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Reasonable Sample Sizes for Convergence to Normality

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  • Carsten Schröder
  • Shlomo Yitzhaki

Abstract

The central limit theorem says that, provided an estimator fulfills certain weak conditions, then, for reasonable sample sizes, the sampling distribution of the estimator converges to normality. We propose a procedure to find out what a “reasonably large sample size” is. The procedure is based on the properties of Gini’s mean difference decomposition. We show the results of implementations of the procedure from simulated datasets and data from the German Socio‐economic Panel.

Suggested Citation

  • Carsten Schröder & Shlomo Yitzhaki, 2014. "Reasonable Sample Sizes for Convergence to Normality," SOEPpapers on Multidisciplinary Panel Data Research 714, DIW Berlin, The German Socio-Economic Panel (SOEP).
    • Handle: RePEc:diw:diwsop:diw_sp714
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    File URL: https://www.diw.de/documents/publikationen/73/diw_01.c.492474.de/diw_sp0714.pdf
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    References listed on IDEAS

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    1. Gert G. Wagner & Joachim R. Frick & Jürgen Schupp, 2007. "The German Socio-Economic Panel Study (SOEP) – Scope, Evolution and Enhancements," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 127(1), pages 139-169.
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    Cited by:

    1. Schröder, Carsten & Yitzhaki, Shlomo, 2017. "Revisiting the evidence for cardinal treatment of ordinal variables," European Economic Review, Elsevier, vol. 92(C), pages 337-358.
    2. Pinkovetskaia Iuliia & Slepova Vladislava, 2018. "Estimation of Fixed Capital Investment in SMEs: the Existing Differentiation in the Russian Federation," Business Systems Research, Sciendo, vol. 9(1), pages 65-78, March.

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    More about this item

    Keywords

    central limit theorem; Gini’s mean difference composition;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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