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
16 - Non-parametric statistics
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
Parametric tests are designed for analysing data from a known distribution, and the majority assume a normally distributed population. Although parametric tests are quite robust to departures from normality, and major ones can often be reduced by transformation, there are some cases where the population is so grossly non-normal that parametric testing is unwise. In these cases a powerful analysis can often still be done by using a non-parametric test.
Non-parametric tests are not just alternatives to the parametric procedures for analysing ratio, interval, and ordinal data described in Chapters 7 to 15. Often life scientists obtain data that have been measured on a nominal scale. For example, Table 3.3 gave the numbers of basal cell carcinomas detected and removed from different areas of the human body. This is a sample containing frequencies in several discrete and mutually exclusive categories and there are non-parametric tests for analysing these types of data (Chapter 17).
The danger of assuming normality when a population is grossly non-normal
Most parametric tests have been specifically designed for analysing data from populations having bell-shaped distributions with 66.27% of values occurring within μ ± 1 standard deviation and 95% within μ ± 1.96 standard deviations (Chapter 6). This distribution is used to determine the range within which 95% of the values of the sample mean, will occur when samples of a particular size are taken from a population.
- Type
- Chapter
- Information
- Statistics ExplainedAn Introductory Guide for Life Scientists, pp. 205 - 207Publisher: Cambridge University PressPrint publication year: 2005