Descriptive Statistics and Testing for Normality

Statistics , as a discipline, is all about the collection, description, and interpretation of data. Within the scope of this book, our first task after ensuring that our data are in the right format and as free of error as possible is to get a “birds-eye view” of our dataset. That view is facilitated by generating descriptive statistics, such as number , mean , median , mode , maximum , minimum , skew , and kurtosis . A set of descriptive statistics can only tell us so much about our data. Even if differences in the mean , mode , and/or median exist between groups, there is always the possibility that those differences are the result of chance; before we can perform those tests, we need to know whether a parametric test (one based on a normal distribution of data) or non-parametric test (one that does not require normal data) is appropriate. In this section, we look at what “normally distributed” means, how to test whether data are normal, and under what conditions non-parametric tests can be used.