⊿ Point. {R} Glossary. ◢ Keyword: C. ◥ University. {q} PhD. {tr} Training. ⚫ UK. ↂ EndNote. ☝️ Weerakkody. Correlation. Statistical concept Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather.
In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation). or , measuring the degree of correlation.
Pearson's product-moment coefficient[edit] The most familiar measure of dependence between two quantities is the Pearson product-moment correlation coefficient (PPMCC), or "Pearson's correlation coefficient", commonly called simply "the correlation coefficient". The population correlation coefficient between two random variables and with expected values and standard deviations is defined as: where . Correlation does not imply causation. The counter assumption, that correlation proves causation, is considered a questionable cause logical fallacy in that two events occurring together are taken to have a cause-and-effect relationship.
This fallacy is also known as cum hoc ergo propter hoc, Latin for "with this, therefore because of this", and "false cause". A similar fallacy, that an event that follows another was necessarily a consequence of the first event, is sometimes described as post hoc ergo propter hoc (Latin for "after this, therefore because of this"). As with any logical fallacy, identifying that the reasoning behind an argument is flawed does not imply that the resulting conclusion is false.
In the instance above, if the trials had found that hormone replacement therapy caused a decrease in coronary heart disease, but not to the degree suggested by the epidemiological studies, the assumption of causality would have been correct, although the logic behind the assumption would still have been flawed. Usage[edit]