exametrika (version 1.1.0)

crr: 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, ...)

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).

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.

Examples

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

# using sample datasaet
crr(J15S500)