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An Interval Estimate for Making Statistical Inferences About True Scores
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Lord, Frederic M.; Stocking, Martha L. – Psychometrika, 1976
A numerical procedure is outlined for obtaining an interval estimate of the regression of true score or observed score, utilizing only the frequency distribution of observed scores. The procedure assumes that the conditional distribution of observed scores for fixed true scores is binomial. Several illustrations are given. (Author/HG)
Descriptors: Correlation, Multiple Regression Analysis, Raw Scores, Statistical Analysis
Isotonic Ordinal Probabilistic Models (ISOP).
Peer reviewed Peer reviewed
Scheiblechner, Hartmann – Psychometrika, 1995
The isotonic ordinal probabilistic model (ISOP) is introduced as a common nonparametric theoretical structure for unidimensional models for quantitative, ordinal, and dichotomous variables. Fundamental theorems on dichotomous and polytomous weakly independent ordered systems are derived, and testing at the observed empirical level is discussed.…
Descriptors: Equations (Mathematics), Nonparametric Statistics, Probability, Raw Scores
A Simple Proof of the Spearman-Brown Formula for Continuous Test Lengths
Peer reviewed Peer reviewed
Allison, Paul A. – Psychometrika, 1976
A direct proof is given for the generalized Spearman-Brown formula for any real multiple of test length. (Author)
Descriptors: Correlation, Error of Measurement, Raw Scores, Test Length
Bayesian Inference and the Classical Test Theory Model: Reliability and True Scores
Peer reviewed Peer reviewed
Novick, Melvin R.; And Others – Psychometrika, 1971
Descriptors: Analysis of Variance, Bayesian Statistics, Error of Measurement, Mathematical Models
Analytic Smoothing for Equipercentile Equating under the Common Item Nonequivalent Populations Design.
Peer reviewed Peer reviewed
Kolen, Michael J.; Jarjoura, David – Psychometrika, 1987
A cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described. Statistical techniques based on bootstrap estimation are presented for choosing an equating method/degree of smoothing. Smoothing decreases the estimate of random error but results in an increase in…
Descriptors: Analysis of Variance, Equated Scores, Error of Measurement, Estimation (Mathematics)