Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 ‘Doing science’ – hypotheses, experiments, and disproof
- 3 Collecting and displaying data
- 4 Introductory concepts of experimental design
- 5 Probability helps you make a decision about your results
- 6 Working from samples – data, populations, and statistics
- 7 Normal distributions – tests for comparing the means of one and two samples
- 7 Type 1 and Type 2 errors, power, and sample size
- 9 Single factor analysis of variance
- 10 Multiple comparisons after ANOVA
- 11 Two factor analysis of variance
- 12 Important assumptions of analysis of variance: transformations and a test for equality of variances
- 13 Two factor analysis of variance without replication, and nested analysis of variance
- 14 Relationships between variables: linear correlation and linear regression
- 15 Simple linear regression
- 16 Non-parametric statistics
- 17 Non-parametric tests for nominal scale data
- 18 Non-parametric tests for ratio, interval, or ordinal scale data
- 19 Choosing a test
- 20 Doing science responsibly and ethically
- References
- Index
18 - Non-parametric tests for ratio, interval, or ordinal scale data
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction
- 2 ‘Doing science’ – hypotheses, experiments, and disproof
- 3 Collecting and displaying data
- 4 Introductory concepts of experimental design
- 5 Probability helps you make a decision about your results
- 6 Working from samples – data, populations, and statistics
- 7 Normal distributions – tests for comparing the means of one and two samples
- 7 Type 1 and Type 2 errors, power, and sample size
- 9 Single factor analysis of variance
- 10 Multiple comparisons after ANOVA
- 11 Two factor analysis of variance
- 12 Important assumptions of analysis of variance: transformations and a test for equality of variances
- 13 Two factor analysis of variance without replication, and nested analysis of variance
- 14 Relationships between variables: linear correlation and linear regression
- 15 Simple linear regression
- 16 Non-parametric statistics
- 17 Non-parametric tests for nominal scale data
- 18 Non-parametric tests for ratio, interval, or ordinal scale data
- 19 Choosing a test
- 20 Doing science responsibly and ethically
- References
- Index
Summary
Introduction
This chapter describes some non-parametric tests for ratio, interval, or ordinal scale data. Non-parametric tests do not use the predictable distribution of sample means, which is the basis of most parametric tests, to infer whether samples are from the same population. Consequently 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 a non-parametric test.
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. Therefore, most non-parametric tests should not be used where there are gross differences in distribution (including the variance) among samples. The general rule that the ratio of the largest to smallest sample variance should not exceed 4:1 discussed in Chapter 12 also applies to non-parametric tests.
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.
First, the raw data are converted to ranks. For example, the lowest value is assigned the rank of ‘1’, the next highest ‘2’ etc. This transforms the data to an ordinal scale (see Chapter 3) with the ranks indicating only their relative order. Under the null hypothesis that the samples are from the same population you would expect a similar range of ranks within each, with differences among samples only occurring by chance.
- Type
- Chapter
- Information
- Statistics ExplainedAn Introductory Guide for Life Scientists, pp. 224 - 245Publisher: Cambridge University PressPrint publication year: 2005