Compute various measures of internal consistencies for tests or item-scales of questionnaires.

## Usage

item_difficulty(x)

## Arguments

x

Depending on the function, x may be a matrix as returned by the cor()-function, or a data frame with items (e.g. from a test or questionnaire).

## 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.

## Details

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 p + (1 - p) / 2, where 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)
#> # Item Difficulty
#>
#>       difficulty  ideal
#>    cyl      0.77   0.56
#>   gear      0.74   0.60
#>   carb      0.35   0.56
#>     hp      0.44   0.50