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
14 - Relationships between variables: linear correlation and linear regression
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
Often life scientists obtain data for two or more variables measured on the same set of subjects or experimental units because they are interested in whether these variables are related and, if so, the type of functional relationship between them.
If two variables are related they vary together – as the value of one variable increases or decreases, the other also changes in a consistent way.
If two variables are functionally related, they vary together and the value of one variable can be predicted from the value of the other.
To detect a relationship between two variables, both are measured on each of several subjects or experimental units and these bivariate data examined to see if there is any pattern. One way to do this, by drawing a scatter plot with one variable on the X axis and the other on the Y axis, was described in Chapter 14, but, although this can reveal patterns, it does not show whether two variables are significantly related, or have a significant functional relationship. This is another case where you have to use a statistical test, because an apparent relationship between two variables may only have occurred by chance in a sample from a population where there is no relationship. A statistic will indicate the strength of the relationship, together with the probability of getting that particular result, or an outcome even more extreme, in a sample from a population where there is no relationship between the two variables.
- Type
- Chapter
- Information
- Statistics ExplainedAn Introductory Guide for Life Scientists, pp. 176 - 185Publisher: Cambridge University PressPrint publication year: 2005