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Multiple choice tests: Power, length and optimal number of choices per item
Author(s) -
Andrés A. Martín,
Castillo J.D. Luna
Publication year - 1990
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.2044-8317.1990.tb00926.x
Subject(s) - set (abstract data type) , mathematics , value (mathematics) , multiple choice , sample (material) , sample size determination , power (physics) , statistics , mathematical economics , discrete mathematics , calculus (dental) , computer science , significant difference , medicine , chemistry , physics , dentistry , chromatography , quantum mechanics , programming language
In an earlier paper (Martín Andrés & Luna del Castillo, 1989), three statistical tests for assigning a mark for a student in multiple choice tests were set out. In the present paper, the authors give the power of all three tests, for the purpose of selecting the best one for each particular case. They also give the formulae for determining the minimum number of questions (sample size) for an examination with k alternatives (only one of which is the correct answer), to satisfy given requirements about the number of students one wishes to pass or fail undeservedly (formulae which are also valid for giving any other mark, or for deciding the student's level of knowledge with given exactitude). Finally, the authors prove that, under certain very general conditions, it is better to set questions with k = 3 alternative answers, whilst under another criterion, the value k = 2 is to be preferred. The results are compared with the equivalent classic methods.