Book contents
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 From cause to correlation and back
- 3 Sewall Wright, path analysis and d-separation
- 4 Path analysis and maximum likelihood
- 5 Measurement error and latent variables
- 6 The structural equations model
- 7 Nested models and multilevel models
- 8 Exploration, discovery and equivalence
- Appendix
- References
- Index
2 - From cause to correlation and back
Published online by Cambridge University Press: 10 December 2009
- Frontmatter
- Contents
- Preface
- 1 Preliminaries
- 2 From cause to correlation and back
- 3 Sewall Wright, path analysis and d-separation
- 4 Path analysis and maximum likelihood
- 5 Measurement error and latent variables
- 6 The structural equations model
- 7 Nested models and multilevel models
- 8 Exploration, discovery and equivalence
- Appendix
- References
- Index
Summary
Translating from causal to statistical models
The official language of statistics is the probability calculus, based on the notion of a probability distribution. For instance, if you conduct an analysis of variance (ANOVA) then the key piece of information is the probability of observing a particular value of Fisher's F statistic in a random sample of data, given a particular hypothesis or model. To obtain this crucial piece of information, you (or your computer) must know the probability density function of the F statistic. Certain other (mathematical) languages are tolerated within statistics but, in the end, one must link one's ideas to a probability distribution in order to be understood. If we wish to study causal relationships using statistics, it is necessary that we translate, without error, from the language of causality to the only language that statistics can understand: probability theory.
Such a rigorous translation device did not exist until recently (Pearl 1988). It is no wonder that statisticians have virtually banished the word ‘cause’ from statistics – it has no equivalent in their language. Within the world of statistics the scientific notion of causality has, until recently, been a stranger in a strange land. Posing causal questions in the language of probability calculus is like a unilingual Englishman asking for directions to the Louvre in Paris from a Frenchman who can't speak English. The Frenchman might understand that directions are being requested, and the Englishman might see fingers pointing in particular directions, but it is not at all sure that works of art will be found. Imperfect translations between the language of causality and the language of probability theory are equally disorienting.
- Type
- Chapter
- Information
- Cause and Correlation in BiologyA User's Guide to Path Analysis, Structural Equations and Causal Inference, pp. 21 - 64Publisher: Cambridge University PressPrint publication year: 2000