When to adjust for Differential Item Functioning

The symptom of DIF is that a "focal" group does better (or worse) on a particular item than a "reference" group, given those groups' performance on the rest of the test. When DIF exists, it prompts an investigation into the nature of the construct for the focal group (leading to test revision), and a re-estimation of respondents' measures.

Since any two samples will inevitably produce slightly different estimates of the difficulty of any item, an important aspect of DIF analysis is to screen out trivial or unreplicable item calibration differences across groups. There are three hurdles to establishing DIF:

1) Is the DIF statistically significant? A significance test between the two item calibrations is often the only screening applied. It is useful because it can save the researcher from taking seriously large calibration differences that have little supporting data. If there are only 10 members of a focal group, and a dichotomous item is reported as 1.0 logits harder for them, is there a statistical case for DIF? No, because the S.E. of 1.0 logits with only 10 replications is at least 0.6 logits, i.e., t<1.6. But DIF analysis is asymmetrical. Lack of statistical significance makes us skeptical that real DIF exists. Statistical significance does not assure us of it. "The most commonly occurring weakness in the application of [statistical] methods is undue emphasis on tests of significance." (Yates 1964).

2) Does the DIF have substantive implications? Are the different item calibrations, obtained from different groups, substantively the same, so that either measure leads to the same conclusions? It may be that dichotomous item 23 calibrates .1 logits easier for 10,000 girls than for 10,000 boys. Is there a case for a DIF adjustment? It might appear so, because the SE of 0.1 logits is statistically .03 logits. But the score impact of this DIF is, at most, .03 score points for an on-target item, .01 for an off- target item. Since such a small difference would not change our conclusions about group performance, it has no general repercussions. At worst, less than 3% of the focal group are penalized one point. Most of these would be at the ability level of the item's difficulty. If the item is far from a cut-point, then even real DIF would have no practical consequence.

But is this fair to everyone? If the DIF is taken as against individual boys, a .05 logit adjustment up in this item for boys may lift some boys above pass-fail. On the other hand, if the DIF is taken as in favor of individual girls, a .05 logit adjustment down in this item for girls may drop some girls below pass-fail. Since the calibration difference is so small, there is no way of knowing which, if either, is a "correct" adjustment. Further, once adjustment is embarked on, fairness mandates that the procedure be repeated for every other item. This leads to endless minuscule changes in measures and pass-fail decisions, and makes the final pass-fail decisions ever more arbitrary.

3) Is the DIF real or accidental? A single statistical test cannot differentiate between a real effect and an accident. A run of 10 coin-tosses producing 10 heads is unlikely, but does not prove the coin is biased. In advance of test administration, expert screening committees struggle in vain to identify and eliminate items that will manifest DIF. Once told that an item exhibits DIF against a focal group, however, it is easy for experts to imagine why this "must" be so. In the end, the "reality" of most statistically-detected DIF remains open to dispute.

The best test for DIF is "Does it replicate?" When the focal group is split in various ways, random or systematic, does the item continue to exhibit DIF in the same way for each subgroup? If so, the DIF shows evidence of being real. If not, it may be just an accident of sampling.

When DIF meets all three criteria there is reason to regard the DIF item as working like two "different" items. The data set may be restructured so that there is one representation of the item for the reference group and another for the focal group. Measures derived from this reconfigured data will be automatically adjusted for the DIF of that item.

Yates Frank (1964) Sir Ronald Fisher and the Design of Experiments. Biometrics 20:307-321

When to adjust for Differential Item Functioning. Du Y, Yates F. … Rasch Measurement Transactions, 1995, 9:1 p.414

MOMS Program. … Rasch Measurement Transactions, 1995, 9:1 p.413

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