Differential Distractor Functioning

DIF compares groups on the probability of answering an item correctly, conditional on ability — it works with right/wrong responses. DDF compares groups on the probability of selecting each individual option, including the distractors. DDF therefore uses more of the response information and can detect and explain bias that DIF misses, for instance when a particular wrong answer differentially attracts one group while the overall correct-answer rate looks similar. DDF is best seen as a finer-grained, diagnostic complement to DIF. See the related Differential Item Functioning entry.

Yes. If two distractors function differently across groups in offsetting directions, the net effect on the probability of a correct response can be small, so the item shows little or no DIF even though its options behave unfairly. DDF detects these compensating distractor effects. Conversely, examining distractors when DIF is present often reveals which option drives the bias. This is precisely why DDF is valued both for detecting otherwise-hidden bias and for explaining DIF.

Because DDF spreads each group's responses across all the options rather than just two categories (correct/incorrect). Estimating the conditional selection of each distractor at each ability level, for each group, divides the data into many more cells, so reliable estimation requires more examinees per group. Sparse distractor-by-group-by-ability cells produce unstable odds ratios, which is why adequate sample size in both reference and focal groups is an important precondition for trustworthy DDF analysis.