In the wonderful statistical language of R there’s a nice little test called Shapiro-Wilk Normality Test which basically, well uhmm, tests for normality. The null hypothesis H0 in this case is that the samples to test comes from a normal distribution y ~ N(μ, σ). Thus in order to reject the null hypothesis we need a small p-value. For old times sake let’s require this to be less than 0.05. To start with I will generate 1000 samples from three identical normal distributions with a zero mean and unit variance. They are shown below.