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 universe. The study of item responses plays no role in the test development process, since item difficulty will vary with instruction, and consideration of item-test correlation would bias the item sampling procedure. Three major emphases are: (1) the association or equivalence between pairs of items; (2) the sensitivity of items to instruction, which may also be a function of instructional effectiveness; and (3) the stability of an item after instruction. Item scores are assumed to be a function of a constant plus a value that characterizes an individual, and the error of measurement is analyzed in two terms. The development of the theory is concerned with data summarized meaningfully in two-by-two or fourfold tables such as the data for a Phi coefficient. There is an annotated list of over 100 selected journal articles plus a list of additional bibliographical references. (CTM)