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

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

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

- x
matrix or data.frame of items

- y
Criterion variable

- discrim
Whether or not the discrimination of item is to be computed

Thomas D. Fletcher t.d.fletcher05@gmail.com

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.

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.

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

`alpha`

, `discrim`

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

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