The implications of a mathematical model of test scores are explored where the data are limited to a random sample of items without replacement from an indefinitely large population or item domain in which items are scored either zero or one. The purpose is to obtain an unbiased estimate of a student's proportion of items correct in the item…

The increased use of criterion-referenced statewide testing programs is an outgrowth of the need for more diagnostic information for planning and decision making than is provided by norm-referenced programs. There remains, however, a need for state agencies to compare the results of local districts to a variety of comparison groups for the purpose…