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Comparing Regressions When Measurement Error Variances Are Known

Stroud, Thomas W. F.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Achievement Tests, Error of Measurement, Mathematical Models, Multiple Regression Analysis, Scores, True Scores


In a multiple (or multivariate) regression model where the predictors are subject to errors of measurement with a known variance-covariance structure, two-sample hypotheses are formulated for (i) equality of regressions on true scores and (ii) equality of residual variance (or covariance matrices) after regression on true scores. The hypotheses are tested using a large-sample procedure based on maximum likelihood estimators. Formulas for the test statistic are presented; these may be avoided in practice by using a general purpose computer program. The procedure has been applied to a comparison of learning in high schools using achievement test data. (Author) (31pp.)

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