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.

中文翻译：

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对抗情况下的物品反应功能

二进制测试的主要特征是项目响应函数（IRF），它表示具有能力a的被测对象（OUT）成功克服困难d的测试项目（TI）的概率P（d，a）。每个特定的测试都需要自己定义TI难度和OUT能力，并具有自己的P（d，a）描述上述“成功”的可能性。这是从统计工程不同领域的几个例子中得到证明的。一个共同的特征是它们都与“对抗”情况有关，在这种情况下，一侧的“成功”可以被正式视为对另一侧的“损失”。在这种情况下，能力和难度是同一枚硬币的两个可互换面，并且对应的IRF是互补的，即，P（d，a）= 1-  P（a，d），以及此属性施加的所有后果和限制。一项研究表明，可行的IRF家族是有限的，并且具有许多有趣的属性，本文对此进行了讨论。提供的分析应有助于避免在有关IRF的决策中出现错误，以充分描述所研究的测试。