Statistics in a Nutshell

Chapter 11. Nonparametric Statistics

The basis of statistics is parameter estimation, i.e., when an attempt is made to estimate the parameters (mean and standard deviation) of a population from a random sample. However, most statistical techniques rely on the underlying distribution being of a particular type, such as the normal distribution, for inferences made from the relevant statistical tests to be valid. What about scenarios where the underlying data is known to be nonnormal? In these cases, a different set of statistical techniques, known as nonparametric statistics, can be fruitfully applied to understand data. These techniques are often known as distribution-free since they make no assumptions about the underlying distribution of the data.

Nonparametric statistics are often applied to data sets where ranks rather than raw scores are used. For example, scholastic testing often involves some ranking of students from highest to lowest scores, and the ranks rather than the scores are often used in analysis. Taking the mean of the ranks of these scores is not a useful measure of central tendency in this scenario. Alternatively, Likert scales asking participants to rate their satisfaction with a product on a scale of values from 1–10, where 1 is very dissatisfied and 10 is extremely satisfied, the appropriate measure of central tendency would be the median rather than the mean, since the scores are ordinal rather than interval or ratio—that is, a score of 10 does not indicate ...