Shapiro-Wilk Test of Normality

Is a qq GOF Test for Class of Distributions, in this case Normal Distributions.

How to perform the test

Make qq-Plot for any Normal Distribution against Standard Normal Distribution. Use simple Linear Regression to fit a diagonal line to the plot and read off the slope $S$.

Calculate Test Statistic $T=\frac{S^2}{s^2}$ where $s$ is the empirical standard deviation for the data sequence.

Given $H_0$ the test statistic will be close to $1$. You can quanitfy this by simulating the test statistic and determening its distribution. You can calculate an Acceptance Domain with $[z_{\alpha /2},z_{1-\alpha /2}]$ where $\alpha$ is the probability for Type 1 Error.