Distractor efficiency

Computes Haladyna's distractor efficiency for each item: the number of functioning distractors per item. A distractor is considered to be functioning if it meets two criteria: (a) it is selected by at least a threshold proportion of examinees (default 5 percent), and (b) it has a negative point-biserial correlation with the total test score (Haladyna & Downing, 1993). The key (correct answer) is excluded from the count.

Usage

distractor_efficiency(responses, key, options = NULL, min_proportion = 0.05)

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.

options

Optional character vector listing all possible response options. If NULL (default), the set of options is inferred from the unique values present in responses.

min_proportion

Minimum proportion of examinees selecting a distractor for it to be considered functioning. Default is 0.05.

Value

A named numeric vector of distractor efficiency values, one per item, representing the count of functioning distractors.

Details

Distractor efficiency provides a simple integer summary of item quality. A four-option multiple-choice item with three functioning distractors (distractor efficiency = 3) is performing optimally. Items with fewer functioning distractors waste examinee time and reduce the item's contribution to score variance, and they are candidates for revision.

References

Haladyna, T. M., & Downing, S. M. (1993). How many options is enough for a multiple-choice test item? Educational and Psychological Measurement, 53(4), 999-1010.

Examples

set.seed(1)
responses <- matrix(
  sample(c("A", "B", "C", "D"), 400, replace = TRUE),
  nrow = 100, ncol = 4,
  dimnames = list(NULL, paste0("Q", 1:4))
)
key <- c("A", "B", "C", "A")
distractor_efficiency(responses, key)
#> Q1 Q2 Q3 Q4 
#>  2  3  3  3