RASCH’S MODEL AS A GAME MODEL

The article describes the application of the famous Rasch’s model of testing as a game model, in which the participants fulfill the tasks that play an equal role. The adequacy of the Rasch’s model is confirmed by the example of A.Elo’s chess classification. It gives «a game» justification of famous method of primary numbers, testing’s latent parameters method according to testing observation results, which has the highest speed calculation. In the beginning of the article the basic principles of A.Elo’s chess classification are presented (1963-1970 years). We consider the mathematical model of two chess players meeting in one game. The adequacy of this model is confirmed by accumulated statistical material, expressed in Elo’s table. The built model coincides with the Rasch’s model for solving test tasks. This coincidence makes it possible to associate the testing as a game, in which the equal «players» are the participants of the testing and test tasks. To build a «game» version of Rasch’s model the author introduces the concept of qualification level of the participant (the participant of testing is either the student solving tasks or test task). Basic properties of qualification level are identified. By means of these properties the main formulas of mathematical model of testing are proved. In particular, a formula is derived to calculate the probability of decision by the participant of testing with a specific qualification level of test task with a specific difficulty level. Further we considered different units of measurement of qualification level: game logit, logit and percent logit. Moreover, the solid change ranges for the units are established. The article considers the two-parameter Birnbaum’s model for testing. One of the variants of this model is used in Elo’s chess classification. Today the primary application of the mathematical Rasch’s model is electronic testing of various levels, e.g. local Olympiads or the Unified State Examination. The paper deals with the methods of calculation for the latent parameters of testing: qualification levels of the participants and difficulty levels of test tasks. This method is based on transformation of primary numbers that has the highest rate of calculation. It gives a «game» justification of primary numbers method by means of two additional players: «the average player» and «test».

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