Summary

In this chapter, we have examined score distributions and how they may differ for CRTs and NRTs. The discussion began with an exploration of the difference between CRT percentage scores and NRT percentile scores. Then there was a brief section on using statistics to describe the central tendency and dispersion of scores. The interpretation of these same statistics was explained so that the reader can understand numerical descriptions of distributions when they are encountered in their own research, in the literature of the field, or elsewhere in this book.

Next, item analysis was discussed. Item facility and discrimination indices, which are traditional NRT item statistics, were defined in terms of how they are calculated and interpreted. Then, Criterion-referenced item analysis techniques were covered. The difference index was defined and two different strategies were explored for gathering appropriate data for a difference index: intervention studies and differential groups studies. Three different cut-score indices were also defined and example calculations were given for the B-index, agreement statistic, and item phi. A discussion presented how to interpret cut-score item statistics and how to select effective Criterion-referenced items when revising a CRT. The chapter ended with a brief discussion of the usefulness of item response theory (including one-, two-, and three-parameter models) for creating equivalent forms and for item banking.