# Kendall's tau

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## Kendall's tau

[¦ken·dəlz ′tȯ]
(statistics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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We also show how Kendall's tau [tau] changes in the infection rate [alpha] for different methods in Figure 1.
Statistic analysis with the help of Kendall's tau correlation has shown that there is weak directly proportional correlation between doctor's eye level and the level of the patient's satisfaction after the examination ([tau] = -0.224--direct question and [tau] = -0.225 for indirect question; in both situations p < 0.001).
For example, for categorical outcomes a different version of Kendall's tau, known as Kendall's tau b can be used for assessing correlation and Kappa can be used for assessing agreement.
Pearson and Spearman correlation coefficients, as well as the non-parametric measure of rank correlation, Kendall's tau were utilized.
Algorithm AS 71: The upper tail probabilities of Kendall's tau. Applied Statististics 23(1):98-100.
We use a nonparametric trend statistic Kendall's tau for monotonic trends, which makes no assumption about the distribution of the data or the linearity of any trend (e.g., Hollander and Wolfe ).
Kendall's tau Year 1997 1998 1999 Independent Cascade 0.007 0.012 0.015 Linear Threshold 0.172 0.167 0.167 DiffusionRank 0.221 0.181 0.160 Proposed(0.00) 0.240 0.204 0.178 Proposed(0.25) 0.243 0.206 0.180 Proposed(0.50) 0.243 0.206 0.180 Proposed(0.75) 0.243 0.206 0.180 Proposed(1.00) 0.230 0.190 0.163 Top 3 Jaccard coefficients Year 1997 1998 1999 Independent Cascade 0.011 0.014 0.015 Linear Threshold 0.171 0.195 0.212 DiffusionRank 0.216 0.222 0.213 Proposed(0.00) 0.242 0.243 0.225 Proposed(0.25) 0.248 0.244 0.226 Proposed(0.50) 0.247 0.243 0.227 Proposed(0.75) 0.246 0.243 0.226 Proposed(1.00) 0.204 0.179 0.156 TABLE 3: Consider the result after k x R rounds for each model, and compare it with the ground truth of year 1996 + k.
Funnel plots (Figure 3), Kendall's tau, and Egger's test for bias are suggestive of low power, low likelihood for unpublished or unreported studies, and not statistically significant for bias across IBS severity at end-of-intervention, (Kendall's tau = 0.333 P = 0.469; Egger = 1.901, 95% CI = -4.376 to 8.182 P = 0.448), on IBS severity at postintervention follow-up (Kendall's tau = 0.4 P = 0.483; Egger = 1.256,95% CI = -3.988 to 6.501, P = 0.501), and on QOL (Kendall's tau = 0 P = 0.817; Egger = 1.345, 95% CI = -6.742 to 9.432, P = 0.633).
It means that the Spearman's rho is given as the probability of concordance reduced by the probability of discordance, in contrast to the Kendall's tau, for the pairs ([x.sub.1],[y.sub.1]) and ([x.sub.2],[y.sub.3]).
TABLE 1 Measures of Relations Between the Rankings in Time Variant with Weights Variant without Weights Coefficient 00/01 01/II02 II02/III02 00/01 01/II02 II02/III02 TMAI Spearman rank 0.886 0.919 0.865 0.797 0.885 0.876 correlation coefficient Kendall's tau 0.742 0.799 0.739 0.648 0.758 0.760 coefficient GDM Spearman rank 0.610 0.666 0.827 0.741 0.726 0.881 correlation coefficient Kendall's tau 0.458 0.546 0.681 0.564 0.595 0.717 coefficient BZW Spearman rank 0.831 0.863 0.940 correlation coefficient Kendall's tau 0.664 0.710 0.797 coefficient Source: The author's own calculations with Statistica 6.1PL.
The frequency of use for each code was calculated for both current (1975-1999) and contemporary (1714-1974) Spanish; ranks were assigned, and Kendall's Tau correlations between periods computed.

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