Two parallel forms of a test are considered "equated" when for a single group of examinees the standard deviations on the two forms are equal and the means on the two forms are equal. Since present test construction procedures are not sufficiently precise to produce forms with equivalent score scales, it is necessary to conduct an equating experiment for the purpose of collecting data for use in adjusting the initial raw score scales. Although the definition of equated score scales is given in terms of equivalence of the first two moments for a single group of examinees, the tests to be equated need not be administered to the same examinees. This paper considers two types of experiments in which the tests to be equated are administered to different examinees. Both types of experiments can be characterized as follows: If two tests (X and Y) are to be equated, X is administered to the first and Y to the second of a pair of samples. In addition, a third test (V) is administered to both samples. V may be either a separate test from X and Y or a number of items contained in both X and Y. In either case, V may be considerably shorter than X and Y. The two types of experiments are identical with respect to these test administration procedures, but they differ with respect to the assumptions made about the characteristics of the two samples of examinees.