What is the difference between correlation and cause and effect?

Definition of Correlation

Correlation refers to the association between two or more variables. The association is measured by a statistic known as the coefficient of correlation (or correlation coefficient), which has a range of -1 to +1 ("0" indicates no correlation and "1" indicates perfect correlation).

Measuring the correlation between variables can be helpful, but a high degree of correlation does not guarantee that a change in one variable was actually caused by the other variable. (Often early medical research indicates the discovery of association between X and Y, but additional studies must be done before they can conclude there is cause and effect.)

To recap, correlation does not assure that there is a cause and effect relationship. However, if there is a cause and effect relationship, there has to be correlation.

Example of Correlation

Assume that during a 10-year period the number of cars sold in the U.S. moved in the same direction as the country's rate of inflation. Even with a 10-year correlation between the two sets of data, it is unlikely that more inflation caused an increase in the number of cars sold.

Accountants can find the level of correlation between variables by using statistical software. For example, simple linear regression analysis (and multiple regression analysis) software can be used to determine the relationship of production machine hours and mixed costs.