The problem of obtaining designs that result in the most precise parameter estimates is encountered in at least two situations where item response theory (IRT) models are used. In so-called two-stage testing procedures, certain designs that match difficulty levels of the test items with the ability of the examinees may be located. Such designs…

A test theory using only ordinal assumptions is presented, based on the idea that the test items are a sample from a universe of items. The sum across items of the ordinal relations for a pair of persons on the universe items is analogous to a true score. (SLD)