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Item response function in antagonistic situations
Author(s) -
Turetsky Vladimir,
Steinberg David M.,
Bashkansky Emil
Publication year - 2020
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2539
Subject(s) - property (philosophy) , test (biology) , function (biology) , object (grammar) , computer science , feature (linguistics) , basis (linear algebra) , binary number , mathematics , algorithm , artificial intelligence , arithmetic , evolutionary biology , biology , paleontology , philosophy , linguistics , geometry , epistemology
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.