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Accumulative Equating Error after a Chain of Linear Equatings

Published online by Cambridge University Press:  01 January 2025

Hongwen Guo
Hongwen Guo*
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Hongwen Guo, Educational Testing Service, Princeton, NJ, USA. E-mail: [email protected]
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Abstract

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and Levine, under the nonequivalent groups with anchor test (NEAT) design. A recursive formula for the ASEE is provided for a series of equatings that makes use of only historical summary statistics. This formula can serve as a new tool to measure the magnitude of equating errors that have accumulated over a series of equatings, and to help monitor and design testing programs.

Keywords

standard error of equatinglinear equatingNEAT design
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 3 , September 2010 , pp. 438 - 453
Copyright
Copyright © 2010 The Psychometric Society

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References

Braun, H., Holland, P. (1982). Observed-score test equating: A mathematical analysis of some ETS equating procedures. In Holland, P., Rubin, B. (Eds.), Test equating (pp. 9–49). New York: Academic Press.Google Scholar
Haberman, S., Guo, H., Liu, J., & Dorans, N. (2008). Consistency of SAT reasoning score conversions (ETS RR-08-67). Educational Testing Service, Princeton, NJ.Google Scholar
Haertel, E. (2006). Reliability. In Brennan, R.L. (Eds.), Educational measurement (pp. 65–110). (4th ed.). Westport: American Council on Education/Praeger.Google Scholar
Kendall, M., Stuart, A. (1977). The advanced theory of statistics, (4th ed.). New York: Macmillan.Google Scholar
Kolen, M. (1985). Standard errors of Tucker equating. Applied Psychological Measurement, 9, 209–223.CrossRefGoogle Scholar
Kolen, M., Brennan, R. (2004). Test equating, scaling, and linking, (2nd ed.). New York: Springer.CrossRefGoogle Scholar
Lord, F.M. (1950). Notes on comparable scales for test scores (ETS RB-50-48). Educational Testing Service, Princeton, NJ.Google Scholar
Lord, F.M. (1981). Standard error of equating by item response theory (ETS Tech. Rep. No. RR-81-49). Educational Testing Service, Princeton, NJ.Google Scholar
Zeng, L., Hanson, B., Kolen, M. (1994). Standard errors of a chain of linear equatings. Applied Psychological Measurement, 18, 369–378.CrossRefGoogle Scholar