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Interval Estimation for True Scores under Various Scale Transformations. ACT Research Report Series.

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Bibliographic Details
Title: Interval Estimation for True Scores under Various Scale Transformations. ACT Research Report Series.
Language: English
Authors: Lee, Won-Chan, Brennan, Robert L., Kolen, Michael J., American Coll. Testing Program, Iowa City, IA.
Peer Reviewed: N
Page Count: 78
Publication Date: 2002
Document Type: Reports - Research
Descriptors: Bayesian Statistics, Error of Measurement, Estimation (Mathematics), Scaling, Simulation, True Scores
Abstract: This paper reviews various procedures for constructing an interval for an individual's true score given the assumption that errors of measurement are distributed as binomial. This paper also presents two general interval estimation procedures (i.e., normal approximation and endpoints conversion methods) for an individual's true scale score; compares the various interval estimation procedures through computer simulation studies by evaluating how close actual coverage probabilities are to selected nominal levels (i.e., 0.95, 0.68, and 0.50); and provides some practical guidelines for the use of the interval estimation procedures. To examine the effects of different types of scale scores, four nonlinearly transformed scale scores are used. The conditional confidence intervals using conditional standard errors of measurement are recommended over the traditional confidence intervals using the overall standard error of measurement, especially for lower nominal levels. The score confidence interval, Bayes confidence interval, and credibility interval tend to provide the actual coverage probabilities that are closest to the nominal levels, on average. Results for scale score intervals appear to favor the endpoints conversion method using the true-score conversions over the normal approximation approach. (Contains 7 tables, 27 figures, and 46 references.) (Author/SLD)
Entry Date: 2003
Accession Number: ED471665
Database: ERIC
Description
Abstract:This paper reviews various procedures for constructing an interval for an individual's true score given the assumption that errors of measurement are distributed as binomial. This paper also presents two general interval estimation procedures (i.e., normal approximation and endpoints conversion methods) for an individual's true scale score; compares the various interval estimation procedures through computer simulation studies by evaluating how close actual coverage probabilities are to selected nominal levels (i.e., 0.95, 0.68, and 0.50); and provides some practical guidelines for the use of the interval estimation procedures. To examine the effects of different types of scale scores, four nonlinearly transformed scale scores are used. The conditional confidence intervals using conditional standard errors of measurement are recommended over the traditional confidence intervals using the overall standard error of measurement, especially for lower nominal levels. The score confidence interval, Bayes confidence interval, and credibility interval tend to provide the actual coverage probabilities that are closest to the nominal levels, on average. Results for scale score intervals appear to favor the endpoints conversion method using the true-score conversions over the normal approximation approach. (Contains 7 tables, 27 figures, and 46 references.) (Author/SLD)