Classical Test Theory Item Analysis for Multiple-Choice Tests

A unified toolkit for classical test theory (CTT) item analysis of multiple-choice test data, including item difficulty (p-value), item discrimination (point-biserial correlation and upper-lower 27-percent discrimination index), per-distractor analysis (frequency, proportion, and discrimination), and Haladyna's distractor efficiency. A wrapper function returns a tidy 'mcq_analysis' object with print, plot (difficulty-discrimination scatter), and APA-style table methods for direct inclusion in journal manuscripts. Implemented in pure R with no compiled code and minimal dependencies.

mcqAnalysis

A unified R toolkit for classical test theory (CTT) item analysis of multiple-choice tests. Compute item difficulty, item discrimination (point-biserial and upper-lower 27 percent), per-distractor analysis, and Haladyna's distractor efficiency in a single call. A wrapper function returns a tidy mcq_analysis object with print, plot (difficulty-discrimination scatter), and APA-style table methods for direct manuscript inclusion.

Installation

Install the released version from CRAN:

install.packages("mcqAnalysis")

Or the development version from GitHub:

# install.packages("devtools")
devtools::install_github("Rafhq1403/mcqAnalysis")

Quick example

library(mcqAnalysis)
data(mcq_example)

# Complete item analysis in one call
result <- mcq_analysis(mcq_example$responses, mcq_example$key)
result
#> Multiple-Choice Item Analysis
#> ------------------------------
#> Students: 200
#> Items:    30
#> Mean total score: 15.765 (SD = 6.342)
#>
#> Item-level statistics:
#>   item key difficulty point_biserial discrimination_index distractor_efficiency
#> item01   D      0.850          0.472                0.426                     2
#> ...

# Item quality map
plot(result)

# Publication-ready APA table
apa_table(result, format = "markdown")

What's included

Function	Purpose
`item_difficulty()`	p-value per item
`item_discrimination()`	Point-biserial or upper-lower discrimination index
`point_biserial()`	Corrected item-total point-biserial correlation
`distractor_analysis()`	Per-option frequency, proportion, point-biserial
`distractor_efficiency()`	Haladyna's count of functioning distractors
`mcq_analysis()`	One-call wrapper returning an S3 object
`plot.mcq_analysis()`	Difficulty-discrimination scatter
`apa_table.mcq_analysis()`	APA-style table (data.frame, markdown, HTML, LaTeX)
`mcq_example` (dataset)	200 students × 30 four-option items

Methods reference

The package implements widely-used classical test theory indices. Conventional cutoffs follow Ebel & Frisbie (1991) for discrimination and Haladyna & Downing (1993) for distractor efficiency. See the getting-started vignette for a complete worked example and references.

Related packages

mcqAnalysis is designed to be a CTT-focused companion to its sister package contentValidity, which computes content-validity indices (I-CVI, S-CVI, modified kappa, Aiken's V, Lawshe's CVR). Together they cover pre-administration content validation (via expert review) and post-administration empirical item analysis (via examinee response data) in a consistent API. For inter-rater agreement statistics beyond content validity, see irrCAC; for broader psychometric utilities, see psych.