Discovering patterns of achievement in Hong Kong students: An application of the Rasch measurement model

Abstract

Researchers have warned of the need to identify accurately students who are underachieving in Hong Kong, particularly among the gifted group. When comparing the relative effectiveness of three methods for estimating the proportion of underachievement, the absolute split method, using an arbitrary upper and lower limits for estimates of both performance and ability, is more useful for identifying gifted underachievers than the simple difference method (where standardized performance scores are subtracted from standardized ability scores) or the regression method. In contrast, the latter two methods are more useful for identifying underachievers at all levels of ability. All three methods, however, depend on measurements that are invariant, unidimensional and additive. With the advent of modern measurement theory using Rasch measurement models, it is now possible to satisfy these requirements. In this study, a sample of Primary 5 students in Hong Kong (n = 957) were asked to complete a test of mathematical achievement and the Ravens Progressive Matrices test in order to estimate the proportion of students who are underachieving at all levels of ability. Measurement scales were created using Rasch models for partial credit and dichotomous responses for each variable, respectively, and students placed on each scale according to their responses. Because the results are based on measurement scales that are invariant between persons, the identification of underachievement in these students across all levels of ability can be regarded as objective rather than sample dependent.