Book contents
- Frontmatter
- Contents
- Preface
- 1 Introduction to statistics
- 2 Frequency distributions and graphs
- 3 Descriptive statistics: measures of central tendency and dispersion
- 4 Probability and statistics
- 5 Hypothesis testing
- 6 The difference between two means
- 7 Analysis of variance (ANOVA)
- 8 Non-parametric comparison of samples
- 9 Simple linear regression
- 10 Correlation analysis
- 11 The analysis of frequencies
- References
- Appendix A Answers to selected exercises
- Appendix B A brief overview of SAS/ASSIST
- Appendix C Statistical tables
- Index
10 - Correlation analysis
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Introduction to statistics
- 2 Frequency distributions and graphs
- 3 Descriptive statistics: measures of central tendency and dispersion
- 4 Probability and statistics
- 5 Hypothesis testing
- 6 The difference between two means
- 7 Analysis of variance (ANOVA)
- 8 Non-parametric comparison of samples
- 9 Simple linear regression
- 10 Correlation analysis
- 11 The analysis of frequencies
- References
- Appendix A Answers to selected exercises
- Appendix B A brief overview of SAS/ASSIST
- Appendix C Statistical tables
- Index
Summary
This chapter deals with a technique that mathematically speaking is very similar to regression analysis. Its purposes, however, are quite different. It is thus important from the start to explain what correlation analysis and its purposes are in contrast with regression.
Correlation analysis deals with two variables collected in one sample, just like regression does. However, the purpose of correlation analysis is to quantify the degree to which the variables vary together. There is no intention of explaining one variable, or of predicting one according to the other. Because correlation analysis does not deal with independent and dependent variables, our nomenclature will not distinguish between the X and Y variables, but will refer to the two as Y1 and Y2. To summarize then, correlation analysis simply attempts to quantify if two variables have a statistically significant co-variation. This chapter offers the reader both a parametric and a nonparametric technique for correlation analysis. The latter will be particularly useful when data can only be rank-ordered, or constitute a small sample.
The Pearson product-moment correlation
The Pearson correlation is a commonly applied technique which quantifies the relation between two variables, and tests the null hypothesis that such relation is not statistically significant. The correlation is quantified with a coefficient whose statistical symbol is ‘r’, and whose parametric symbol is ρ. The coefficient ranges in value from –1 to +1. If r= –1 or close to it then, as Y1 increases, Y1 decreases.
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- Information
- Statistics for Anthropology , pp. 179 - 191Publisher: Cambridge University PressPrint publication year: 1998