ItemTotalCorr: Item-Total Correlation

In exametrika: Test Theory Analysis and Biclustering

Item-Total Correlation

Description

Item-Total correlation (ITC) is a Pearson's correlation of an item with the Number-Right Score (NRS) or total score. This function is applicable only to binary response data.

The ITC is a measure of item discrimination, indicating how well an item distinguishes between high and low performing examinees.

Usage

ItemTotalCorr(U, na = NULL, Z = NULL, w = NULL)

## Default S3 method:
ItemTotalCorr(U, na = NULL, Z = NULL, w = NULL)

## S3 method for class 'binary'
ItemTotalCorr(U, na = NULL, Z = NULL, w = NULL)

## S3 method for class 'ordinal'
ItemTotalCorr(U, na = NULL, Z = NULL, w = NULL)

Arguments

U	Either an object of class "exametrika" or raw data. When raw data is given, it is converted to the exametrika class with the dataFormat function.
na	Values to be treated as missing values.
Z	Missing indicator matrix of type matrix or data.frame. Values of 1 indicate observed responses, while 0 indicates missing data.
w	Item weight vector specifying the relative importance of each item.

Details

The correlation is calculated between:

• Each item's responses (0 or 1)

• The total test score (sum of correct responses)

Higher positive correlations indicate items that better discriminate between high and low ability examinees.

Value

A numeric vector of item-total correlations. Values typically range from -1 to 1, where:

• Values near 1: Strong positive discrimination

• Values near 0: No discrimination

• Negative values: Potential item problems (lower ability students performing better than higher ability students)

Note

This function is implemented using a binary data compatibility wrapper and will raise an error if used with polytomous data.

Values below 0.2 might indicate problematic items that should be reviewed. Values above 0.3 are generally considered acceptable.

Examples

# using sample dataset
ItemTotalCorr(J15S500)

exametrika documentation built on Aug. 21, 2025, 5:27 p.m.