Order statistics and item bank analysis in computer adaptive testing

This paper addresses the problem of items exposure rate in computer adaptive testing and its relation with the structure of an item bank. An item is a structure defined by real and/or virtual components possibly containing text, image, audio and/or video elements, which are useful to build a context where a question is made about, and of diverse elements or mechanisms for information acquisition to provide an answer to this question. Every item has an associated difficulty that depends on how easy is to answer the question about the defined context. An item bank is a deposit of this kind of structures and, in this paper, the item bank structure is defined in terms of statistical indexes arising from the onedimensional Order Statistics Theory, namely, nearest neighbor index and the standard variate of normal curve; and another one from the concept of compactness of intervals of real numbers. In this sense, the work talks about items difficulty exposure rate assuming that the item bank is, in fact, defined by a finite discrete set of items difficulties. Therefore, the emphasis is given on the items difficulty and it is assumed that the number of items per difficulty in the item bank is unlimited. The experimental results are obtained through a simulation environment that takes into account the definition of the structure of an item bank, the definition of a testing subject and the definition of an item administration context. Therefore, the results are mainly experimental rather than theoretical, although the validation of the simulation environment is based on theoretical results of other authors in the field.