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, ...)

Arguments

U

U is a data matrix of the type matrix or data.frame.

na

na argument specifies the numbers or characters to be treated as missing values.

Z

Z is a missing indicator matrix of the type matrix or data.frame

w

w is item weight vector

...

Internal parameters for maintaining compatibility with the binary data processing system. Not intended for direct use.

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 1.1.0 Index]