% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/psychometric_utils.R
\name{reliability_change_score}
\alias{reliability_change_score}
\title{Compute change-score reliability}
\usage{
reliability_change_score(reliability, r_pre_post)
}
\arguments{
\item{reliability}{single-occasion reliability coefficient (e.g., Cronbach's alpha or ICC)}

\item{r_pre_post}{pre-post correlation of observed scores}
}
\value{
A data.frame containing the change-score reliability (\code{rel_change}).
}
\description{
Compute change-score reliability
}
\details{
Computes the reliability of a change (difference) score from a single-occasion
reliability coefficient and the pre-post correlation of observed scores,
assuming equal variances AND equal reliabilities at pre and post
(Lord, 1963; Cronbach & Furby, 1970):

\deqn{rel_{change} = \frac{rel - r_{12}}{1 - r_{12}}}

This is the equal-variance/equal-reliability special case of the general
Lord (1963) formula; when the pre and post variances (or reliabilities)
differ materially, the general formula should be used instead.

This is useful for disattenuating change-score correlations, where the
reliability of the change score is needed rather than the single-occasion reliability.

A negative result (which occurs when \code{r_pre_post} exceeds
\code{reliability}) is population-impossible under classical test theory
and signals inconsistent inputs; it is returned as computed but triggers a
warning, since a negative value fed to \code{\link{es_disattenuate}} as a
reliability would produce \code{NaN} (square root of a negative number).
}
\examples{
reliability_change_score(reliability = 0.85, r_pre_post = 0.60)
}
\references{
Lord, F. M. (1963). Elementary models for measuring change.
In C. W. Harris (Ed.), Problems in measuring change. University of Wisconsin Press.

Cronbach, L. J., & Furby, L. (1970). How we should measure "change" - or should we?
Psychological Bulletin, 74(1), 68-80.
}
