Predetermination of test weights

Derivations are presented relating the length of a test to its weight in a composite. Tests of varying length are constructed so that their weights will be of predetermined magnitudes, and the results compared with expectations. Weighting schemes involving standard deviations of raw scores and of true scores are compared. An important secondary derivation is presented from which it is possible to estimate test reliability knowing only the relative length of a test, its shortened form, and the standard deviation of each.