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Phillips, Gary W.; Jiang, Tao – Practical Assessment, Research & Evaluation, 2016
Power analysis is a fundamental prerequisite for conducting scientific research. Without power analysis the researcher has no way of knowing whether the sample size is large enough to detect the effect he or she is looking for. This paper demonstrates how psychometric factors such as measurement error and equating error affect the power of…
Descriptors: Error of Measurement, Statistical Analysis, Equated Scores, Sample Size
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Garcia-Perez, Miguel A. – Journal of Educational and Behavioral Statistics, 2010
A recent comparative analysis of alternative interval estimation approaches and procedures has shown that confidence intervals (CIs) for true raw scores determined with the Score method--which uses the normal approximation to the binomial distribution--have actual coverage probabilities that are closest to their nominal level. It has also recently…
Descriptors: Computation, Statistical Analysis, True Scores, Raw Scores
Werts, Charles E.; And Others – 1971
To resolve a recent controversy between Klein and Cleary and Levy, a model for dichotomous congeneric items is presented which has mean errors of zero, dichotomous true scores that are uncorrelated with errors, and errors that are mutually uncorrelated. (Author)
Descriptors: Correlation, Hypothesis Testing, Mathematical Models, Mathematics
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Groen, Guy J. – Psychometrika, 1971
The problem of whether a precise connection exists between the stochastic processes considered in mathematical learning theory and the Guttman simplex is investigated. The approach used is to derive a set of conditions which a probabilistic model must satisfy in order to generate inter-trial correlations with the perfect simplex property.…
Descriptors: Correlation, Learning Theories, Mathematical Models, Probability
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Zimmerman, Donald W. – Educational and Psychological Measurement, 1976
Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)
Descriptors: Career Development, Correlation, Mathematical Models, Measurement
Epstein, Kenneth I. – 1975
Since the primary purpose of classical testing is to rank order examinees consistently, the absolute value of the true score has been relatively unimportant. However, the major purpose of criterion referenced testing is to estimate the true capabilities of examinees to perform specific tasks. Hence, the problems of true score determination assume…
Descriptors: Bayesian Statistics, Criterion Referenced Tests, Mathematical Models, Military Personnel
Macready, George B.; Dayton, C. Mitchell – 1977
A probabilistic hypothesis testing procedure to assess the fit of hypothesized hierarchical structures for test item data is discussed. Statistical procedures are presented which are useful for evaluating the fit of data of a certain class of probabilistic models. These models apply to sets of dichotomous (O,1) responses for which there are…
Descriptors: Error of Measurement, Goodness of Fit, Hypothesis Testing, Mathematical Models
Wilcox, Rand R. – 1978
Two fundamental problems in mental test theory are to estimate true score and to estimate the amount of error when testing an examinee. In this report, three probability models which characterize a single test item in terms of a population of examinees are described. How these models may be modified to characterize a single examinee in terms of an…
Descriptors: Achievement Tests, Comparative Analysis, Error of Measurement, Mathematical Models
Moore, William E. – 1970
The previous theoretical development of the Poisson process as a strong model for the true-score theory of mental tests is discussed, and additional theoretical properties of the model from the standpoint of individual examinees are developed. The paper introduces the Erlang process as a family of test theory models and shows in the context of…
Descriptors: Arithmetic, Goodness of Fit, Grade 10, Mathematical Models