
argLengths <- c(length(F1),
length(n1), length(n2));
if (length(unique(argLengths)) > 1) {
stop(.errmsg(differentLengths =
list(argNames=c("F1", "n1", "n2"),
argLengths=argLengths),
callingFunction = .curfnfinder()))
}
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
###
### Actual functionality
###
### At this point, we *must* have (with valid values):
###
### - F1
### - n1
### - n2
### - sign
### ~ bias_correct (has a default value)
###
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
### Effect size point estimate
###--------------------------------------------------------------------------
d <- sqrt(F * ((n1 + n2) / (n1 * n2)) * ((n1 + n2) / (n1 + n2 - 2)))
###--------------------------------------------------------------------------
### Effect size variance
###--------------------------------------------------------------------------
# https://stats.stackexchange.com/questions/144084/variance-of-cohens-d-statistic
dVar <- ((n1 + n2) / (n1 * n2)) + ((d^2) / (2 * (n1 + n2)))
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
###
### Prepare dataframe and return result
###
###--------------------------------------------------------------------------
###--------------------------------------------------------------------------
.minimalMissingMessage <-
.minimalMissingMessage(d, dVar,
callingFunction = .curfnfinder(),
stopOnErrors=stopOnErrors)
return(stats::setNames(data.frame(d, dVar, .minimalMissingMessage),
c(opts$get("EFFECTSIZE_POINTESTIMATE_NAME_IN_DF"),
opts$get("EFFECTSIZE_VARIANCE_NAME_IN_DF"),
opts$get("EFFECTSIZE_MISSING_MESSAGE_NAME_IN_DF"))))
}
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