Estimation of true score and error variance for tests under various equivalence assumptions1
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In this paper, maximum likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements and statistical properties of the estimators are examined.Abstract:
Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentiallyτ-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.read more
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References
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TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.
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William G. Madow,T. W. Anderson +1 more
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Statistical Theories of Mental Test Scores
TL;DR: In this paper, the authors present a survey of test theory models and their application in the field of mental test analysis. But the focus of the survey is on test-score theories and models, and not the practical applications and limitations of each model studied.
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Theory of mental tests
TL;DR: In this paper, the authors outline the mathematical theories and equations that are necessary for evaluating a test and for quantifying its characteristics, and provide the means for evaluating the reliability and validity of total test scores and individual item analysis.
Journal ArticleDOI
Coefficient alpha and the reliability of composite measurements.
Melvin R. Novick,Charles Lewis +1 more
TL;DR: It is pointed out that the statement that “coefficientα is equal to the mean of the split-half reliabilities” is true only under the restricted condition assumed by Cronbach in the body of his derivation of this result.