OPTIMAL NUMBER OF OPTIONS: AN INVESTIGATION OF THE ASSUMPTION OF PROPORTIONALITY

One assumption common to all models for determining the optimal number of options per item (e. g., Lord, 1977) is that total testing time is proportional to the number of items and the number of options per item. Therefore, under this assumption given a fixed testing time, the test can be shortened or lengthened by deleting or adding a proportional number of options. The present study examines the validity of this assumption in three tests which were administered with 2, 3, 4, and 5 options per item. The number of items attempted in the first 10 and 15 minutes of the testing session and the time needed to complete the tests were recorded. Thus, the rate of performance for both fixed time and fixed test length was analyzed. A strong and consistently negative relationship between rate of performance and the number of options was detected in all tests. Thus, the empirical results did not support the assumption of proportionality. Furthermore, the data indicated that the method by which options are deleted can play a role in this context. A more realistic assumption of generalized proportionality, proposed by Grier (1976), was supported by the results from a Mathematical Reasoning test, but was only partially supported for a Vocabulary and a Reading Comprehension test.