The problem of dimensionality with respect to Raven's Advanced Progressive Matrices (APM) specifically and, more generally, "g" or fluid intelligence, has been a long-standing issue. The present article reports two studies examining the dimensionality of both the original Set II of the APM (n = 506) and a short form (n = 644), using principal…

Order Analysis is a multidimensional scaling (MDS) technique for determining order among items. This paper reviews articles by different authors describing various components of ordering theory. A common nomenclature is constructed to link together the various ideas and is applied to a fairly simple set of data. Topics discussed include a more…

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…

Geometric approaches to representing interrelations among tests and items are compared with an additive tree model (ATM), using 2,644 examinees and 2 other data sets. The ATM's close fit to the data and its coherence of presentation indicate that it is the best means of representing tests and items. (TJH)

Various methods used to assess the content of a test are reviewed, and a new procedure designed to improve on these methods is presented. The two tests considered are a professional licensure examination, the auditing section of the Uniform Certified Public Accountant Examination, and an educational achievement test, a nationally standardized…