% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/es_from_PAIRED_STATISTICS.R
\name{es_from_paired_t}
\alias{es_from_paired_t}
\title{Convert two paired t-test value of two independent groups into several effect size measures}
\usage{
es_from_paired_t(
  paired_t_exp,
  paired_t_nexp,
  n_exp,
  n_nexp,
  r_pre_post_exp,
  r_pre_post_nexp,
  smd_to_cor = "viechtbauer",
  pre_post_to_smd = "cooper",
  reverse_paired_t
)
}
\arguments{
\item{paired_t_exp}{Paired t-test value of the experimental/exposed group.}

\item{paired_t_nexp}{Paired t-test value of the non-experimental/non-exposed group.}

\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{r_pre_post_exp}{pre-post correlation in the experimental/exposed group}

\item{r_pre_post_nexp}{pre-post correlation in the non-experimental/non-exposed group}

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

\item{pre_post_to_smd}{formula used to convert the paired t-test value into a SMD (see details).}

\item{reverse_paired_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 16. Paired: Paired F- or t-test'\cr
\tab https://metaconvert.org/input.html\cr
\tab \cr
}
}
\description{
Convert two paired t-test value of two independent groups into several effect size measures
}
\details{
This function converts paired t-tests of two independent groups value into a Cohen's d (D) and Hedges' g (G) (table 12.2 in Cooper).
Odds ratio (OR) and correlation coefficients (R/Z) are then converted from the Cohen's d.

\strong{To estimate the Cohen's d,} the following formulas are used (Cooper et al., 2019):
\deqn{cohen\_d\_exp = paired\_t\_exp * \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp}}}
\deqn{cohen\_d\_nexp = paired\_t\_nexp * \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp}}}
\deqn{cohen\_d\_se\_exp = \sqrt{\frac{2 * (1 - r\_pre\_post\_exp)}{n\_exp} + \frac{d\_exp^2}{2 * n\_exp}}}
\deqn{cohen\_d\_se\_nexp = \sqrt{\frac{2 * (1 - r\_pre\_post\_nexp)}{n\_nexp} + \frac{d\_nexp^2}{2 * n\_nexp}}}
\deqn{cohen\_d = d\_exp - d\_nexp}
\deqn{d\_se = \sqrt{cohen\_d\_se\_exp^2 + cohen\_d\_se\_nexp^2}}

When \code{pre_post_to_smd = "morris_dz"}, the mean difference is standardized by the standard deviation
of the change score and the pre-post correlation is no longer involved (Morris & DeShon, 2002):
\deqn{cohen\_d\_exp = \frac{paired\_t\_exp}{\sqrt{n\_exp}}}
\deqn{cohen\_d\_nexp = \frac{paired\_t\_nexp}{\sqrt{n\_nexp}}}

Note that the Cohen's d obtained from a paired t-test strongly depends on the pre-post correlation.
When \code{r_pre_post_exp} / \code{r_pre_post_nexp} are not indicated, a value of 0.8 is assumed and
users should conduct sensitivity analyses with other plausible values.

\strong{No \code{pool_sd} argument.} Unlike the means and mean-change converters, this function cannot
pool the standardizing SD across arms: a paired t-statistic identifies each arm's
\eqn{mean\_change / sd\_change} ratio but NOT the ratio of the two arms' SDs, so the pooled
standardizer is not recoverable from the reported statistic. Each arm is therefore standardized by
its own SD and the two within-group values are subtracted -- a construction that coincides with the
pooled one only when the arms' SDs are equal. When rows from this route are combined in one pool
with rows that DO use a pooled standardizer, \code{summary(..., flags = TRUE)} raises an
informational flag. If the arm SDs are reported, prefer \code{\link{es_from_means_sd_pre_post}} or
\code{\link{es_from_mean_change_sd}}.

\strong{To estimate other effect size measures},
calculations of the \code{\link{es_from_cohen_d}()} are applied.
}
\examples{
es_from_paired_t(paired_t_exp = 2.1, paired_t_nexp = 4.2, 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.

Morris, S. B., & DeShon, R. P. (2002). Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological Methods, 7(1), 105-125. https://doi.org/10.1037/1082-989X.7.1.105
}
