% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/cvr.R
\name{cvr_critical}
\alias{cvr_critical}
\title{Critical CVR value for a given panel size}
\usage{
cvr_critical(n_experts, alpha = 0.05)
}
\arguments{
\item{n_experts}{Positive integer. Number of experts on the panel.}

\item{alpha}{Numeric. One-tailed significance level. Defaults to 0.05.}
}
\value{
Numeric. The critical CVR value. CVR values at or above this
threshold are statistically significant. Returns \code{NA_real_} if no CVR
value can reach significance at the specified alpha (which can happen
for very small panels with stringent alpha).
}
\description{
Returns the minimum Content Validity Ratio considered statistically
significant for a panel of N experts at the specified alpha level. The
calculation uses the exact binomial distribution under the null
hypothesis that each expert independently rates "essential" with
probability 0.5, following the corrected approach of Wilson, Pan, and
Schumsky (2012).
}
\details{
The critical value is determined as the smallest \eqn{k} such that
\eqn{P(X \geq k) \leq \alpha} when \eqn{X \sim Binomial(N, 0.5)}, then
transformed to the CVR scale via \eqn{CVR_{crit} = (k - N/2) / (N/2)}.

Wilson, Pan, and Schumsky (2012) demonstrated that Lawshe's (1975)
original critical-value table contained errors, especially for small
panels. The exact binomial computation used here is their recommended
replacement.
}
\examples{
cvr_critical(10)         # 0.80 — need 9 of 10 experts to call it essential
cvr_critical(20)         # 0.50
cvr_critical(40)         # 0.25
cvr_critical(10, alpha = 0.01)

}
\references{
Wilson, F. R., Pan, W., & Schumsky, D. A. (2012). Recalculation of the
critical values for Lawshe's content validity ratio. \emph{Measurement and
Evaluation in Counseling and Development}, 45(3), 197-210.
\doi{10.1177/0748175612440286}
}
\seealso{
\code{\link[=cvr]{cvr()}}
}
