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The Reliability and Precision of Total Scores and IRT Estimates as a Function of Polytomous IRT Parameters and Latent Trait Distribution
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Culpepper, Steven Andrew – Applied Psychological Measurement, 2013
A classic topic in the fields of psychometrics and measurement has been the impact of the number of scale categories on test score reliability. This study builds on previous research by further articulating the relationship between item response theory (IRT) and classical test theory (CTT). Equations are presented for comparing the reliability and…
Descriptors: Item Response Theory, Reliability, Scores, Error of Measurement
Reliability of Total Test Scores When Considered as Ordinal Measurements
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Biswas, Ajoy Kumar – Applied Psychological Measurement, 2006
This article studies the ordinal reliability of (total) test scores. This study is based on a classical-type linear model of observed score (X), true score (T), and random error (E). Based on the idea of Kendall's tau-a coefficient, a measure of ordinal reliability for small-examinee populations is developed. This measure is extended to large…
Descriptors: True Scores, Test Theory, Test Reliability, Scores
Is Reliability Obsolete? A Commentary on "Are Simple Gain Scores Obsolete?"
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Collins, Linda M. – Applied Psychological Measurement, 1996
The clarification provided by Williams and Zimmerman on the reliability of gain scores is translated into recognizable patterns of change that tend to produce reliable or unreliable gain scores. The relevance of the traditional idea of reliability to the measurement of change is also discussed. (SLD)
Descriptors: Achievement Gains, Change, Measurement Techniques, Reliability
Item Response Theory Models and Spurious Interaction Effects in Factorial ANOVA Designs.
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Embretson, Susan E. – Applied Psychological Measurement, 1996
Conditions under which interaction effects estimated from classical total scores, rather than item response theory trait scores, can be misleading are discussed with reference to analysis of variance (ANOVA). When no interaction effects exist on the true latent variable, spurious interaction effects can be observed from the total score scale. (SLD)
Descriptors: Analysis of Variance, Interaction, Item Response Theory, Models
Linear Dependence on Gain Scores in Their Components Imposes Constraints on Their Use and Interpretation: Comment on "Are Simple Gain Scores Obsolete?"
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Humphreys, Lloyd G. – Applied Psychological Measurement, 1996
The reliability of a gain is determined by the reliabilities of the components, the correlation between them, and their standard deviations. Reliability is not inherently low, but the components of gains in many investigations make low reliability likely and require caution in the use of gain scores. (SLD)
Descriptors: Achievement Gains, Change, Correlation, Error of Measurement
Commentary on the Commentaries of Collins and Humphreys.
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Williams, Richard H.; Zimmerman, Donald W. – Applied Psychological Measurement, 1996
The critiques by L. Collins and L. Humphreys in this issue illustrate problems with the use of gain scores. Collins' examples show that familiar formulas for the reliability of differences do not reflect the precision of measures of change. Additional examples demonstrate flaws in the conventional approach to reliability. (SLD)
Descriptors: Achievement Gains, Change, Correlation, Error of Measurement
Modeling Incorrect Responses to Multiple-Choice Items with Multilinear Formula Score Theory.
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Drasgow, Fritz; And Others – Applied Psychological Measurement, 1989
Multilinear formula scoring (MFS) is reviewed, with emphasis on estimating option characteristic curves (OCSs). MFS was used to estimate OCSs for the arithmetic reasoning subtest of the Armed Services Vocational Aptitude Battery for 2,978 examinees. A second analysis obtained OCSs for simulated data. The use of MFS is discussed. (SLD)
Descriptors: Estimation (Mathematics), Mathematical Models, Multiple Choice Tests, Scores