Interval Estimation for True Raw and Scale Scores Under the Binomial Error Model

Won-Chan Lee, Robert L. Brennan and Michael J. Kolen

Journal of Educational and Behavioral Statistics, 2006, vol. 31, issue 3, 261-281

Abstract: Assuming errors of measurement are distributed binomially, this article reviews various procedures for constructing an interval for an individual’s true number-correct score; presents two general interval estimation procedures for an individual’s true scale score (i.e., normal approximation and endpoints conversion methods); compares various interval estimation procedures through a computer simulation study; and provides some practical guidelines for use of the interval estimation procedures. To examine the effects of different types of scale scores, three nonlinearly transformed scale scores are employed. The conditional confidence intervals using conditional standard errors of measurement are recommended over the traditional confidence intervals using the overall standard error of measurement. For raw scores, the score confidence intervals, in general, tend to provide actual coverage probabilities that are closest to the nominal level. Results for scale score intervals seem to favor the endpoints conversion method using the true-score conversions over the normal approximation approach.

Keywords: binomial error model; confidence interval; credibility interval; scale scores (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:31:y:2006:i:3:p:261-281

DOI: 10.3102/10769986031003261

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