Classical Test Theory Item Analysis for Multiple-Choice Tests.
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.
Citation
citation("mcqAnalysis")
License
MIT © Rashed Alqahtani.