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Questions tagged [kendall-tau]

A measure of concordance between two random variables based on ranks.

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69
votes
5answers
66k views

Kendall Tau or Spearman's rho?

In which cases should one prefer the one over the other? I found someone who claims an advantage for Kendall, for pedagogical reasons, are there other reasons?
31
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3answers
11k views

How do the Goodman-Kruskal gamma and the Kendall tau or Spearman rho correlations compare?

In my work, we are comparing predicted rankings versus true rankings for some sets of data. Up until recently, we've been using Kendall-Tau alone. A group working on a similar project suggested we try ...
27
votes
3answers
3k views

If linear regression is related to Pearson's correlation, are there any regression techniques related to Kendall's and Spearman's correlations?

Maybe this question is naive, but: If linear regression is closely related to Pearson's correlation coefficient, are there any regression techniques closely related to Kendall's and Spearman's ...
15
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2answers
2k views

Canonical correlation analysis with rank correlation

Canonical correlation analysis (CCA) aims to maximize the usual Pearson product-moment correlation (i.e. linear correlation coefficient) of the linear combinations of the two data sets. Now, consider ...
10
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0answers
686 views

Picking block length in a block bootstrap

I am using the Mann-Kendall test to assess trends in a data time-series. I believe there is autocorrelation in my data and therefore need to use a block bootstrap to correct for it. I have plotted ...
9
votes
1answer
1k views

Correlation coefficients for ordered data: Kendall's Tau vs Polychoric vs Spearman's rho

It seems like for managing with ordered measurements researchers usually deal with Polychoric Correlation. (For example, for making matrix before doing Factor Analysis.) Why so? Kendall Tau Rank ...
8
votes
1answer
382 views

Bound the difference between Spearman's Correlation and Kendall's Correlation

I am trying to prove or disprove that the difference between Spearman's Correlation and Kendall's Correlation is no more than 1 (or less, the tighter the merrier). I am assuming there are no ties. ...
7
votes
1answer
980 views

Confidence intervals for Kendall's tau

I am working on some stats coursework, and have non parametric bivariate data. n=19, so small sample. There are a number of tied ranks, so I'm planning to use Kendall's tau rather than Spearman's rho, ...
7
votes
1answer
2k views

Spearman or Kendall correlation? [duplicate]

I would like to assess the correlation between a 7-category ordinal variable (X) and a number of other variables some of which are ordinal with 3-6 categories, others are continuous and a couple are ...
7
votes
1answer
253 views

Kendall-tau and RKHS spaces

Given two random variables $X_1$ and $X_2$, the Kendall-tau correlation coefficient could be defined as $$ \tau(X_{1},X_{2})=\mathbb{P}\Big((X_{1}-\tilde{X}_{1})(X_{2}-\tilde{X}_{2})>0\Big)-\mathbb{...
6
votes
2answers
2k views

Test for randomness - randtests - fails

Suppose I have a data set provided by PRNG in a matrix form with 400,000 rows and 20 columns. Each row consists 20 unique integer values from 1 to 80. I need to check the correctness of the PRNG. For ...
6
votes
1answer
240 views

Kendall's tau derivation from first principles?

I know that Kendall's tau is given by: $$\tau = P[(x_1-x_2)(y_1-y_2)>0]-P[(x_1-x_2)(y_1-y_2)<0]$$ However I cannot see how this gives: $$\tau = {2 \over n^2-n} \sum_{1\leq i<j\leq n}\, \...
6
votes
3answers
1k views

Weighted Kendall tau rank correlation coefficient

I need to use a measure to compare two rankings: Consider the ground truth as 1,2,3,4,5,6. Let two rankings be R1 and ...
6
votes
1answer
2k views

Rank correlation statistics comparison

I am trying to understand the relative behavior of the following rank correlation statistics: Spearman coefficient Kendall Tau / Concordance percentage Normalized Gini coefficient (area under curve ...
5
votes
4answers
4k views

What's the Kendall Tau's distance between these 2 rankings?

ranking i: {3, 1, 2} ranking j: {2, 1, 3} I am referring to the Wikipedia page here, and to calculate the Kendall distance, I just need to count the number of times the values in ranking i are in ...
5
votes
1answer
188 views

Making two vectors uncorrelated in terms of Kendall Tau correlation

Assume that we have two normalized $n\times 1$ vectors $\bf x$ and $\bf y$. In terms of Pearson correlation, these two signals are uncorrelated if ${\bf x}^T {\bf y} = 0$. Now, assume that ${\bf x}^T {...
5
votes
1answer
527 views

