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A Critical Examination of The Analysis of Dichotomous Data

Published online by Cambridge University Press:  01 April 2022

William H. Batchelder  and
Louis Narens
William H. Batchelder
Affiliation:
University of California, Irvine
Louis Narens
Affiliation:
University of California, Irvine
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Abstract

This paper takes a critical look at theory-free, statistical methodologies for processing and interpreting data taken from respondents answering a set of dichotomous (yes-no) questions. The basic issue concerns to what extent theoretical conclusions based on such analyses are invariant under a class of “informationally equivalent” question transformations. First the notion of Boolean equivalence of two question sets is discussed. Then Lazarsfeld's latent structure analysis is considered in detail. It is discovered that the best fitting latent model depends on which one of the many informationally equivalent question sets is used. This fact raises a number of methodological problems and pitfalls with latent structure analysis. Related problems with other methodologies are briefly discussed.

Type
Research Article
Information
Philosophy of Science , Volume 44 , Issue 1 , March 1977 , pp. 113 - 135
Copyright
Copyright © 1977 by the Philosophy of Science Association

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Footnotes

†

The authors would like to thank Albert Ahumada and Jerry Kaiwi for helpful discussions during the development of this paper.

References

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