Participants in achievement tests or psychometric scales can be naturally divided into various sub-groups such as gender, race, social economic status, school district, etc. In order to make meaningful comparison between groups, each item in the test/scale should measure the same underlying construct for participants came from different groups.…

Three techniques for assessing the adequacy of correlation matrices for factor analysis were applied to four examples from the literature. The methods compared were: (1) inspection of the off diagonal elements of the anti-image covariance matrix S(to the 2nd) R(to the -1) and S(to the 2nd); (2) the Measure of Sampling Adequacy (M.S.A.), and (3)…

A subject by item matrix of test responses is shown to be a useful heuristic in criterion referenced and norm referenced test analysis, and in the teaching of measurement. The pattern of responses within the matrix provides indications of item interactions, weak deceptors, and conventional test statistics. The strong visual analogy between the…

Multiple matrix sampling (MMS) theory indicates how data may be gathered to most efficiently convey information about levels of attainment in a population, but standard analyses of these data require random sampling of items from a fixed pool of items. This assumption proscribes the retirement of flawed or obsolete items from the pool as well as…

Empirical results are presented as regards the implementation of a latent-trait psychometric model by means of conditional maximum likelihood estimation. Items are scored polychotomously into varying numbers of nominal categories and the test and item characteristic curves and information functions are examined. It is concluded that scoring items…