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Measurement Error and ANCOVA: Functional and Structural Relationship Approaches

Published online by Cambridge University Press:  01 January 2025

Jeroen G. W. Raaijmakers  and
Jo P. M. Pieters
Jeroen G. W. Raaijmakers*
Affiliation:
TNO Institute for Perception, Soesterberg, The Netherlands
Jo P. M. Pieters
Affiliation:
Rijks Psychologische Dienst, The Hague, The Netherlands
*
Requests for reprints should be addressed to Jeroen G. W. Raaijmakers, TNO Institute for Perception, Kampweg 5, 3769 DE Soesterberg, THE NETHERLANDS.
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Abstract

This article discusses alternative procedures to the standard F-test for ANCOVA in case the covariate is measured with error. Both a functional and a structural relationship approach are described. Examples of both types of analysis are given for the simple two-group design. Several cases are discussed and special attention is given to issues of model identifiability. An approximate statistical test based on the functional relationship approach is described. On the basis of Monte Carlo simulation results it is concluded that this testing procedure is to be preferred to the conventional F-test of the ANCOVA null hypothesis. It is shown how the standard null hypothesis may be tested in a structural relationship approach. It is concluded that some knowledge of the reliability of the covariate is necessary in order to obtain meaningful results.

Keywords

ANCOVAmeasurement errorfunctional relationshipstructural relationship
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 4 , December 1987 , pp. 521 - 538
Copyright
Copyright © 1987 The Psychometric Society

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