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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).
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.
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 .
Charles Spearman developed in 1904 a procedure for correcting correlations for regression dilution, [10] i.e., to "rid a correlation coefficient from the weakening effect of measurement error". [11] In measurement and statistics, the procedure is also called correlation disattenuation or the disattenuation of correlation. [12]
In statistics, inter-rater reliability (also called by various similar names, such as inter-rater agreement, inter-rater concordance, inter-observer reliability, inter-coder reliability, and so on) is the degree of agreement among independent observers who rate, code, or assess the same phenomenon.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [ a ] The variables may be two columns of a given data set of observations, often called a sample , or two components of a multivariate random variable with a known distribution .
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).
It can be computationally expensive to solve the linear regression problems. Actually, the nth-order partial correlation (i.e., with |Z| = n) can be easily computed from three (n - 1)th-order partial correlations. The zeroth-order partial correlation ρ XY·Ø is defined to be the regular correlation coefficient ρ XY.