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Scoring Formulas and Probability Considerations

Published online by Cambridge University Press:  01 January 2025

Alexander Calandra
Alexander Calandra*
Affiliation:
Department of Chemistry, Brooklyn College
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Abstract

Bayes' theorem of inverse probability is made the basis of a general equation for scoring objective examinations. The equation so obtained is evaluated by assuming a binomial distribution of examinee knowledge and guessing tendency. A graphical illustration of the application of this equation to a hypothetical test situation is presented. The limitations inherent in the use of Bayes' theorem make it inadvisable to recommend the practical use of the equation unless future experimental evidence indicates an increase in scoring validity which more than compensates for the increase in scoring difficulty.

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 1 , February 1941 , pp. 1 - 9
Copyright
Copyright © 1941 Psychometric Society

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References

* The use of Bayes’ theorem as a basis for scoring formulas was suggested by the writer in his unpublished doctorate dissertation at the School of Education of New York University.

† Fisher, A. The mathematical theory of probabilities. New York: The MacMillan Co., 1930.