Kendall’s Rank Correlation

Kendall s rank correlation, represented by r(tau), should be used to evaluate the degree of association between two sets of data when the nature of the data is such that the relationship may not be linear. Most commonly, this is when the data are not continuous and/or normally distributed. An example of such a case is when we are trying to determine if there is a relationship between the length of hydra and their survival time in a test medium in hours. Both of our variables here are discontinuous, yet we suspect a relationship exists. Another common use is in comparing the subjective scoring done by two different observers. 

To measure how well ordering is reproduced, we will use Kendall s rank correlation coefficient. In order to construct it, we first define the pairs (yi.exp> yucalc)- For tWO pahS, i andy, H yi,calc> yi.exp> yj,exp or if... 

Kendall s tau correlation r Kendall) also measures the extent of monotonically increasing or decreasing relationships between the variables. It is also a nonparametric measure of association. It is computationally more intensive than the Spearman rank correlation because all slopes of pairs of data points have to be computed. Then Kendall s tau correlation is defined as the average of the signs of all pairwise slopes. The range of r is —1 to +1 the method is relatively robust against outliers for many applications p and r give similar answers. 

Correlation coefficient Spearman s Rank Correlation Kendall Tau Coefficient gamma Chi square Phi coefficient Fisher exact test Kendall coefficient of concordance... 

Pearson s product-moment correlation coefficient (r) is the most commonly used correlation coefficient. If both variables are normally distributed, then r can be used in statistical tests to test whether the degree of correlation is significant. If one or both variables are not normally distributed you can use Kendall s coefficient of rank correlation (t) or Spearman s coefficient of rank correlation (rs). They require that data are ranked separately and calculation can be complex if there are tied ranks. Spearman s coefficient is said to be better if there is uncertainty about the reliability of closely ranked data values. 

If correlation analysis is used with the raw data, ideally both data types should have similar ranges and distributions. If data is directly linearly correlated, this can be neglected, but is rarely the case for metabolome and transcriptome data. Changes in gene expression may not alter metabolite pools significantly. Therefore, data have to be normalized in an appropriate way and correlation methods other than linear correlation have to be used (e.g., Spearman s rank-order correlation or Kendall rank correlation should be preferred over Pearson correlation). 

This technique is concerned with quantitative analysis of data when analysing a pair of variables. Data can be displayed using a scatter diagram, and numerically, using simple correlation and regression - the product-moment correlation coefficient measures the strength of a linear relationship between the variables. If variables are measured using an ordinal scale then Spearman s rank or Kendall s tau may be used to indi-... 

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