Single-Facet Designs

Abstract

Throughout this chapter it is assumed that the universe of admissible observations and the universe of generalization involve conditions from the same single facet, usually referred to as an item facet. Also, it is usually assumed that the population consists of persons. For a single-faceted universe, there are two designs that might be employed in a G study: the p × i or the i:p design, where the letter p is used to index persons (or examinees), i indexes items, “×” is read “crossed with,” and “:” is read “nested within.” For the p × i design, each person is administered the same random sample of items. For the i:p design, each person is administered a different random sample of items. Similarly, there are two possible D study designs: p × I and I:p, where uppercase I is used to emphasize that D study considerations involve mean scores over sets of items.