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Tests and intervals in multiple choice tests: A modification of the simplest classical model
Author(s) -
Andrés A. Martín,
Castillo J. D. Luna
Publication year - 1989
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1989.tb00914.x
Subject(s) - multiple choice , test (biology) , set (abstract data type) , estimator , mathematics , selection (genetic algorithm) , statistical hypothesis testing , interval (graph theory) , type (biology) , mathematical economics , statistics , mathematics education , computer science , artificial intelligence , combinatorics , significant difference , paleontology , ecology , biology , programming language
When a multiple choice test is carried out, each student is set the same series of questions composed of two or more alternatives, only one of which is correct, and from which he or she must choose only one. The simplest and most common criterion for deciding what a student knows is based on a sole and minimum quota for all the students of the total number of right answers; this criterion derives from the assumption that the student, when he or she does not know the correct answer to a question, answers any of the possible alternatives with equal probability. In this paper, the authors show that this method may be unsatisfactory if the student is unable to imitate random selection, and they put forward an alternative model which allows one to find an estimator for the student's level of knowledge that depends on the sum of the proportions of correct answers of each type and on the total number of each type which the student gives. Likewise, they give a hypothesis test for verifying the model, two methods for finding confidence intervals for the student's level of knowledge, and three hypothesis tests for awarding a mark for it. Numerical calculations show how inefficient the usual multiple choice tests are (100 or 150 questions with five alternative answers each) for ascertaining the student's level of knowledge.