Item response function in antagonistic situations. (4th May 2020) - Turetsky, Vladimir; Steinberg, David M.; Bashkansky, Emil
Abstract: The main characteristic of a binary test is the item response function (IRF) expressing the probability P ( d, a ) of an object under test (OUT), possessing ability a, to successfully overcome the test item (TI) of difficulty d . Each specific test requires its own definitions of TI difficulty and OUT ability and has its own P ( d, a ) describing the probability of "success" mentioned above. This is demonstrated on the basis of several examples taken from different areas of statistical engineering. A common feature is that they all relate to "antagonistic" situations, in which the "success" of one side may formally be considered as a "loss" to the opposite side. For such situations ability and difficulty are two interchangeable sides of the same coin and the corresponding IRFs are complementary, that is, P ( d, a ) = 1 − P ( a, d ), with all consequences and restrictions imposed by this property. A study shows that the family of feasible IRFs is limited and has a number of interesting properties, which are discussed in the article. The analysis provided should facilitate avoiding errors in decisions about an IRF adequately describing the studied test.