Difficulty Factors and Non‐linear Factor Analysis 1

The performances of a group of children (Group C) and a group of adults (Group A) on 12 sub‐tests formed from Raven's Progressive Matrices Test (1947) have been separately factor analyzed. In the Group C results, the second factor can be recognized as a difficulty factor , but the corresponding factor in Group A is not significantly related to the difficulty of the sub‐tests. When the analysis is carried further by methods described previously, both sets of data can readily be accounted for by non‐linear regression functions relating the sub‐tests to a single factor. The difficulty factor in Group C is shown to correspond to differences in curvature of the regression functions. These differences in curvature correspond in turn to the expectation that an easy test will discriminate best at the lower end of an ability continuum and a difficult test at the higher end. In terms of the non‐linear treatment, the curves for Group A form a plausible continuation of the curves for Group G.