Compute various measures of internal consistencies for tests or item-scales of questionnaires.
Arguments
- x
Depending on the function,
x
may be amatrix
as returned by thecor()
-function, or a data frame with items (e.g. from a test or questionnaire).- maximum_value
Numeric value, indicating the maximum value of an item. If
NULL
(default), the maximum is taken from the maximum value of all columns inx
(assuming that the maximum value at least appears once in the data). IfNA
, each item's maximum value is taken as maximum. If the required maximum value is not present in the data, specify the theoreritcal maximum usingmaximum_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.
Details
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 p + (1 - p) / 2
, where p = 1 / max(x)
. In most cases, the ideal item
difficulty lies between 0.5 and 0.8.
References
Bortz, J., and Döring, N. (2006). Quantitative Methoden der Datenerhebung. In J. Bortz and N. Döring, Forschungsmethoden und Evaluation. Springer: Berlin, Heidelberg: 137–293
Kelava A, Moosbrugger H (2020). Deskriptivstatistische Itemanalyse und Testwertbestimmung. In: Moosbrugger H, Kelava A, editors. Testtheorie und Fragebogenkonstruktion. Berlin, Heidelberg: Springer, 143–158