An Improved Liu’s Ordering Theory Based on Empirical Distributive Critical Value

Abstract

Since the Ordering Theory (OT) has only considered the item ordering relationship rather than the item non-independence, and the Item Relational Structure theory (IRS) has only focused on the item non-independence but no thought for the item ordering relationship, the first author of this paper proposed his improved theory, called Liu’s Ordering Theory (LOT), which has considered both the item ordering relationship and item non-independence. However, all of the critical values of the ordering index of above-mentioned three theories are subjectively fixed numbers. In this paper, for overcoming the lack of statistical meaning, an empirical distributive critical value of the ordering index based improved LOT theory, denoted as ILOT, was proposed, this new theory is more reasonable and useful than OT, IRS and LOT. Furthermore, by using the new method ILOT, based on the theory of the ideal test proposed by the first author of this paper, we can construct the validity index of item ordering structure of any group of examinees to compare the performances of any different groups of examinees.