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International Encyclopedia of Statistical Science pp 999–1000Cite as

Normality Tests

The Importance of Testing for Normality

Many statistical procedures such as estimation and hypothesis testing have the underlying assumption that the sampled data come from a normal distribution. This requires either an effective test of whether the assumption of normality holds or a valid argument showing that non-normality does not invalidate the procedure. Tests of normality are used to formally assess the assumption of the underlying distribution.

Much statistical research has been concerned with evaluating the magnitude of the effect of violations of the normality assumption on the true significance level of a test or the efficiency of a parameter estimate. Geary (1947) showed that for comparing two variances, having a symmetric non-normal underlying distribution can seriously affect the true significance level of the test. For a value of 1.5 for the kurtosis of the alternative distribution, the actual significance level of the test is 0.000089, as compared to the nominal level...

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Author information

Authors and Affiliations

  1. Associate Professor, Stony Brook University, Stony Brook, NY, USA

    Henry C. Thode

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  1. Henry C. Thode
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Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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Thode, H.C. (2011). Normality Tests. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_423

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