Beyond matching on the mean in developmental disabilities research

The matching of groups is a traditional way to control for confounding variables in developmental disability research. The equivalency of means across groups is routinely checked for these variables, but not the homogeneity of their variances or the shapes of their distributions. In the present paper, it is argued that group matching can go seriously wrong unless it directly confronts the distributional concerns by the use of well-known statistical indices and very simple graphical displays of the distributions. The question of the equivalency of item response profiles is also addressed since two participants or two groups of participants can obtain the same overall score on the matching variable by passing different items. In this case, the matching cannot be considered satisfactory because of poor concordance between the molar (overall score) and molecular (item scores) levels of matching. Angoff's Delta plot method, a statistical approach for detecting differential item functioning across small groups is described. It is promising as a simple way to prove whole test/individual item
correspondence and, in addition, a useful tool for making post-hoc statistical analyses at the item level on the dependant variables.