% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/es_from_ANCOVA_statistics.R
\name{es_from_ancova_t}
\alias{es_from_ancova_t}
\title{Convert a t-statistic obtained from an ANCOVA model into several effect size measures.}
\usage{
es_from_ancova_t(
  ancova_t,
  cov_outcome_r,
  n_cov_ancova,
  n_exp,
  n_nexp,
  smd_to_cor = "viechtbauer",
  smd_var = "borenstein",
  reverse_ancova_t
)
}
\arguments{
\item{ancova_t}{a t-statistic from an ANCOVA (binary predictor)}

\item{cov_outcome_r}{correlation between the outcome and covariate(s) (multiple correlation when multiple covariates are included in the ANCOVA model).}

\item{n_cov_ancova}{number of covariates in the ANCOVA model.}

\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 adjusted \code{cohen_d} 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_ancova_t}{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 D + G\cr
\tab \cr
\code{converted effect size measure} \tab OR + R + Z \cr
\tab \cr
\code{required input data} \tab See 'Section 18. Adjusted: ANCOVA statistics, eta-squared'\cr
\tab https://metaconvert.org/input.html\cr
\tab \cr
}
}
\description{
Convert a t-statistic obtained from an ANCOVA model into several effect size measures.
}
\details{
This function first computes an "adjusted" Cohen's d (D), and
Hedges' g (G) from the t-value of an ANCOVA (binary predictor).
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 12.3 in Cooper):
\deqn{cohen\_d =  ancova\_t* \sqrt{\frac{(n\_exp+n\_nexp)}{n\_exp*n\_nexp}}\sqrt{1 - cov\_out\_cor^2}}

\strong{To estimate other effect size measures},
Calculations of the \code{\link{es_from_cohen_d_adj}()} are applied.
}
\note{
The Cohen's d point estimate is recovered from the reported ANCOVA t (which
already embeds the covariate adjustment), but its sampling variance is rebuilt
from Cooper's eq. 12.26, which assumes a covariate balanced across groups and
treats \code{cov_outcome_r} as known. In observational or otherwise
covariate-imbalanced designs the standard error is a lower bound
(anti-conservative), while the point estimate remains unbiased. See Lai and
Kelley (2012).
}
\examples{
es_from_ancova_t(ancova_t = 2, cov_outcome_r = 0.2, n_cov_ancova = 3, n_exp = 20, n_nexp = 20)
}
\references{
Cooper, H., Hedges, L. V., & Valentine, J. C. (Eds.). (2019). The handbook of research synthesis and meta-analysis. Russell Sage Foundation.

Lai, K., & Kelley, K. (2012). Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65(2), 350-370.
}
