IN DEFENCE OF UNIDIMENSIONALIIY

In commenting on my review (Lumsden, 1961) of methods of constructing unidimensional tests, Banta (1962) claims that for many purposes it is unnecessary and, indeed, undesirable that psychological tests should be unidimensional. It is true that for predictive purposes, particularly with multiple criteria, a heterogeneous tesr will usually be preferable since it is more likely to cover relevant aspects of the criteria and is cheaper to construct than a unidimensional test. For measurement, however, it seems essential that the scores should have an unequivocal relation to the items. If the same test score can be obtained in systematically different ways, then the interpretation of the scores as measurements will be impossible (McNemar, 1946). Banta's statement that a complex test is required for a complex trait is irrelevant. It has been shown (Loevinger, 1948; Lumsden, 1957) that a unidimensional test may be factorially quite complex when considered in a space external to the item intercorrelations. Banta argues that heterogeneous tests are essential for the suppression of biasing components such as response sets. Cattell (personal communication) has made a similar sugjicst~on for the development of factorially pure tests. This argument is based on a confus~on between tests as administrative unities and tests as conceptual unities. Scores on a heterogeneous test may, and for theoretical purposes should, be regarded as unweighted sums of scores on component unidimensional tests. The systematic approach to the suppression of, say, the acquiescence response set would appear to be best directed to developing separate unidimensional tests for "true" and "false" items and then combining them with appropriate weights. If the two tests are not unidimensional, then the desired suppression could not take place, except by the happiest of accidents, because different sets of items will be measuring different combinacions of content and acquiescence factors and the meaning of the scores (and of weighted or unweighted sums or differences of scores) will remain equivocal. To illustrate the terrible difficulties of what may be termed auto-suppression consider a two item test consisting of one "true" and one "false" item with the same content. It is clear that the set component will only be suppressed by taking the total score if the weights for the set component in the two items are equal. This is an extremely onerous restriction and nothing in the usual procedures for test construction can guarantee that it will hold. If there are several "true" and "false" items with differing relarive proportions of content and set variance, the problem becomes extremely complex. If, however, the "true" set and the "false" set can each be shown to be unidimensional then the problem reduces to that of finding a weighting factor. Unfortunately this appears to require information external to the item analysis and the possession of this information would eliminate the necessity for auto-suppression. REFEIlENCES