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Bias and Error in Multiple-Choice Tests

Published online by Cambridge University Press:  01 January 2025

C. Horace Hamilton
C. Horace Hamilton*
Affiliation:
North Carolina State College
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Abstract

A formula for estimating real scores on a multiple-choice test from a knowledge of raw scores is derived. This formula does not involve the assumption of a binomial distribution of real scores as does the Calandra formula. Other important formulas derived show: the variance of real scores in terms of the variance of raw scores and the correlation between real scores and raw scores. If the variance of real scores (or of raw scores also) is binomial, the regression of real scores on raw scores is linear; but, otherwise the regression is curvilinear. Yet the linear estimating formula is a close approximation to the curvilinear relationship. Factors affecting the regression of real scores on raw scores and the correlation coefficient are: (1) the number of choices per question; (2) the number of questions answered; (3) the ratio of the average group raw score to the variance of raw scores.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 2 , June 1950 , pp. 151 - 168
Copyright
Copyright © 1950 Psychometric Society

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References

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