% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/mod_kappa.R
\name{mod_kappa}
\alias{mod_kappa}
\title{Modified kappa - I-CVI adjusted for chance agreement}
\usage{
mod_kappa(ratings, relevant_threshold = 3, na.rm = FALSE)
}
\arguments{
\item{ratings}{A numeric matrix or data frame of expert ratings (rows =
experts, columns = items). A numeric vector is also accepted, treated
as a single item.}

\item{relevant_threshold}{Integer. Minimum rating considered "relevant".
Defaults to 3.}

\item{na.rm}{Logical. If \code{TRUE}, missing ratings are excluded when
counting experts and agreements. Defaults to \code{FALSE}.}
}
\value{
A named numeric vector of modified-kappa values, one per item. If \code{ratings}
is a vector, returns a single numeric value.
}
\description{
Computes modified kappa for each item, as proposed by Polit, Beck,
and Owen (2007). Modified kappa adjusts the Item-level Content Validity
Index (I-CVI) for chance agreement under the assumption that each expert
independently rates an item as relevant with probability 0.5.
}
\details{
The formula is:

\deqn{\kappa^* = (\mathrm{I\text{-}CVI} - P_c) / (1 - P_c)}

where the chance agreement probability is

\deqn{P_c = \binom{N}{A} \times 0.5^N}

with N = number of experts and A = number of experts rating the item as
relevant.

Common interpretation cutoffs (Cicchetti and Sparrow, 1981; adopted by
Polit et al., 2007):
\itemize{
\item kappa* < 0.40: poor
\item kappa* 0.40-0.59: fair
\item kappa* 0.60-0.74: good
\item kappa* > 0.74: excellent
}
}
\examples{
ratings <- matrix(
  c(4, 4, 3, 4, 4,
    3, 4, 4, 4, 3,
    2, 3, 3, 4, 3,
    1, 2, 3, 2, 3),
  nrow = 5,
  dimnames = list(NULL, paste0("item", 1:4))
)
mod_kappa(ratings)

}
\references{
Cicchetti, D. V., & Sparrow, S. A. (1981). Developing criteria for
establishing interrater reliability of specific items: Applications to
assessment of adaptive behavior. \emph{American Journal of Mental Deficiency},
86(2), 127-137.

Polit, D. F., Beck, C. T., & Owen, S. V. (2007). Is the CVI an acceptable
indicator of content validity? Appraisal and recommendations.
\emph{Research in Nursing & Health}, 30(4), 459-467.
\doi{10.1002/nur.20199}
}
\seealso{
\code{\link[=icvi]{icvi()}}
}
