Calculating Balanced Incomplete Block Design for Educational Assessments.

A popular design in large-scale educational assessments is the balanced incomplete block design. The design assumes that the item pool is split into a set of blocks of items that are assigned to assessment booklets. This paper shows how the technique of 0-1 linear programming can be used to calculate a balanced incomplete block design. Several structural as well as practical constraints on this type of design are formulated as linear (in)equalities. In addition, possible objective functions to optimize the design are discussed. The technique is demonstrated using an item pool from the 1996 Grade 8 Mathematics National Assessment of Educational Progress Project. (Contains 2 tables and 16 references.) (Author/SLD)