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
9 - Single factor analysis of variance
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
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.
- Type
- Chapter
- Information
- Statistics ExplainedAn Introductory Guide for Life Scientists, pp. 105 - 118Publisher: Cambridge University PressPrint publication year: 2005