Coefficient alpha and the internal s t r u c t u r e of tests

Abstract

A general formula (a) of which a special case is the Kuder-Richardson 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 sam-ples 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 di-visible 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 un-necessary 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 sub-interpretability of scores is obtained by increasing the firat-facter concentration in any separately-scored subtest and avoiding sub-stantial group-factor clusters within a subtest. Scalability is not a requisite.