A general formula (a) of which a special case is the KuderRichardson coefficient of equivalence is shown to be the mean of all split-half coefficients resulting from different splittings of a test. is therefore an estimate of the correlation between two random samples of items from a universe of items like those in the test. ~ is found to be an appropriate index of equivalence and, except for very short tests, of the first-factor concentration in the test. Tests divisible into distinct subtests should be so divided before using the formula. The index ~j, derived from a, is shown to be an index of inter-item homogeneity. Comparison is made to the Guttmau and Loevinger approaches. Parallel split coefficients are shown to be unnecessary for tests of common types. In designing tests, maximum interpretability of scores is obtained by increasing the firat-facter concentration in any separately-scored subtest and avoiding substantial group-factor clusters within a subtest. Scalability is not a requisite. I. Historical Resum~Any research based on measurement must be concerned with the accuracy or dependability or, as we usually call it, reliability of measurement. A reliability coefficient demonstrates whether the test designer was correct in expecting a certain collection of items to yield interpretable statements about individual differences (25).Even those investigators who regard reliability as a pale shadow of the more vital matter of validity cannot avoid considering the reliability of their measures. No validity coefficient and no factor analysis can be interpreted without some appropriate estimate of the magnitude of the error of measurement. The preferred way to find out how accurate one's measures are is to make two independent measurements and compare them. In practice, psychologists and educators have often not had the opportunity to recapture their subjects for a second test. Clinical tests, or those used for vocational guidance, are generally worked into a crowded schedule, and there is always a de-*The assistance of Dora Damrin and Willard Warrington is gratefully acknowledged. Miss Damrin took major responsibility for the empirical studies reported. This research was supported by the Bureau of Research and Service, College of Education. 297 298 PSYCHOMETRIKA sire to give additional tests if any extra time becomes available. Purely scientific investigations fare little better. It is hard enough to schedule twenty tests for a factorial study, let alone scheduling another twenty just to determine reliability.This difficulty was first circumvented by the invention of the splithail approach, whereby the test is rescored, half the items at a time, to get two estimates. The Spearman-Brown formula is then applied to get a coefficient similar to the correlation between two forms. The split-half Spearman-Brown procedure has been a standard method of test analysis for forty years. Alternative formulas have been developed, some of which have advantages over the original. In the course of our development, we shall re...

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Procedures previously recommended by various authors for the estimation of "change" scores, "residual" or "basefree" measures of change, and other kinds of difference scores are examined. A procedure proposed by Lord is extended to obtain more precise estimates, and an alternative to the Tucker-Damarin-Messick procedure is offered. A consideration of the purposes for which change measures have been sought in the past leads to a series of recommended procedures which solve research and personnel-decision problems without estimation of change scores for individuals.

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N o man can be acquainted with all of psychology today, as our convention program proves. The scene resembles that of a circus, but a circus grander and more bustling than any Barnum ever envisioned-a veritable week-long diet of excitement and pink lemonade. Three days of smartly paced performance are required just to display the new tricks the animal trainers have taught their charges. We admire the agile paper-readers swinging high above us in the theoretical blue, saved from disaster by only a few gossamer threads of fact, and we gasp as one symposiast thrusts his head bravely between another's sharp toothed jaws. This 18-ring display of energies and talents gives plentiful evidence that psychology is going places. But whither?In the simpler days of psychology, the presidential address provided a summing-up and a statement of destination.