Chapter 7: Some Non-Parametric Tests

Remember that you use statistics to make inferences about populations from samples. Most of the techniques statisticians use require that two assumptions are met. First, the population that the sample comes from is normal. Second, whenever means and variances were computed, the numbers in the data are cardinal or interval, meaning that the value given an observation not only tells you which observation is larger or smaller, but how much larger or smaller. There are many situations when these assumptions are not met, and using the techniques developed so far will not be appropriate. Fortunately, statisticians have developed another set of statistical techniques, non-parametric statistics, for these situations. Three of these tests will be explained in this chapter. These three are the Mann-Whitney U-test, which tests to see if two independently chosen samples come from populations with the same location; the Wilcoxon rank sum test, which tests to see if two paired samples come from populations with the same location; and Spearman’s rank correlation, which tests to see if two variables are related. The Mann-Whitney U-test is also presented in an interactive Excel template.