% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/item_difficulty.R
\name{item_difficulty}
\alias{item_difficulty}
\title{Difficulty of Questionnaire Items}
\usage{
item_difficulty(x, maximum_value = NULL)
}
\arguments{
\item{x}{Depending on the function, \code{x} may be a \code{matrix} as
returned by the \code{cor()}-function, or a data frame
with items (e.g. from a test or questionnaire).}

\item{maximum_value}{Numeric value, indicating the maximum value of an item.
If \code{NULL} (default), the maximum is taken from the maximum value of all
columns in \code{x} (assuming that the maximum value at least appears once in
the data). If \code{NA}, each item's maximum value is taken as maximum. If the
required maximum value is not present in the data, specify the theoreritcal
maximum using \code{maximum_value}.}
}
\value{
A data frame with three columns: The name(s) of the item(s), the item
difficulties for each item, and the ideal item difficulty.
}
\description{
Compute various measures of internal consistencies
for tests or item-scales of questionnaires.
}
\details{
\emph{Item difficutly} of an item is defined as the quotient of the sum
actually achieved for this item of all and the maximum achievable score.
This function calculates the item difficulty, which should range between
0.2 and 0.8. Lower values are a signal for more difficult items, while
higher values close to one are a sign for easier items. The ideal value
for item difficulty is \code{p + (1 - p) / 2}, where \code{p = 1 / max(x)}. In most
cases, the ideal item difficulty lies between 0.5 and 0.8.
}
\examples{
data(mtcars)
x <- mtcars[, c("cyl", "gear", "carb", "hp")]
item_difficulty(x)
}
\references{
\itemize{
\item Bortz, J., and Döring, N. (2006). Quantitative Methoden der Datenerhebung.
In J. Bortz and N. Döring, Forschungsmethoden und Evaluation. Springer:
Berlin, Heidelberg: 137–293
\item Kelava A, Moosbrugger H (2020). Deskriptivstatistische Itemanalyse und
Testwertbestimmung. In: Moosbrugger H,  Kelava A, editors. Testtheorie und
Fragebogenkonstruktion. Berlin, Heidelberg: Springer, 143–158
}
}
