Skip to main content

Evaluating Equating Transformations from Different Frameworks

  • Conference paper
  • First Online:
Quantitative Psychology (IMPS 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 233))

Included in the following conference series:

Abstract

Test equating is used to ensure that test scores from different test forms can be used interchangeably. This paper aims to compare the statistical and computational properties from three equating frameworks: item response theory observed-score equating (IRTOSE), kernel equating and kernel IRTOSE. The real data applications suggest that IRT-based frameworks tend to provide more stable and accurate results than kernel equating. Nonetheless, kernel equating can provide satisfactory results if we can find a good model for the data, while also being much faster than the IRT-based frameworks. Our general recommendation is to try all methods and examine how much the equated scores change, always ensuring that the assumptions are met and that a good model for the data can be found.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Andersson, B., & Wiberg, M. (2017). Item response theory observed-score kernel equating. Psychometrika, 82(1), 48–66. https://doi.org/10.1007/s11336-016-9528-7.

    Article  MathSciNet  Google Scholar 

  • Andersson, B., Bränberg, K., & Wiberg, M. (2013). Performing the kernel method of test equating with the package kequate. Journal of Statistical Software, 55(6), 1–25.

    Article  Google Scholar 

  • Battauz, M. (2015). equateIRT: An R package for IRT test equating. Journal of Statistical Software, 68(7), 1–22.

    Article  Google Scholar 

  • Braun, H. I., & Holland, P. W. (1982). Observed-score test equating: A mathematical analysis of some ETS equating procedures. In P. W. Holland & D. B. Rubin (Eds.), Test equating (Vol. 1, pp. 9–49). New York: Academic Press.

    Google Scholar 

  • von Davier, A. A., Holland, P. W., & Thayer, D. T. (2004). The kernel method of test equating. New York: Springer.

    Book  Google Scholar 

  • Dorans, N. J., & Feigenbaum, M. D. (1994). Equating issues engendered by changes to the SAT and PSAT/NMSQT. Technical issues related to the introduction of the new SAT and PSAT/NMSQT (pp. 91–122).

    Google Scholar 

  • González, J., & Wiberg, M. (2017). Applying test equating methods using R. New York: Springer.

    Book  Google Scholar 

  • González, J., Wiberg, M., & von Davier, A. A. (2016). A note on the Poisson’s binomial distribution in item response theory. Applied Psychological Measurement, 40(4), 302–310.

    Article  Google Scholar 

  • Haebara, T. (1980). Equating logistic ability scales by a weighted least squares method. Japanese Psychological Research, 22(3), 144–149.

    Article  Google Scholar 

  • Harris, D. J., & Crouse, J. D. (1993). A study of criteria used in equating. Applied Measurement in Education, 6(3), 195–240.

    Article  Google Scholar 

  • Jiang, Y., von Davier, A. A., & Chen, H. (2012). Evaluating equating results: Percent relative error for chained kernel equating. Journal of Educational Measurement, 49(1), 39–58.

    Article  Google Scholar 

  • Kolen, M. J., & Brennan, R. L. (2014). Test equating, scaling, and linking: Methods and practices (3rd ed.). New York: Springer.

    Book  Google Scholar 

  • van der Linden, W. J. (2011). Local observed-score equating. In A. von Davier (Ed.), Statistical models for test equating, scaling, and linking (pp. 201–223). New York: Springer.

    Google Scholar 

  • Lord, F. M. (1977). Practical applications of item response theory. Journal of Educational Measurement, 14(2), 177–138.

    Article  Google Scholar 

  • Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Lord, F. M., & Wingersky, M. S. (1984). Comparison of IRT true-score and equipercentile observed-score ‘equatings’. Applied Psychological Measurement, 8(4), 453–461.

    Article  Google Scholar 

  • Meng, Y. (2012). Comparison of kernel equating and item response theory equating methods. Dissertation submitted to the graduate school of the University of Massachusetts Amherst in partial fulfillment of the requirements for the degree of doctor of education, University of Massachusetts Amherst.

    Google Scholar 

  • R Core Team. (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. https://www.R-project.org/.

  • Rizopoulos, D. (2006). ltm: An R package for latent variable modelling and item response theory analyses. Journal of Statistical Software, 17(5), 1–25. http://www.jstatsoft.org/v17/i05/.

  • Wiberg, M., & González, J. (2016). Statistical assessment of estimated transformations in observed-score equating. Journal of Educational Measurement, 53(1), 106–125.

    Article  Google Scholar 

  • Wiberg, M., van der Linden, W. J., & von Davier, A. A. (2014). Local observed-score kernel equating. Journal of Educational Measurement, 51, 57–74.

    Article  Google Scholar 

Download references

Acknowledgements

The research in this article was funded by the Swedish Research Council grant 2014-578 and by the Fondazione Cassa di Risparmio di Padova e Rovigo.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Waldir Leôncio .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Leôncio, W., Wiberg, M. (2018). Evaluating Equating Transformations from Different Frameworks. In: Wiberg, M., Culpepper, S., Janssen, R., González, J., Molenaar, D. (eds) Quantitative Psychology. IMPS 2017. Springer Proceedings in Mathematics & Statistics, vol 233. Springer, Cham. https://doi.org/10.1007/978-3-319-77249-3_9

Download citation

Publish with us

Policies and ethics