Korrelieren

Korrelieren, in statistics, refers to the assessment of whether and how strongly two variables are related. Practically, researchers ask whether changes in one variable accompany changes in another, and whether the association is positive, negative, or absent. The most common quantitative measure is the correlation coefficient. The Pearson correlation coefficient, r, measures linear association and ranges from -1 to 1; values near 1 indicate a strong positive linear relation, near -1 a strong negative linear relation, and values near 0 little or no linear relationship. For non-linear or non-parametric relationships, Spearman's rho and Kendall's tau are used.

Correlation expresses association, not causation. A high correlation does not prove that one variable causes changes in the other; both may be influenced by a third variable, or the observed link may be coincidental. Analysts also distinguish correlation from covariance and from regression, which models a dependent variable as a function of one or more predictors.

Interpreting a correlation requires attention to assumptions and data quality. Pearson's r assumes approximately interval data, linearity, and homoscedasticity; outliers can inflate or deflate the coefficient; restricted range can obscure true associations. In reporting, confidence intervals and significance tests indicate whether the observed correlation is unlikely under independence.

Korrelieren appears in many fields, including psychology, economics, biology, and engineering, where it supports exploratory data analysis, model validation, and feature selection. Proper use emphasizes the limits of correlation and the need to consider causality, confounding factors, and study design.