Examinees are stratified on the matching total score; each stratum
gives a 2 x 2 table of group by correctness and the common odds ratio
pools them. The MH chi-square uses the hypergeometric mean and
variance of the reference-correct cell with the continuity
correction, and the ETS delta scale rescales the log odds ratio.
Usage
Irtmh1(X, group, total_score, alpha = 0.05)
Arguments
- X
Matrix of 0/1 item responses, one row per examinee.
- group
Length-n vector, 0 reference and 1 focal.
- total_score
Length-n matching variable forming the strata.
- alpha
Significance level for the MH chi-square.
Value
List with estimate (largest |Delta|),
odds_ratio, chisq, p_value, delta,
ets_class, flagged, n, method.
Details
Formula: alpha_MH = sum_m A_m D_m / n_m / sum_m B_m C_m / n_m;
Delta = -2.35 log(alpha_MH).
References
Holland and Thayer (1988), Differential item performance
and the Mantel-Haenszel procedure, in Wainer and Braun (eds), Test
Validity, Lawrence Erlbaum, pp. 129-145.
