Rangkorrelationen

Rangkorrelationen, often referred to in English as rank correlation, is a statistical measure used to assess the degree of association between two quantitative variables based on the order, or rank, of the observations rather than their raw values. Unlike conventional correlation coefficients such as Pearson’s r, rank correlation is non‑parametric and thus robust to outliers and to non‑linear monotonic relationships. It is particularly useful when the underlying distribution of the data is unknown, when the relationship is not expected to be linear, or when only ordinal information is available.

The most common rank‑correlation coefficient is Spearman’s rank‑order correlation, denoted by ρ (rho). It is computed by ranking each variable separately, converting the data to ranks, and then applying the Pearson correlation formula to those ranks. A secondary measure, Kendall’s tau, assesses the concordance between pairs of observations: it counts how often pairs of observations preserve their relative ordering in both variables. Kendall’s tau is often considered more interpretable in small samples, while Spearman’s ρ is more commonly reported in larger datasets.

Both τ (tau) and ρ (rho) take values between −1 and +1. A value of +1 indicates perfect positive concordance—higher values of one variable are always associated with higher values of the other. A value of −1 indicates perfect negative concordance. A value near 0 suggests no monotonic association.

In practice, rank correlation is applied across many scientific domains: ecological studies often use it to compare species abundance rankings; psychology evaluates correlations between test scores; finance uses it to examine the monotonic relationship between stock returns and market indices. Because it does not require assumptions about the frequency distribution of the variables, it remains a versatile tool for exploratory data analysis and hypothesis testing when data violate parametric assumptions.