correlation

If a change in the amount of one variable is accompanied by a comparable change in the amount of another variable, and the latter change does not occur in the absence of the former change, then the variables are said to be correlated. This is sometimes called the method of concomitant variation, after the terminology devised by John Stuart Mill , who spelled out many of the basic designs of logical proof in the nineteenth century (see A System of Logic, Ratiocinative and Deductive, 1843). Correlations may be linear (where there is a constant ratio between the rates of change in each of the variables) or curvilinear (where the rate of change of one variable is at an increasing or decreasing ratio to the rate of change in the other variable). They may be positive (increase in one variable is associated with increase in the other) or negative (increase in one variable is associated with decrease in the other). Negative correlations are sometimes termed inverse correlations; positive correlations are occasionally referred to as direct correlations. When two (or more) variables are correlated, but there is no causal link between them, then the correlation is said to be spurious: both may be affected by a third (antecedent) variable. See also association coefficients ; causal modelling ; curvilinear relationship ; multivariate analysis.