Population version of Kendall's tau

I am reading about concordance and Kendall's tau. The empirical formula for Kendall's tau is given by $$ t = \frac{c-d}{c+d},$$ where $c$ and $d$ are the numbers of concordant pairs and discordant ...
5
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0answers
81 views

Analysis of “The advantage of short paper titles”

After seeing the paper, The advantage of short paper titles showing a relationship between paper length rank and citation rank, I wondering what to make of the results. As a layman, my questions are: ...
5
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0answers
615 views

can I use PCA and PAF on Kendall's and Spearman's correlation matrix?

I have a dataset of 77 items, ranked by 17 people, with many ties (actually: Q-sorted under a forced quasi-normal distribution ...
4
votes
1answer
3k views

Kendall's tau for Clayton Copula

When $\theta =-\frac{1}{2}$ the Clayton copula is given by $C(x,y)=(\sqrt{x}+\sqrt{y}-1)^2$. I've been asked to show in this case that Kendall's tau is $-\frac{1}{3}$. Using $$\rho_{\tau}=4 \int_0^1 \...
4
votes
1answer
60 views

Can you use Kendall's Tau to compute covariance matrix?

I am working with multivariate archimedean copulas, and I am wondering how I can extract a covariance matrix out of them? I can get Kendall's Tau matrix of correlation so I was thinking that maybe I ...
4
votes
1answer
828 views

Statistical significance for many instances of Kendall tau correlation

I am working on a dataset, which contains multiple instances of ranking vectors, done by two annotators. In particular, I have about 20,000 data samples. Each sample contains a ranking of 4-5 items ...
4
votes
1answer
930 views

Metafor package in R: Ranktest for multivariate meta analysis

I have done a multivariate meta analysis with R, with support from metafor package. I am using rma.mv-method which gives an R object of class c("rma.mv","rma"). My question is about looking for funnel ...
4
votes
1answer
280 views

Theoretical computation Kendall's tau [closed]

While working with rank correlation statistics of samples, specifically Spearman's rho and Kendall's tau, I came across the interesting theoretical interpretation of Kendall's tau. It can be viewed as ...
4
votes
1answer
6k views

How to interpret the tau statistics in the Mann-Kendall test

How should the tau number from a Mann-Kendall test be interpreted? I've read that for trends to be detected by the test they must be monotonic. If I have data across years, group them by calendar ...
4
votes
1answer
5k views

Interpretation of Mann-Kendall statistics

I am doing a trend analysis for vegetation dynamics using Mann-Kendall test for trend detection and Sen's slope for computing the magnitude of the trend. There are 6 sites inside a conservation area ...
4
votes
1answer
398 views

What's the bias of calculating the Kendall coefficient of correlation on a sample instead of a whole population?

I am trying to calculate Kendall coefficient of correlation but my data frame in R contains 6 million observations and 17 variables. It is numerically hard for R to compute the estimator on a whole ...
3
votes
1answer
259 views

Why is Kendall's tau not consistent?

Kendall's tau measures the concordance between the two observations. For example, for $(X_1, Y_1)$, and $(X_2, Y_2)$, the pair is said to be concordant if $X_1 > X_2$ and $Y_1 > Y_2$, or $...
3
votes
2answers
1k views

Does it “rarely make sense” to compute Kendall's $\tau$ for a large sample?

The manual page for R's cor says: Some people have noted that the code for Kendall's tau is slow for very large datasets (many more than 1000 cases). It rarely ...
3
votes
1answer
2k views

Equivalent to Spearman correlation for non-monotonic data

I have several datasets of independent variables that have a monotonic (but non-linear) relationship. If I want to assess if they're correlated, the test of choice is Spearman's (rho) or Kendall's (...
3
votes
1answer
3k views

Kendall Tau-b correlation coefficient becomes more significant with many additional ties

Say I have two vectors of length N, x = [1, 10, 12, ..., 5, 6] y = [2, 11, 10, ..., 7, 9] I compute the Kendall tau-b rank order correlation on these two vectors ...
3
votes
1answer
5k views

How to interpret the level of Kendall's Tau-b

Besides saying that a relation is positive or negative is it possible to interpret the Kendall's Tau-B depending on its level? E.g.: I have two significant values 0.2 and 0.6, would be the ...
3
votes
1answer
148 views

Kendall correlation between $X$ and $X^2$

Let $X \sim N(0, 1)$. Can you confirm that the Kendall's correlation coefficient between $X$ and $X^2$ is equal to $0$. The way I interpret this, is that Kendall's tau only measures monotonic ...
3
votes
1answer
2k views

Compute significance of Kendall tau-b?

