Wright Map Analysis

Because the Rasch model defines the probability of a correct response through the difference between person ability and item difficulty, both must be expressed in the same units (logits) for that difference to make sense. This shared metric is the model's defining feature, and it is what makes the map possible: when a person's location equals an item's location, the difference is zero and the success probability is exactly one-half. The map simply visualizes this common scale, with the alignment of people and items carrying direct probabilistic meaning.

It signals poor test targeting. If items pile up at easy locations while many examinees sit higher on the scale, those higher-ability students are measured imprecisely because few items challenge them — the test provides little information where it is needed. Conversely, items far above the persons make the test too hard. Good targeting places items across the range where examinees actually fall, and the Wright map is the standard way to detect and correct such mismatches by adding or removing items.

They are tightly linked in Wilson's framework. A construct map is the theorized ordering of increasingly sophisticated understanding; the Wright map provides the empirical counterpart, showing the actual difficulty order of items designed to capture those levels. Comparing the two validates the progression: if items meant to tap higher levels indeed sit higher on the Wright map, the empirical evidence supports the theorized order. Mismatches prompt revision of the items, the progression, or the scoring. See the related Learning Progressions Analysis entry.