Presents both logical and empirical evidence to illustrate that the conventional scoring algorithm for ranking tasks significantly underestimates the initial level of group ability and that Slevin's alternative scoring algorithm significantly overestimates the initial level of ability. Presents a modification of Slevin's algorithm which authors…

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…