The Relationship between Factorial Composition of Test Items and Measures of Test Reliability

For continuous distributions associated with dichotomous item scores, the proportion of common-factor variance in the test, H 2 , may be expressed as a function of intercorrelations among items. H 2 is somewhat larger than the coefficient a except when the items have only one common factor and its loadings are restricted in value. The dichotomous item scores themselves are shown not to have a factor structure, precluding direct interpretation of the Kuder-Richardson coefficient, r K-R , in terms of factorial properties. The value of r K-R is equal to that of a coefficient of equivalence, H 2 Φ , when the mean item variance associated with common factors equals the mean interitem covariance. An empirical study with synthetic test data from populations of varying factorial structure showed that the four parameters mentioned may be adequately estimated from dichotomous data.