The normal distribution (also called the Gaussian distribution: named after Johann Gauss, a German scientist and mathematician who justified the least squares method in 1809) is the most widely used family of statistical distributions on which many statistical tests are based. Many measurements of physical and psychological phenomena can be approximated by the normal distribution and, hence, the widespread utility of the distribution. In many areas of research, a sample is identified on which measurements of particular phenomena are made. These measurements are then statistically tested, via hypothesis testing, to determine whether the observations are different because of chance. Assuming the test is valid, an inference can be made about the population from which the sample is drawn.

Hypothesis testing involves assumptions about the underlying distribution ...