Mode: Most Probable Category

The values are relative to the relevant item difficulty.

The category labels are located at the measures where they commence to be the most probable observations. Omitted categories are never most probable. ^ indicates location of category peak probability. (^) indicates point at which extreme category becomes very probable.

Median: Rasch-Thurstone Threshold

The values are relative to the relevant item difficulty.

The category labels are located at the measures where there is the same probability (0.5) of being rated below that category as there is of being rated in that category or above. Conceptually, each category label is at the left-hand end of its "zone" on the variable. ^ indicate the mid-points of each zone. (^) indicates a conceptual mid-point of the infinitely long extreme zones.

Mean: Expected Score

The values are relative to the relevant item difficulty.

The mean values are usually more dispersed than the median, and the median than the mode.

The category labels are located at the measures where the expected values become closer to that score than the preceding score, i.e., at the half score-points. ^ indicates the locations where the category score is the expected score. (^) indicates the location at which the expected score is 0.25 score points away from the extreme category score.

the "mean" values below Table 8.2 (shown above) are the "scale" values on the right side of Table 6.0, and are the "Expectation" measures in Table 8.1. They answer the question: if we had 1,000 people at a particular measure relative to the item difficulty, what would we expect their average (mean) rating to be?

Measr: Measure relative to item difficulty

The scale of relative measures, e.g., persons relative to an item. The local origin is the mean of the Rasch-Andrich thresholds (step calibrations) or as determined by the anchored categories.