korrelation

Korrelation, the German term for correlation, describes the extent to which two variables move together. It captures both the direction of their association (positive or negative) and the strength of that relationship, whether linear or monotonic.

The most widely used measure is the Pearson correlation coefficient r, which assesses linear association and ranges from -1 to 1. A value near 1 indicates a strong positive linear relationship, near -1 a strong negative linear relationship, and near 0 little linear relation. For nonparametric or monotonic relationships, Spearman's rho or Kendall's tau are often employed; these coefficients also range between -1 and 1 but rely on ranks rather than raw values.

Calculation, in the simplest form, involves standardizing variables and computing the covariance divided by the product of their standard deviations. In practice, statistical software provides these coefficients and associated p-values to test whether the observed correlation differs from zero.

Interpretation emphasizes that correlation measures association, not causation. A high correlation does not imply that changes in one variable cause changes in the other; the relationship may be due to a third variable, reverse causation, or coincidence in the sample.

Limitations and pitfalls include sensitivity to outliers, restricted or non-representative data ranges, and nonlinearity. Correlation also assumes a consistent, linear or monotonic relationship across the data; in nonlinear or heterogeneous samples, correlations can be misleading.

Extensions include partial correlation (controlling for a third variable), correlation matrices for multiple variables, and methods tailored to time series data such as cross-correlation and autocorrelation.