The selection of an appropriate booklet design is an important element of large-scale assessments of student achievement. Two design properties that are typically optimized are the "balance" with respect to the positions the items are presented and with respect to the mutual occurrence of pairs of items in the same booklet. The purpose…

Multiple matrix designs are commonly used in large-scale assessments to distribute test items to students. These designs comprise several booklets, each containing a subset of the complete item pool. Besides reducing the test burden of individual students, using various booklets allows aligning the difficulty of the presented items to the assumed…