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Activity Number:
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12
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Type:
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Topic Contributed
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Date/Time:
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Sunday, August 6, 2006 : 2:00 PM to 3:50 PM
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Sponsor:
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Social Statistics Section
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| Abstract - #306586 |
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Title:
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Estimation of Measurement Errors at Observed and Scaled Scores
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Author(s):
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Michelle Liou*+ and Philip E. Cheng
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Companies:
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Academia Sinica and Academia Sinica
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Address:
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Institute of Statistical Science, Taipei, 115, Taiwan
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Keywords:
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arcsine transformation ; beta-binomial ; standard errors of measurement ; log-linear smoothing ; scaled scores ; true scores
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Abstract:
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In the placement service and licensure examination, the observed scores or scaled observed scores are used to assign test-takers into competence levels. It is well-known that measurement errors may vary widely according to score levels. We derived computational formulae for estimating bias and error variance at each observed score and extended the use of the formulae to scaled scores that were nonlinear transformations of observed scores. In the empirical study, the formulae were applied to assessing conditional measurement errors at observed scores on an English test administered to 58,054 takers in a national assessment. The scores were transformed using an arcsine function for stabilizing error variances across the score range. The estimated bias and error variance at each observed and scaled score was compared to validate the use of the arcsine transformation.
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