% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/es_from_ANOVA_statistics.R
\name{es_from_student_t}
\alias{es_from_student_t}
\title{Convert a Student's t-test value to several effect size measures}
\usage{
es_from_student_t(
  student_t,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  smd_var = "borenstein",
  reverse_student_t
)
}
\arguments{
\item{student_t}{Student's t-test value.}

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

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

\item{smd_to_cor}{formula used to convert the \code{student_t} value into a coefficient correlation (see details).}

\item{smd_var}{name of the sampling-variance formula for the standardized mean difference: "borenstein" (default) or "hedges_olkin" (alias "viechtbauer"). The two differ by a squared small-sample-correction factor (J^2); "hedges_olkin" is a few percent larger at small samples.}

\item{reverse_student_t}{a logical value indicating whether the direction of 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 D + G\cr
\tab \cr
\code{converted effect size measure} \tab OR + R + Z\cr
\tab \cr
\code{required input data} \tab See 'Section 11. ANOVA statistics, Student's t-test, or point-bis correlation'\cr
\tab https://metaconvert.org/html/input.html\cr
\tab \cr
}
}
\description{
Convert a Student's t-test value to several effect size measures
}
\details{
This function converts the Student's t-test value into a Cohen's d (D) and Hedges' g (G),
Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

\strong{To estimate a Cohen's d} the formula used is (table 12.1 in Cooper):
\deqn{cohen\_d = student\_t * \sqrt{\frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}}}

\strong{To estimate other effect size measures},
calculations of the \code{\link{es_from_cohen_d}()} are applied.

\strong{Important - Student's t, not Welch's t.} This formula is the exact inverse of the
pooled-variance (Student) t-test, so \code{student_t} must be the \emph{equal-variance} t.
It should NOT be used with a Welch (unequal-variance) t-test, which is the default of
R's \code{t.test()}. A Welch t uses \eqn{\sqrt{s_1^2/n_1 + s_2^2/n_2}} rather than
\eqn{s_{pooled}\sqrt{1/n_1 + 1/n_2}}, so when group sizes and variances both differ,
plugging a Welch t into this formula yields a biased Cohen's d (the bias can exceed
50\% and may flip sign depending on which arm carries the larger variance; it vanishes
only when \eqn{n_1 = n_2}). A Welch t cannot be converted to Cohen's d from
\code{(t, n_exp, n_nexp)} alone: recovering the pooled SD requires the two arm SDs, in
which case \code{\link{es_from_means_sd}} should be used directly.
}
\examples{
es_from_student_t(student_t = 2.1, n_exp = 20, n_nexp = 22)
}
\references{
Cooper, H., Hedges, L.V., & Valentine, J.C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.
}
