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Simplified Formulas for Item Selection and Construction

Published online by Cambridge University Press:  01 January 2025

Dorothy C. Adkins  and
Herbert A. Toops
Dorothy C. Adkins
Affiliation:
The University of Chicago
Herbert A. Toops
Affiliation:
The Ohio State University
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Abstract

The formula for the Pearson correlation coefficient of a dichotomous variable with a multiple-categoried variable is simplified for computational purposes by effecting in the multiple-categoried variable two types of arbitrary distributions: (1) rectangular and (2) proportional to binomial expansion coefficients. The formulas which result are convenient for the selection of test items and are applicable to the objective estimation of the comparative merits of the alternatives in multiple-choice test items. It is shown that the authoritative answer should have a high positive criterion coefficient, while the omissions and several wrong-answer alternatives should each have low (algebraic) negative criterion coefficients.

Type
Original Paper
Information
Psychometrika , Volume 2 , Issue 3 , September 1937 , pp. 165 - 171
Copyright
Copyright © 1937 The Psychometric Society

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References

* With the appropriate assumptions, the modifications to be presented are equally applicable to the biserial correlation coefficient, as well as to other simple item indices, and they a r e adapted to either an external or an internal criterion.

* Such a restriction is of value regardless of the use of automatic equip~nent, such as the Hollerith tabulating machinery, to which the recommended formulas are readily adapted.

* If N is too large, a random selection of cases may be discarded; and, if N is too small, possibly a few cases may be duplicated. One may also consider the possibility of altering the size of k.

* This prediction assumes that the implied result actually will occur. It will be noted, also, that one may allow two different answers as correct and, by combining frequencies, determine the predictive value of allewing either, but not both, when checked by any examinee. Multiple testee responses, however, should be treated as omissions or resolved into a unitary score.