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Tau-c (also called Stuart-Kendall Tau-c) [15] was first defined by Stuart in 1953. [16] Contrary to Tau-b, Tau-c can be equal to +1 or -1 for non-square (i.e. rectangular) contingency tables, [15] [16] i.e. when the underlying scale of both variables have different number of possible values. For instance, if the variable X has a continuous ...
Kendall 1970 [2] showed that his (tau) and Spearman's (rho) are particular cases of a general correlation coefficient. Suppose we have a set of n {\displaystyle n} objects, which are being considered in relation to two properties, represented by x {\displaystyle x} and y {\displaystyle y} , forming the sets of values { x i } i ≤ n ...
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 is a measure of how well the relationship between two variables can be described by a monotonic function. The Kendall tau rank correlation coefficient is a measure of the portion of ranks that match between two data sets.
Either Pearson's , Kendall's τ, or Spearman's can be used to measure pairwise correlation among raters using a scale that is ordered. Pearson assumes the rating scale is continuous; Kendall and Spearman statistics assume only that it is ordinal.
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).
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Thus low Pearson correlation coefficient with high Spearman or Kendal tau correlation coefficient indicate that there might be a monotonous relationship between two variables, but it is not linear. For example, it could be that one variable is proportional to the the cube of the other. You might wish to look at a scatter graph to find out more.