Hostname: page-component-5f745c7db-sbzbt Total loading time: 0 Render date: 2025-01-06T06:02:15.808Z Has data issue: true hasContentIssue false
  • English
  • Français

New Equating Methods and Their Relationships with Levine Observed Score Linear Equating Under the Kernel Equating Framework

Published online by Cambridge University Press:  01 January 2025

Haiwen Chen  and
Paul Holland
Haiwen Chen*
Affiliation:
ETS, Princeton, NJ
Paul Holland
Affiliation:
ETS, Princeton, NJ
*
Requests for reprints should be sent to Haiwen Chen, ETS, 666 Rosedale Rd. MS 02-T, Princeton, NJ 08541, USA. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of post-stratification equating, we obtain a family of observed score equipercentile equating functions, which also includes the classical Levine observed score linear equating and the Tucker linear equating as special cases.

Keywords

NEAT designcurvilinear Levine observed score equating (CLOSE)Levine observed score linear equating (LOSLE)Tucker linear equating (TLE)kernel equating (KE)Mean preserving linear transformation (MPLT)Post-stratification equating (PSE)
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 3 , September 2010 , pp. 542 - 557
Copyright
Copyright © 2010 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Paul W. Holland is retired from Frederic M. Lord Chair in Measurement & Statistics, ETS, Princeton, NJ 08541, USA. e-mail: [email protected]

References

Anderson, T.W. (1984). An introduction to multivariate statistical analysis, (2nd ed.). New York: Wiley.Google Scholar
Angoff, W.H. (1971). Scales, norms, and equivalent scores. In Thorridike, R.L. (Eds.), Educational measurement (pp. 508–600). (2nd ed.). Washington: American Council on Education.Google Scholar
Angoff, W.H. (1982). Summary and derivation of equating methods used at ETS. In Holland, P.W., Rubin, D.B. (Eds.), Test equating (pp. 55–69). New York: Academic Press.Google Scholar
Braun, H.I., Holland, P.W. (1982). Observed-score test equating: a mathematical analysis of some ETS equating procedures. In Holland, P.W., Rubin, D.B. (Eds.), Test equating (pp. 9–49). New York: Academic Press.Google Scholar
Chen, H., & Holland, P.W. (2008a). Construction of chained true score equipercentile equatings under the KE framework and their relationship to Levine true score equating. Paper presented at the annual meeting of the National Council of Measurement in Education, New York (ETS Research Rep. No. RR-09-24). Princeton, NJ: ETS.Google Scholar
Chen, H., & Holland, P.W. (2008b). Fit log-linear model with a linear transformation on the discrete distribution. Manuscript in preparation.Google Scholar
Chen, H., Livingston, S.A., Holland, P.W. (2010). Generalized equating functions for NEAT designs. In von Davier, A.A. (Eds.), Statistical models for test equating, scaling and linking, New York: Springer.Google Scholar
Feldt, L.S., Brennan, R.L. (1989). Reliability. In Linn, R.L. (Eds.), Educational measurement (pp. 105–146). (3rd ed.). New York: Macmillan.Google Scholar
Holland, P.W., & Thayer, D.T. (1989). The kernel method of equating score distributions (ETS Research Rep. No. RR-89-07). Princeton, NJ: ETS.CrossRefGoogle Scholar
Kolen, M.J., Brennan, R.L. (2004). Test equating, scaling, and linking: methods and practices, (2nd ed.). New York: Springer.CrossRefGoogle Scholar
Kelley, T.L. (1947). Fundamentals of statistics, Cambridge: Harvard University Press.Google Scholar
Lord, F.M., Novick, M.R. (1968). Statistical theories of mental test scores, Reading: Addison-Wesley.Google Scholar
von Davier, A.A., Fournier-Zajac, S., & Holland, P.W. (2006). An equipercentile version of the Levine linear observed-score equating function using the methods of kernel equating. Paper presented at the annual meeting of the National Council of Measurement in Education, San Francisco (ETS Research Rep. No. RR-07-14). Princeton, NJ: ETS.Google Scholar
von Davier, A.A., Holland, P.W., Thayer, D.T. (2004). The kernel method of test equating, New York: Springer.CrossRefGoogle Scholar
Wang, T., & Brennan, R.L. (2007). A modified frequency estimation equating method for the common-item non-equivalent groups design. Paper presented at the annual meeting of the National Council of Measurement in Education, Chicago.Google Scholar