Does your data violate normality test assumptions?

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If the population from which data to be analyzed by a normality test were sampled violates one or more of the normality test assumptions, the results of the analysis may be incorrect or misleading. For example, if the assumption of mutual independence of the sampled values is violated, then the normality test results will not be reliable. If outliers are present, then the normality test may reject the null hypothesis even when the remainder of the data do in fact come from a normal distribution. Often, the effect of an assumption violation on the normality test result depends on the extent of the violation. Some small violations may have little practical effect on the analysis, while other violations may render the normality test result uselessly incorrect or uninterpretable.

Potential assumption violations include:

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