item.exam: Item Analysis

In psychometric: Applied Psychometric Theory

Item Analysis

Description

Conducts an item level analysis. Provides item-total correlations, Standard deviation in items, difficulty, discrimination, and reliability and validity indices.

Usage

item.exam(x, y = NULL, discrim = FALSE)

Arguments

x	matrix or data.frame of items
y	Criterion variable
discrim	Whether or not the discrimination of item is to be computed

Details

If someone is interested in examining the items of a dataset contained in data.frame x, and the criterion measure is also in data.frame x, one must parse the matrix or data.frame and specify each part into the function. See example below. Otherwise, one must be sure that x and y are properly merged/matched. If one is not interested in assessing item-criterion relationships, simply leave out that portion of the call. The function does not check whether the items are dichotomously coded, this is user specified. As such, one can specify that items are binary when in fact they are not. This has the effect of computing the discrimination index for continuously coded variables.
The difficulty index (p) is simply the mean of the item. When dichotomously coded, p reflects the proportion endorsing the item. However, when continuously coded, p has a different interpretation.

Value

A table with rows representing each item and columns repsenting :

Sample.SD	Standard deviation of the item
Item.total	Correlation of the item with the total test score
Item.Tot.woi	Correlation of item with total test score (scored without item)
Difficulty	Mean of the item (p)
Discrimination	Discrimination of the item (u-l)/n
Item.Criterion	Correlation of the item with the Criterion (y)
Item.Reliab	Item reliability index
Item.Rel.woi	Item reliability index (scored without item)
Item.Validity	Item validity index

Warning

Be cautious when using data with missing values or small data sets.

Listwise deletion is employed for both X (matrix of items to be analyzed) and Y (criterion). When the datasets are small, such listwise deletion can make a big impact. Further, since the upper and lower groups are defined as the upper and lower 1/3, the stability of this division of examinees is greatly increased with larger N.

Note

Most all text books suggest the point-biserial correlation for the item-total. Since the point-biserial is equivalent to the Pearson r, the cor function is used to render the Pearson r for each item-total. However, it might be suggested that the polyserial is more appropriate. For practical purposes, the Pearson is sufficient and is used here.

If discrim = TRUE, then the discrimination index is computed and returned EVEN IF the items are not dichotomously coded. The interpretation of the discrimination index is then suspect. discrim computes the number of correct responses in the upper and lower groups by summation of the '1s' (correct responses). When data are continuous, the discrimination index represents the difference in the sum of the scores divided by number in each group (1/3*N).

Author(s)

Thomas D. Fletcher [e-mail]

References

Allen, M. J. & Yen, W. M. (1979). Introduction to measurement theory. Monterey, CA: Brooks/Cole.

See Also

alpha, discrim

Examples

data(TestScores)
# Look at the data
TestScores
# Examine the items
item.exam(TestScores[,1:10], y = TestScores[,11], discrim=TRUE)

psychometric documentation built on Nov. 6, 2023, 1:06 a.m.