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Normality Tests: Power Comparison

The assumption of normality is required by several methods in parametricstatistical inference, some of which are robust toward mild or moderatenon-normality. The histogram in Fig. 1a was prepared with 20 values randomlygenerated with the standard normal distribution; however, one could arguethat the normality of the variable is not evident from the histogram. Ifthese were real observations instead of generated data, a test would beapplied with the null hypothesis being that the variable has a normaldistribution; frequently no specific distribution is mentioned as alternativehypothesis. The normal quantile plot (Fig. 1b) compares the ordered values\({x}_{(i)}\)in the sample, also calledorder statistics, with thencorresponding quantiles of the normal distribution. If the sample comes from anormal distribution, the dots tend to suggest a linear pattern. Other versions ofthe quantile plot do exist.

Numerous tests for normality have been defined. Tests are generally compared in terms of...

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Normality Tests: Power Comparison. Figure 1

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Seier, E. (2011). Normality Tests: Power Comparison. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_421

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