Some properties of ipsative score matrices and their relevance for some current interest tests

Abstract

Normative and ipsative deviational and ordinal scores are defined within a subject's X tests matrix. In a more generalized treatment and using simpler algebra than in Clemans' (1956) analysis it is shown that: (a) With deviational ipsative scores, (i) test variances and covariances are predictable from their normative equivalents; and (ii) ipsatization partially or totally removes normative first centroid factor variance and decreases positive but increases negative test validity covariance. (b) With both deviational and ordinal ipsative scores, both (i) the sums of the columns of the inter-test covariance matrix; and (ii) the average test validity covariance are zero. Similar conclusions apply to subject variances and covariances only when the ipsative score matrix is doubly centred. That investigators need to be cautious in the correlational use of ipsative scores is illustrated with some current interest tests.