Question

Up to this point, the data analysis procedures that I have been learning about have all assumed a normal distribution of the population. However, there are times when the distribution of a population is not normal, at which time I would need to choose a different analysis strategy. Why must I use a different test if a population does not have a normal distribution?

Answer 1

A short and simple answer to this question is that the parametric tests like regression, z-test, t-test, factorial designs etc. are designed in fo use when the sample data follows a normal distribution. The assumption of normality is very important and it must be fulfilled, if we use these tests when the assumption is not valid, then the results will be inaccurate. Hence, we should use other tests like non-parametric tests if the normality assumption is not valid.
The reason for normality assumption is also that this is actually a simple mathematical distribution model which can be used. Also, it occurs in most real scenarios.