Mantel-Haenszel DIF effect on the ETS delta scale

Converts a Mantel-Haenszel odds ratio to the delta metric, \(\Delta_{MH} = -2.35 \ln(\alpha_{MH})\), and applies the three-category classification used in operational test review: negligible (A) below 1, moderate (B) from 1 to below 1.5, large (C) at 1.5 and above. The odds ratio is Holland and Thayer's \(\alpha_{MH}\), the reference group's odds of success over the focal group's (as Difmh returns it), so negative delta (\(\alpha_{MH} > 1\)) indicates the item favours the reference group and positive delta favours the focal group.

Usage

morie_dif_delta_mh(or_mh)

Arguments

or_mh: Mantel-Haenszel odds ratio \(\alpha_{MH}\) (reference odds over focal odds), or a vector of them.

Value

A data frame with or_mh, delta_mh, magnitude (A, B or C) and favours (reference, focal or neither).

Details

The classification is a reporting convention, not a significance test; an item may be classified C on a large sample and B on a small one for the same underlying difference, which is why morie_dif_sample_size belongs in the same planning step.

References

Holland, P. W. and Thayer, D. T. (1988) Differential item performance and the Mantel-Haenszel procedure. In H. Wainer and H. I. Braun (eds), Test Validity, 129–145. Lawrence Erlbaum.

Examples

morie_dif_delta_mh(c(1.0, 1.35, 1.9, 0.5))
#>   or_mh   delta_mh magnitude   favours
#> 1  1.00  0.0000000         A   neither
#> 2  1.35 -0.7052458         A reference
#> 3  1.90 -1.5083566         C reference
#> 4  0.50  1.6288959         C     focal