Statistics Explained An Introductory Guide for Life Scientists

Introduction

This chapter describes some non-parametric tests for ratio, interval or ordinal scale univariate data. These tests do not use the predictable normal distribution of sample means, which is the basis of most parametric tests, to assess whether samples are from the same population. Because of this, non-parametric tests are generally not as powerful as their parametric equivalents but if the data are grossly non-normal and cannot be satisfactorily improved by transformation it is necessary to use one.

Non-parametric tests are often called ‘distribution free tests’, but most nevertheless assume that the samples being analysed are from populations with the same distribution. They should not be used where there are gross differences in distribution (including the variance) among samples and the general rule that the ratio of the largest to smallest sample variance should not exceed 4:1 discussed in Chapter 14 also applies. Many non-parametric tests for ratio, interval or ordinal data calculate a statistic from a comparison of two or more samples and work in the following way.