% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/convert_tFz_to_d.R, R/convert_tFz_to_r.R
\name{t_to_d}
\alias{t_to_d}
\alias{z_to_d}
\alias{F_to_d}
\alias{t_to_r}
\alias{z_to_r}
\alias{F_to_r}
\title{Convert test statistics (t, z, F) to effect sizes of differences (Cohen's d) or association (\strong{partial} r)}
\usage{
t_to_d(t, df_error, paired = FALSE, ci = 0.95, pooled, ...)

z_to_d(z, n, paired = FALSE, ci = 0.95, pooled, ...)

F_to_d(f, df, df_error, paired = FALSE, ci = 0.95, pooled, ...)

t_to_r(t, df_error, ci = 0.95, ...)

z_to_r(z, n, ci = 0.95, ...)

F_to_r(f, df, df_error, ci = 0.95, ...)
}
\arguments{
\item{t, f, z}{The t, the F or the z statistics.}

\item{paired}{Should the estimate accout for the t-value being testing the
difference between dependant means?}

\item{ci}{Confidence Interval (CI) level}

\item{pooled}{Deprecated. Use \code{paired}.}

\item{...}{Arguments passed to or from other methods.}

\item{n}{The number of observations (the sample size).}

\item{df, df_error}{Degrees of freedom of numerator or of the error estimate
(i.e., the residuals).}
}
\value{
A data frame with the effect size(s)(\code{r} or \code{d}), and their CIs
(\code{CI_low} and \code{CI_high}).
}
\description{
These functions are convenience functions to convert t, z and F test
statistics to Cohen's d and \strong{partial} r. These are useful in cases where
the data required to compute these are not easily available or their
computation is not straightforward (e.g., in liner mixed models, contrasts,
etc.).
\cr
See \href{https://easystats.github.io/effectsize/articles/from_test_statistics.html}{Effect Size from Test Statistics vignette.}
}
\details{
These functions use the following formulae to approximate \emph{r} and \emph{d}:
\cr\cr
\deqn{r_{partial} = t / \sqrt{t^2 + df_{error}}}
\cr\cr
\deqn{r_{partial} = z / \sqrt{z^2 + N}}
\cr\cr
\deqn{d = 2 * t / \sqrt{df_{error}}}
\cr\cr
\deqn{d_z = t / \sqrt{df_{error}}}
\cr\cr
\deqn{d = 2 * z / \sqrt{N}}

The resulting \code{d} effect size is an \emph{approximation} to Cohen's \emph{d}, and
assumes two equal group sizes. When possible, it is advised to directly
estimate Cohen's \emph{d}, with \code{\link[=cohens_d]{cohens_d()}}, \code{\link[emmeans:eff_size]{emmeans::eff_size()}}, or similar
functions.
}
\section{Confidence Intervals}{

Unless stated otherwise, confidence intervals are estimated using the
Noncentrality parameter method; These methods searches for a the best
non-central parameters (\code{ncp}s) of the noncentral t-, F- or Chi-squared
distribution for the desired tail-probabilities, and then convert these
\code{ncp}s to the corresponding effect sizes. (See full \link{effectsize-CIs} for
more.)
}

\examples{
## t Tests
res <- t.test(1:10, y = c(7:20), var.equal = TRUE)
t_to_d(t = res$statistic, res$parameter)
t_to_r(t = res$statistic, res$parameter)

res <- with(sleep, t.test(extra[group == 1], extra[group == 2], paired = TRUE))
t_to_d(t = res$statistic, res$parameter, paired = TRUE)
t_to_r(t = res$statistic, res$parameter)
\donttest{
## Linear Regression
model <- lm(rating  ~ complaints + critical, data = attitude)
library(parameters)
(param_tab <- parameters(model))

(rs <- t_to_r(param_tab$t[2:3], param_tab$df_error[2:3]))

if (require(see)) plot(rs)

# How does this compare to actual partial correlations?
if (require("correlation")) {
  correlation::correlation(attitude[, c(1, 2, 6)], partial = TRUE)[1:2, c(2, 3, 7, 8)]
}

## Use with emmeans based contrasts (see also t_to_eta2)
if (require(emmeans)) {
  warp.lm <- lm(breaks ~ wool * tension, data = warpbreaks)


  # Also see emmeans::eff_size()
  em_tension <- emmeans(warp.lm, ~tension) #'
  diff_tension <- summary(pairs(em_tension))
  t_to_d(diff_tension$t.ratio, diff_tension$df)
}
}

}
\references{
\itemize{
\item Friedman, H. (1982). Simplified determinations of statistical power, magnitude of effect and research sample sizes. Educational and Psychological Measurement, 42(2), 521-526. \doi{10.1177/001316448204200214}
\item Wolf, F. M. (1986). Meta-analysis: Quantitative methods for research synthesis (Vol. 59). Sage.
\item Rosenthal, R. (1994) Parametric measures of effect size. In H. Cooper and L.V. Hedges (Eds.). The handbook of research synthesis. New York: Russell Sage Foundation.
\item Steiger, J. H. (2004). Beyond the F test: Effect size confidence intervals and tests of close fit in the analysis of variance and contrast analysis. Psychological Methods, 9, 164-182.
\item Cumming, G., & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61(4), 532-574.
}
}
\seealso{
Other effect size from test statistic: 
\code{\link{F_to_eta2}()},
\code{\link{chisq_to_phi}()}
}
\concept{effect size from test statistic}
