Introduction

So far, this book has only covered tests for one and two samples. Often, however, you are likely to have univariate data from three or more samples, from different locations or experimental groups, and wish to test the hypothesis that, ‘The means of the populations from which these samples have come from are not significantly different to each other’, or ‘μ1 = μ2 = μ3 = μ4 = μ5 etc …’.

For example, you might have data for the length in millimetres of adult grasshoppers of the same species from five different regions and wish to test the hypothesis that the samples have come from populations with the same mean.

Here you could test this hypothesis by doing a lot of two sample t tests that compare all of the possible pairs of means (e.g. mean 1 compared with mean 2, mean 1 compared with mean 3, mean 2 compared with mean 3 etc.). The problem with this approach is that every time you do a two sample test and the null hypothesis applies you run a 5% risk of a Type 1 error. So, as you do more and more tests on the same set of data, the risk of a Type 1 error rises rapidly.

Put simply, every time you do a two sample test it is like having a ticket in a lottery where the chance of winning is 5% – the more tickets you have, the more likely you are to win.