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
11 - Two 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
A single factor ANOVA gives the probability that two or more sample means have come from populations with the same mean (Chapter 9). Single factor ANOVA is used to analyse univariate data from samples exposed to different levels or aspects of only one factor. For example, it could be used to compare the oxygen consumption of a species of intertidal crab (the variable) at two or more temperatures (the factor), the growth of brain tumours (the variable) exposed to a range of drugs (the factor), or the insecticide resistance of a moth (the variable) from several different locations (the factor).
Often, however, life scientists obtain univariate data in relation to more than one factor. Examples of two factor experiments are the oxygen consumption of an intertidal crab at several combinations of temperature and humidity, the growth of brain tumours exposed to a range of drugs and different levels of radiation therapy, or the insecticide resistance of an agricultural pest from different locations and different host plants.
It would be very useful to have an analysis that gave separate F ratios (and the probability that the treatment means had come from populations with the same mean) for each of the two factors. That is what two factor ANOVA does.
Why do an experiment with more than one factor?
Experiments that simultaneously include the effects of more than one factor on a particular variable may be far more revealing than looking at each factor separately because you may detect certain combinations of factors that have a synergistic effect.
- Type
- Chapter
- Information
- Statistics ExplainedAn Introductory Guide for Life Scientists, pp. 127 - 150Publisher: Cambridge University PressPrint publication year: 2005