DIF p-difference per item — Difpst • rmorie

Formula: p_focal - p_reference per item

Usage

Difpst(X, group, focal = 1)

Arguments

X: An n x k matrix of 0/1 item responses.
group: Group label per examinee.
focal: Label of the focal group.

Value

List with estimate, p_diff, p_focal, p_reference, mh_alpha, mh_delta, ets, flagged, n_focal, n_reference, k, method.

Details

The raw difference in proportion correct. It is not by itself evidence of item bias, because it confounds impact (a real difference in ability) with DIF – which is why the ETS rules also use the Mantel-Haenszel odds ratio on the delta scale, -2.35 log(alpha_MH), reported here alongside. ETS classes: A below 1, B up to 1.5, C above.

References

Holland & Wainer (1993), Differential Item Functioning, Erlbaum; Dorans & Holland (1993), ibid., ch. 3.

Examples

set.seed(11)
X <- matrix(rbinom(200 * 4, 1, 0.6), 200, 4)
grp <- rep(1:2, each = 100)
X[grp == 1, 2] <- rbinom(100, 1, 0.3)       # item 2 harder for the focal group
round(Difpst(X, grp, focal = 1)$p_diff, 2)
#> [1]  0.18 -0.16  0.02  0.02