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The Effect of Difficulty and Chance Success on Correlations between Items or between Tests

Published online by Cambridge University Press:  01 January 2025

John B. Carroll
John B. Carroll*
Affiliation:
ENS., H(S), U. S. N. R.
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Abstract

A study is made of the extent to which correlations between items and between tests are affected by the difficulties of the items involved and by chance success through guessing. The Pearsonian product-moment coefficient does not necessarily give a correct indication of the relation between items or sets of items, since it tends to decrease as the items or tests become less similar in difficulty. It is suggested that the tetrachoric correlation coefficient can properly be used for estimating the correlation between the continua underlying items or sets of items even though they differ in difficulty, and a method for correcting a 2 × 2 table for the effect of chance is proposed.

Type
Original Paper
Information
Psychometrika , Volume 10 , Issue 1 , March 1945 , pp. 1 - 19
Copyright
Copyright © 1945 Psychometric Society

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Footnotes

*

The opinions expressed in this article are the private ones of the writer and are not to be construed as official or reflecting the views of the Navy Department or the naval service at large. The writer is indebted to Lt. C. L. Vaughn, H (S) USNR, for critical comments on this paper.

†

This assumption precludes the analysis of a set of items in a time-limit test where the subjects are exposed to varying numbers of items.

References

* Most factors of ability, but not necessarily all, are probably of this nature.

† If one moves out of the context of these assumptions, however, the fact that any given pair of items is characterized by such a relation does not guaxantee that the items are factorially homogeneous.

* Ferguson, G. A. The factorial interpretation of test difficulty. Psychometrika, 1941, 5, 323-329.

* Values cannot be determined from Thurstone tables on seeount of small side-entry values.