Point-biserial correlation — point_biserial • mcqAnalysis

Computes the point-biserial correlation between each item and the total test score (excluding the item itself, i.e., corrected for item overlap). This is the standard classical test theory discrimination index based on the correlation between item performance and overall test performance.

Usage

point_biserial(responses, key, corrected = TRUE)

Arguments

responses: A matrix or data frame of student responses, with students in rows and items in columns.
key: A vector of correct answers with length equal to the number of items.
corrected: Logical. If TRUE (default), the total score is computed excluding the item being correlated, yielding the corrected item-total correlation. If FALSE, the total score includes the item.

Value

A named numeric vector of point-biserial correlations, one per item.

Details

Items with point-biserial correlations of 0.30 or above are generally considered to discriminate well between high- and low-ability students. Values between 0.20 and 0.29 are marginal; values below 0.20 indicate poor discrimination, and negative values suggest a problem with the item (Ebel & Frisbie, 1991).

References

Ebel, R. L., & Frisbie, D. A. (1991). Essentials of educational measurement (5th ed.). Prentice Hall.

Examples

set.seed(1)
responses <- matrix(
  sample(c("A", "B", "C", "D"), 100, replace = TRUE),
  nrow = 20, ncol = 5,
  dimnames = list(NULL, paste0("Q", 1:5))
)
key <- c("A", "B", "C", "A", "B")
point_biserial(responses, key)
#>          Q1          Q2          Q3          Q4          Q5 
#> -0.21352448 -0.21352448 -0.22091804  0.02252458  0.29149154