Compute significance of Kendall tau-b? I have so-far tried all ways of computing kendall tau significance (where there are ties) described here. However, none of them works good, even for relatively ...
3
votes
1answer
762 views

How do I compare individual likert scale items

I am looking to compare individual likert scale items. I measured respondent's level of agreement (in a 5 point-scale) for several items (e.g. from 1 to 5 how much is A competent to treat your ...
3
votes
0answers
25 views

Comparing a predicted order of events to actual order of events

Sorry about my somewhat limited knowledge of statistics, it's just this is a tad too complex for my knowledge of the subject. I'm running a competition where entrants are told what events happen, and ...
3
votes
0answers
2k views

Fast Kendall Tau in Matlab (and if necessary another language)

As I understand, there are two ways to compute Kendall Tau for a data matrix $X$ (n rows of data points in $\mathbb{R}^p$): corr(X,'type','kendall') http://www.mathworks.com/matlabcentral/...
3
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0answers
61 views

Generate two sequences that have a pre-specified rank correlation

I have two samples $ X_1,\cdots,X_n $ and $ Y_1, \cdots, Y_n $, and would like to re-order them so that they have a pre-specified value of rank correlation such as Kendall's tau. I do know that there ...
2
votes
2answers
2k views

How to compute Kendall tau for more than two variables

I am new to statistics. I decided to use Kendall tau correlation. I want to find correlations between every variable of the data set. (For example, if there are three variables in the data $x, y$ ...
2
votes
1answer
558 views

What does “significant rank correlation” mean in the context of Kendall Tau-B?

I am trying to understand how to correctly interpret "significant rank correlation" in the context of Kendall Tau-B. What can I conclude if the correlation is 1? The relationship is monotonic? Edit: ...
2
votes
1answer
731 views

Choosing the right correlation coefficient

Let $X \in \{0,1\}^{n \times m}$ be a matrix with $n,m \geq 600$. I want to calculate the correlations between the columns of the matrix $X$. To be more precise, I need the correlation matrix $C \in [...
2
votes
1answer
115 views

Sample size calculation for Kendall's Tau in reproducibility study

Can anyone help with justifying (or rubbishing) a couple of aspects of a sample size calculation for a grant proposal. A pilot study gave significant results for the correlation of a continuous (non-...
2
votes
1answer
176 views

Copula dependency

Prior to copula fitting, we must identify the dependency between two variable. What are the purpose of calculating the dependency? Some research said dependency value for example Kendall Tau value ...
2
votes
1answer
235 views

Kendall's tau or Kruskal Wallis Test?

I have data which is not normally distributed. Each participant ranked six actions in order of preference (so this is ordinal data right?) I want to see whether there is a significant difference in ...
2
votes
1answer
1k views

Differences in sample size when calculating weighted correlations (Pearson, Kendall-tau) in SPSS

Please consider the following dataset in SPSS: ...
2
votes
1answer
2k views

Spearman's rho to correlate discrete with binary variables

Is it ok to use the Spearman's rho if one has to correlate a binary and a discrete (from 0 to 100) variable? Or Kendall's tau b would be a better choice?
2
votes
0answers
27 views

How do I choose between Kendall's tau and Spearman's rho correlations? [duplicate]

I am trying to choose between the two correlation tests. I am trying to see if a trait is correlated with the area of a habitat patch for a number of different habitat types. The data is non-...
2
votes
0answers
127 views

How to choose rank correlation coefficient?

I want to quantify correlation between rankings. Rankings in this case have got ties. Also rankings don't rank all the same entries, the rankings might be of different sizes and rank different sets, ...
2
votes
0answers
284 views

Covariance between ordinal variable and discrete variable

I have two variables $y$ and $p$. Since $p$ is a discrete variable (numeric vector) and $y$ is an ordinal variable (total time watching TV). ...
2
votes
0answers
423 views

Correlation between counts

I'm trying on attendance data to find relationships between where people go. For example, say I have information on users A, B, C & D and what kinds of places they've visited in the past few ...