% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/es_from_spearman_COR.R
\name{es_from_spearman_rho}
\alias{es_from_spearman_rho}
\title{Convert a Spearman's rank correlation coefficient to several effect size measures}
\usage{
es_from_spearman_rho(
  spearman_r,
  n_sample,
  n_exp,
  n_nexp,
  cor_to_smd = "viechtbauer",
  sd_iv,
  unit_increase_iv,
  unit_type = "raw_scale",
  reverse_spearman_r
)
}
\arguments{
\item{spearman_r}{a Spearman's rank correlation coefficient value}

\item{n_sample}{the total number of participants}

\item{n_exp}{number of the experimental/exposed group}

\item{n_nexp}{number of the non-experimental/non-exposed group}

\item{cor_to_smd}{formula used to convert the derived Pearson's r value into a SMD.}

\item{sd_iv}{the standard deviation of the independent variable}

\item{unit_increase_iv}{a value of the independent variable that will be used to estimate the Cohen's d (see details).}

\item{unit_type}{the type of unit for the \code{unit_increase_iv} argument. Must be either "sd" or "value"}

\item{reverse_spearman_r}{a logical value indicating whether the direction of the generated effect sizes should be flipped.}
}
\value{
This function estimates and converts between several effect size measures.

\tabular{ll}{
\code{natural effect size measure} \tab R + Z\cr
\tab \cr
\code{converted effect size measure} \tab D + G + OR\cr
\tab \cr
\code{required input data} \tab See 'Section 4. Pearson's r or Fisher's z'\cr
\tab https://metaconvert.org/input.html\cr
\tab \cr
}
}
\description{
Convert a Spearman's rank correlation coefficient to several effect size measures
}
\details{
This function first converts a Spearman's rank correlation coefficient to an approximate Pearson's
correlation coefficient using the formula proposed by Rupinski & Dunlap (1996):
\deqn{r_p = 2 \sin(\pi / 6 \times r_s)}

The standard error of the resulting Pearson's r is derived via the delta method.
The sampling variance of the Spearman rho under bivariate normality carries an
extra \eqn{(1 + r_s^2 / 2)} factor relative to the Pearson variance
(Bonett & Wright, 2000); omitting it would understate the SE, increasingly so
for strong correlations:
\deqn{r_p\_se = \sqrt{\left(\frac{\pi}{3} \cos\left(\frac{\pi}{6} r_s\right)\right)^2 \times \left(1 + \frac{r_s^2}{2}\right)\frac{(1 - r_s^2)^2}{n - 1}}}

The converted Pearson's r is then further converted to a Fisher's z, Cohen's d, Hedges' g, and
odds ratio using the same formulas as \code{\link{es_from_pearson_r}()}. This
delta-method SE is propagated to the Fisher's z and (for the
\code{cor_to_smd = "viechtbauer"} and \code{cor_to_smd = "cooper"} paths,
whose SMD standard errors are proportional to the input r SE) to the Cohen's d,
Hedges' g and odds ratio, so all measures share the corrected r variance.
The \code{cor_to_smd = "mathur"} SMD variance contains no r SE term, so its
d/g/OR standard errors are left as computed by \code{\link{es_from_pearson_r}()}.
}
\examples{
es_from_spearman_rho(
  spearman_r = .55, n_sample = 100
)
}
\references{
Rupinski, M. T., & Dunlap, W. P. (1996). Approximating Pearson product-moment correlations from
Kendall's tau and Spearman's rho. Educational and Psychological Measurement, 56(3), 419-429.

Bonett, D. G., & Wright, T. A. (2000). Sample size requirements for estimating Pearson, Kendall
and Spearman correlations. Psychometrika, 65(1), 23-28.
}
