A Simplified Method for Predicting Pattern Match Ratio

Cognitive diagnostic test design (CDTD) has a direct impact on the pattern match ratio (PMR) of the classification of examinees. It is more helpful to know the quality of a test during the stage of the test design than after the examination is taken. The theoretical construct validity (TCV) is an index of the test quality that can be calculated without testing, and the relationship between the PMR and the TCV will be revealed. The TCV captures the three aspects of the appeal of the test design as follows: (1) the TCV is a measure of test construct validity, and this index will navigate the processes of item construction and test design toward achieving the goal of measuring the intended objectives, (2) it is the upper bound of the PMR of the knowledge states of examinees, so it can predict the PMR, and (3) it can detect the defects of test design, revise the test in time, improve the efficiency of test design, and save the cost of test design. Furthermore, the TCV is related to the distribution of knowledge states and item categories and has nothing to do with the number of items.