I was asked if a type I error in the Shapiro-Wilk test would impact the main analysis and if the wrong test was used if it would matter or not if my data was normally distributed…

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#### Best Answer

In statistical analysis, if your data follow a parametric distribution, you should utilize the benefit of knowing the distribution, and employ the statistical methods based on that distribution.

But sometimes we do not know the distribution of the random variable, so the nonparametric statistical methods were developed to embrace the wide range of the distributions while sacrificing some efficiency.

Given you know the distribution of random variable and use the nonparametric statistical method, instead of parametric statistical methods based on knowing the distribution, it will be inefficient, i.e., the power of test will decrease, standard error will increase, and the confidence intervals will be wider than with the parametric method.