% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/es_from_ALPHA.R
\name{es_from_cronbach_alpha}
\alias{es_from_cronbach_alpha}
\title{Convert Cronbach's alpha into an effect size measure}
\usage{
es_from_cronbach_alpha(
  cronbach_alpha,
  n_sample,
  n_items,
  alpha_to_es = "bonett"
)
}
\arguments{
\item{cronbach_alpha}{Cronbach's alpha reliability coefficient}

\item{n_sample}{the total number of participants that completed the scale}

\item{n_items}{number of items in the scale}

\item{alpha_to_es}{method used to compute the effect size from Cronbach's alpha.
Must be either \code{"bonett"} or \code{"raw"}.}
}
\value{
This function estimates the standard error of the Cronbach's alpha.

\tabular{ll}{
\code{natural effect size measure} \tab alpha\cr
\tab \cr
\code{converted effect size measure} \tab N/A\cr
\tab \cr
\code{required input data} \tab cronbach_alpha + n_sample + n_items\cr
\tab \cr
}
}
\description{
Convert Cronbach's alpha into an effect size measure
}
\details{
This function computes an effect size from a Cronbach's alpha.
\enumerate{
\item When \code{alpha_to_es = "bonett"} (default), the Bonett (2002) transformation
is applied:
\deqn{T(\alpha) = \ln(1 - \alpha)}
\deqn{T\_se = \sqrt{\frac{2k}{(k - 1)(n - 2)}}}
\item When \code{alpha_to_es = "raw"}, the raw alpha is used. Its standard error is
the delta-method back-transform of the Bonett (2002) transformed variance
(equivalently the van Zyl, Neudecker & Nel, 2000, asymptotic variance; this is
the form implemented by \code{metafor}'s \code{measure = "ARAW"}):
\deqn{\alpha\_se = (1 - \alpha) \sqrt{\frac{2k}{(k - 1)(n - 2)}}}
Note that Feldt et al.'s (1987) classical asymptotic variance instead uses an
\eqn{(n - 1)} denominator; the \eqn{(n - 2)} form above follows Bonett (2002)
for consistency with the Bonett transformation used in method 1.
}

The Bonett transformation stabilizes the variance and is recommended for meta-analysis.
}
\examples{
es_from_cronbach_alpha(
  cronbach_alpha = 0.85, n_sample = 200, n_items = 10
)
}
\references{
Bonett, D. G. (2002). Sample size requirements for testing and estimating coefficient alpha.
Journal of Educational and Behavioral Statistics, 27(4), 335-340.

Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha.
Applied Psychological Measurement, 11(1), 93-103.

van Zyl, J. M., Neudecker, H., & Nel, D. G. (2000). On the distribution of the maximum likelihood
estimator of Cronbach's alpha. Psychometrika, 65(3), 271-280.
}
