Wilcoxon’s two-sample test

It one has a group of samples from one population and a group of samples from another population, one is often faced with the question whether both populations are the same or not. For this situation several statistical tests are available, one of these being the well-known Student's test (cf. Dixon and Massey, 1951, chapter 9). One of the assumptions underlying Student's test is that the quantities, of which observations are available, have a normal distribution. In many cases, however, it is not known whether or not this assumption is satisfied. In these cases it is advisable to use a statistical test, not based on the assumption of normal distributions. In the problem concerned one can use, e.g., Wilcoxon's two-sample test. The assumptions underlying this test are : a. all observations are taken at random and are independent; b. the observations in group I are taken from the same population; c. the observation in group II are taken from the same population. As an example we take the following situation. A type of rock has been found in two localities; at each locality one has taken 6 samples* at random. The sodium content (in percentages) of these samples is: locality I; 6.3; 3.9; 3.5; 10.0; 2.5; 3.4. locality II; 5.6; 5.2; 6.0; 3.3; 1.1; 3.0.