Analysis

Most of the parametric tests are based on the Normal distribution. Therefore, if you have a small sample (n < 25), it is a good practise to check whether the data are normally distributed before conducting a hypothesis test. According to the central limit Theorem, sample mean is approximately normally distributed if the sample size is large. Therefore, if the test statistics of the hypothesis is based on the sample mean and the sample size is large, checking the normality assumption is not mandatory.

In some statistical techniques, it is essential to convert a set of correlated variables to a set of uncorrelated variables. This can be done by using Principal Component Analysis (PCA). The converted uncorrelated variables are called principal components that represent most of the information in the original set of variables. This statistical technique is also a useful descriptive tool to examine your data, and to reduce the number of variables of the original data set.