Descriptive statistics

Non-parametric methods (also called Distribution-free methods) are statistical analyses that do not rely on assumptions about normality. For many standard statistical tests, there is a non-parametric equivalent. If your data are normally-distributed and you use a non-parametric test, then you will lose some power. That is, you would need a larger sample size to demonstrate the same level of statistical significance; however, that loss is not large (5% - 10%). On the other hand, if you use a standard test when the data are not normally-distributed, your results could be invalid. So the message is – if in doubt, go non-parametric.

Ranks

Most non-parametric tests are based on ranks. To obtain the rank of an observation, we sort them in to size order, and call the lowest observation 1, the second lowest 2, etc. The final observation will have the rank of the sample size. Here is an example with 6 observations.

Note that ties are handles by giving each of the observations the average rank of the tied observations. Note also that the final rank is 6, the sample size.

Many non-parametric analyses work by simply applying the test to the ranked data, rather than the original.