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In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman [1] and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables).
A rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. For example, two common nonparametric methods of significance that use rank correlation are the Mann–Whitney U test and the Wilcoxon signed-rank test.
In 1904, [2] Charles Spearman had developed a statistical procedure called factor analysis.In factor analysis, related variables are tested for correlation to each other, then the correlation of the related items are evaluated to find clusters or groups of the variables. [1]
Charles Edward Spearman, FRS [1] [3] (10 September 1863 – 17 September 1945) was an English psychologist known for work in statistics, as a pioneer of factor analysis, and for Spearman's rank correlation coefficient.
Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y. Pearson/Spearman correlation coefficients between X and Y are shown when the two variables' ranges are unrestricted, and when the range of X is restricted to the interval (0,1).
Intuitively, the Kendall correlation between two variables will be high when observations have a similar (or identical for a correlation of 1) rank (i.e. relative position label of the observations within the variable: 1st, 2nd, 3rd, etc.) between the two variables, and low when observations have a dissimilar (or fully different for a ...
Examples are Spearman’s correlation coefficient, Kendall’s tau, Biserial correlation, and Chi-square analysis. Pearson correlation coefficient. Three important notes should be highlighted with regard to correlation: The presence of outliers can severely bias the correlation coefficient.
Spearman's rank correlation coefficient; Mann–Whitney U test; Wilcoxon signed-rank test; Van der Waerden test; The distribution of values in decreasing order of rank is often of interest when values vary widely in scale; this is the rank-size distribution (or rank-frequency distribution), for example for city sizes or word frequencies.