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Standard Errors and Confidence Intervals of Norm Statistics for Educational and Psychological Tests

Author

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  • Hannah E. M. Oosterhuis

    (Tilburg University)

  • L. Andries Ark

    (University of Amsterdam)

  • Klaas Sijtsma

    (Tilburg University)

Abstract

Norm statistics allow for the interpretation of scores on psychological and educational tests, by relating the test score of an individual test taker to the test scores of individuals belonging to the same gender, age, or education groups, et cetera. Given the uncertainty due to sampling error, one would expect researchers to report standard errors for norm statistics. In practice, standard errors are seldom reported; they are either unavailable or derived under strong distributional assumptions that may not be realistic for test scores. We derived standard errors for four norm statistics (standard deviation, percentile ranks, stanine boundaries and Z-scores) under the mild assumption that the test scores are multinomially distributed. A simulation study showed that the standard errors were unbiased and that corresponding Wald-based confidence intervals had good coverage. Finally, we discuss the possibilities for applying the standard errors in practical test use in education and psychology. The procedure is provided via the R function check.norms, which is available in the mokken package.

Suggested Citation

  • Hannah E. M. Oosterhuis & L. Andries Ark & Klaas Sijtsma, 2017. "Standard Errors and Confidence Intervals of Norm Statistics for Educational and Psychological Tests," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 559-588, September.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-016-9535-8
    DOI: 10.1007/s11336-016-9535-8
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    References listed on IDEAS

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    1. Alan Agresti & Yongyi Min, 2001. "On Small-Sample Confidence Intervals for Parameters in Discrete Distributions," Biometrics, The International Biometric Society, vol. 57(3), pages 963-971, September.
    2. Herbert M. Kritzer, 1977. "Analyzing Measures of Association Derived From Contingency Tables," Sociological Methods & Research, , vol. 5(4), pages 387-418, May.
    3. L. Ark & Marcel Croon & Klaas Sijtsma, 2008. "Mokken Scale Analysis for Dichotomous Items Using Marginal Models," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 183-208, June.
    4. van der Ark, L. Andries, 2012. "New Developments in Mokken Scale Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i05).
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    Cited by:

    1. Alexandra Lenhard & Wolfgang Lenhard & Sebastian Gary, 2019. "Continuous norming of psychometric tests: A simulation study of parametric and semi-parametric approaches," PLOS ONE, Public Library of Science, vol. 14(9), pages 1-30, September.

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