crr {exametrika}R Documentation

Correct Response Rate

Description

The correct response rate (CRR) is one of the most basic and important statistics for item analysis. This is an index of item difficulty and a measure of how many students out of those who tried an item correctly responded to it. This function is applicable only to binary response data.

The CRR for each item is calculated as:

p_j = \frac{\sum_{i=1}^n z_{ij}u_{ij}}{\sum_{i=1}^n z_{ij}}

where z_{ij} is the missing indicator and u_{ij} is the response.

Usage

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

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

## S3 method for class 'binary'
crr(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.

Value

A numeric vector of weighted correct response rates for each item. Values range from 0 to 1, where higher values indicate easier items (more students answered correctly).

Note

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

Examples

# Simple binary data
U <- matrix(c(1, 0, 1, 1, 0, 1), ncol = 2)
crr(U)

# using sample datasaet
crr(J15S500)

[Package exametrika version 1.5.1 Index]