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Evaluating the Equal-Interval Hypothesis with Test Score Scales

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  • Ben Domingue

Abstract

The axioms of additive conjoint measurement provide a means of testing the hypothesis that testing data can be placed onto a scale with equal-interval properties. However, the axioms are difficult to verify given that item responses may be subject to measurement error. A Bayesian method exists for imposing order restrictions from additive conjoint measurement while estimating the probability of a correct response. In this study an improved version of that methodology is evaluated via simulation. The approach is then applied to data from a reading assessment intentionally designed to support an equal-interval scaling. Copyright The Psychometric Society 2014

Suggested Citation

  • Ben Domingue, 2014. "Evaluating the Equal-Interval Hypothesis with Test Score Scales," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 1-19, January.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:1:p:1-19
    DOI: 10.1007/s11336-013-9342-4
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    References listed on IDEAS

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    1. Jan Toporowski & Jo Michell, 2012. "Introduction," Chapters, in: Jan Toporowski & Jo Michell (ed.), Handbook of Critical Issues in Finance, pages i-ii, Edward Elgar Publishing.
    2. H. Brogden, 1977. "The rasch model, the law of comparative judgment and additive conjoint measurement," Psychometrika, Springer;The Psychometric Society, vol. 42(4), pages 631-634, December.
    3. Iverson, G. & Falmagne, J. -C., 1985. "Statistical issues in measurement," Mathematical Social Sciences, Elsevier, vol. 10(2), pages 131-153, October.
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    Cited by:

    1. Benjamin R. Shear & Sean F. Reardon, 2021. "Using Pooled Heteroskedastic Ordered Probit Models to Improve Small-Sample Estimates of Latent Test Score Distributions," Journal of Educational and Behavioral Statistics, , vol. 46(1), pages 3-33, February.
    2. George Karabatsos, 2018. "On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 321-332, June.
    3. David M. Quinn & Andrew D. Ho, 2021. "Ordinal Approaches to Decomposing Between-Group Test Score Disparities," Journal of Educational and Behavioral Statistics, , vol. 46(4), pages 466-500, August.

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