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The Spearman's rank correlation can then be computed, based on the count matrix , using linear algebra operations (Algorithm 2 [18]). Note that for discrete random variables, no discretization procedure is necessary. This method is applicable to stationary streaming data as well as large data sets.
Dave Kerby (2014) recommended the rank-biserial as the measure to introduce students to rank correlation, because the general logic can be explained at an introductory level. The rank-biserial is the correlation used with the Mann–Whitney U test, a method commonly covered in introductory college courses on statistics. The data for this test ...
Rank correlation is a measure of the relationship between the rankings of two variables, or two rankings of the same variable: . Spearman's rank correlation coefficient is a measure of how well the relationship between two variables can be described by a monotonic function.
"In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter ρ (rho) or as rs, is a non-parametric measure of statistical dependence between two variables. It assesses how well the relationship between two variables can be described using a monotonic function.
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.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
The test can be seen as a special case of Maurice Kendall’s more general method of rank correlation [3] and makes use of the Kendall's S statistic. This can be computed in one of two ways: This can be computed in one of two ways:
Kendall's W (also known as Kendall's coefficient of concordance) is a non-parametric statistic for rank correlation. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters and in particular inter-rater reliability. Kendall's W ranges from 0 (no agreement) to 1 (complete agreement).