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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...
References and Further Reading
- D’Agostino RB, Lee AFS (1977) Robustness of location estimators under changes of population kurtosis. J Am Stat Assoc 72:393–396Google Scholar
- Tukey JW (1960) A survey of sampling from contaminated distributions. In: Olkin I, Ghurye SG, Hoeffding W, Madow WG, Mann HB (eds) Contributions to probability and statistics. Stanford University Press, CA, pp 448–485Google Scholar