Question

What is the best strategy to decide whether a collected sample is from a normal distribution or not?

Answer 1

Answer:

The normal distribution is important for three main reasons: • Some statistical hypothesis tests assume that the data follow a normal distribution The central limit theorem states that, for a large number of observations (n > 30), no matter what is the underlying distribution of the original variable, the distribution of the sample means and of the sum (Sn = Xi) may be approached by a normal distribution • Linear and nonlinear regression assume that the residuals are normally- distributed

We can test the  normality assumption by the following way

Histogram:

Histogram A histogram displays the spread and shape of a distribution, so it is a good starting point to evaluate normality. Let's have a look at the histogram of a distribution that we would expect to follow a normal distribution, the height of 1,000 adults in cm: Histogram of adult height and normal curve N = 1000, mean = 164.87, variance = 25.13 0.08 0.06 density 0.04 0.02 0.00 150 160 170 180 Height (cm)

Density plot,

QQ plot

and by some of the normailty test like shapiro wilk and kolmogrov simernov test.