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Item discrimination

Source: R/item_discrimination.R
item_discrimination.Rd

Computes a discrimination index for each item using one of two classical methods: the point-biserial correlation between item and total test score, or the upper-lower 27 percent discrimination index proposed by Kelley (1939).

Usage

item_discrimination(
  responses,
  key,
  method = c("point_biserial", "discrimination_index"),
  group_pct = 0.27
)

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.

method

One of "point_biserial" (default) or "discrimination_index".

group_pct

For method = "discrimination_index", the proportion of students assigned to each extreme group. Default is 0.27 following Kelley (1939).

Value

A named numeric vector of discrimination values, one per item.

Details

The point-biserial method is the most widely used CTT discrimination index. The discrimination index D compares the proportion of the upper-scoring group (top 27 percent by total score) who answered the item correctly to the proportion of the lower-scoring group (bottom 27 percent) who answered it correctly. Kelley (1939) demonstrated that the 27 percent cutoff maximizes the difference between extreme groups under a normal distribution of ability.

Interpretive guidelines for D (Ebel & Frisbie, 1991):

  • D >= 0.40: very good item

  • 0.30 <= D < 0.40: good item, possibly subject to improvement

  • 0.20 <= D < 0.30: marginal item, needs improvement

  • D < 0.20: poor item, revise or discard

References

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

Kelley, T. L. (1939). The selection of upper and lower groups for the validation of test items. Journal of Educational Psychology, 30(1), 17-24.

Examples

set.seed(1)
responses <- matrix(
  sample(c("A", "B", "C", "D"), 200, replace = TRUE),
  nrow = 40, ncol = 5,
  dimnames = list(NULL, paste0("Q", 1:5))
)
key <- c("A", "B", "C", "A", "B")
item_discrimination(responses, key)
#>          Q1          Q2          Q3          Q4          Q5 
#> -0.24699867 -0.24699867 -0.23966555 -0.18093672 -0.02105466 
item_discrimination(responses, key, method = "discrimination_index")
#>  Q1  Q2  Q3  Q4  Q5 
#> 0.4 0.4 0.3 0.4 0.3