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Norm-Referenced Scoring on Real Data: A Comparative Study of GRiSTEN and STEN

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  • Mehmet Guven Gunver

Abstract

STEN (Standard Ten) is the most frequently preferred score generating method among the norm reference scores (e.g., percentile rank, STANINE) However, it is usually misleading because of the skewness presented with the data. In this study, rather than STEN, GRiSTEN (Golden Ratio in Statistics) approach is proposed to generate relatively fair outcomes. The GRiSTEN method acknowledges the effects of skewness by accounting for the contribution of each data element to the center point based on its specific location in the data stack. Generating norms using the GRiSTEN approach enables us to mark “the most capable†or “the least capable†scores regarding the test without involving too many arithmetic operations. In order to verify the applicability of the psychometric tests based on System Sigma run by Mevasis IT Consultancy in Turkey, a watch test, which is designed to observe respondents’ estimation of velocity, is carried out with a pilot group consisting of 407 male respondents aged between 30 and 50. By using GRiSTEN approach, it is shown that consistent outputs can be obtained without changing, ignoring, or transforming any elements regardless of the number of elements, skewness, distribution, and values of the data array.

Suggested Citation

  • Mehmet Guven Gunver, 2022. "Norm-Referenced Scoring on Real Data: A Comparative Study of GRiSTEN and STEN," SAGE Open, , vol. 12(2), pages 21582440221, April.
    • Handle: RePEc:sae:sagope:v:12:y:2022:i:2:p:21582440221091253
    DOI: 10.1177/21582440221091253
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    References listed on IDEAS

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    1. Tsiang, S C, 1972. "The Rationale of the Mean-Standard Deviation Analysis, Skewness Preference, and the Demand for Money," American Economic Review, American Economic Association, vol. 62(3), pages 354-371, June.
    2. Lutz Bornmann, 2013. "The problem of percentile rank scores used with small reference sets," Journal of the American Society for Information Science and Technology, Association for Information Science & Technology, vol. 64(3), pages 650-650, March.
    3. Ivan A. Canay & Joseph P. Romano & Azeem M. Shaikh, 2017. "Randomization Tests Under an Approximate Symmetry Assumption," Econometrica, Econometric Society, vol. 85, pages 1013-1030, May.
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