Kendall's tau when to use?

Not sure this is the right statistical method? Use the Choose Your StatsTest workflow to select the right method.

Kendall’s Tau is used to understand the strength of the relationship between two variables. Your variables of interest can be continuous or ordinal and should have a monotonic relationship. See more below.

Kendall’s Tau is also called Kendall rank correlation coefficient, and Kendall’s tau-b.

Every statistical method has assumptions. Assumptions mean that your data must satisfy certain properties in order for statistical method results to be accurate.

The assumptions for Kendall’s Tau include:

Let’s dive in to each one of these individually.

The variables that you care about must be continuous or ordinal. Continuous means that the variable can take on any reasonable value. Some good examples of continuous variables include age, weight, height, test scores, survey scores, yearly salary, etc. Kendall’s Tau is often used for correlation on continuous data if there are outliers in the data.

Ordinal variables are categories that have an inherent order. For instance, education level (GDE/Bachelors/Masters/PhD), income level (if grouped into high/medium/low) etc.

Your two variables should have a monotonic relationship. This means that the direction of the relationship between the variables is consistent. For instance, when one variable goes up, the other goes up (in general). In this case, a plot of the two variables would move consistently in the up-right direction. The relationship would also be monotonic if when one variable goes up, the other goes down (in general). In this case, the plot of the two variables would move consistently in the down-right direction.

You should use Kendall’s Tau in the following scenario:

Let’s clarify these to help you know when to use Kendall’s Taup

You are looking for a statistical test to look at how two variables are related. Other types of analyses include testing for a difference between two variables or predicting one variable using another variable (prediction).

Your variables of interest must be either continuous or ordinal. Continuous means that your variables of interest can basically take on any value, such as heart rate, height, weight, number of ice cream bars you can eat in 1 minute, etc. Kendall’s Tau is often used on continuous data when the data have outliers.

Ordinal variables are categories that have an inherent order. For instance, education level (GDE/Bachelors/Masters/PhD), income level (if grouped into high/medium/low) etc.

If your data are continuous and do not have outliers, you should probably use Pearson Correlation instead. If one of your variables is continuous and the other is binary, you should use Point Biserial Correlation. And if your variables are categorical, you should use the Phi Coefficient or Cramer’s V.

Kendall’s Tau can only be used to compare two variables.

Variable 1: Hours worked per week.Variable 2: Income.

In this example, we are interested in investigating the relationship between a person’s average hours worked per week and income. To begin, we collect these data from a group of people.

Depending on the population, one or both of these variables is likely skewed, or does not fit a bell curve. For this reason, we use Kendall’s Tau instead of Pearson Correlation. We double check that the other assumptions of Kendall’s Tau are met.

The analysis will result in a correlation coefficient (called “Tau”) and a p-value. Tau values range from -1 to 1. A negative value of Tau indicates that the variables are inversely related, or when one variable increases, the other decreases. On the other hand, positive values indicate that when one variable increases, so does the other.

The p-value represents the chance of seeing our results if there was no actual relationship between our variables. A p-value less than or equal to 0.05 means that our result is statistically significant and we can trust that the difference is not due to chance alone.

Q: What is the difference between Spearman’s Rho and Kendall’s Tau?A: Spearman’s Rho and Kendall’s Tau are very similar tests and are used in similar scenarios. We recommend using Kendall’s Tau first and Spearman’s Rho as a backup.

Q: How do I run Kendall’s Tau in SPSS or R?A: StatsTest is focused on helping you pick the right statistical method every time. There are many resources available to help you figure out how to run this method with your data:SPSS article: https://statistics.laerd.com/spss-tutorials/kendalls-tau-b-using-spss-statistics.phpSPSS video: https://www.youtube.com/watch?v=dTUTvqY4f0ER article: http://www.r-tutor.com/gpu-computing/correlation/kendall-tau-bR video: https://www.youtube.com/watch?v=PC8HXz4P06c

There are two accepted measures of non-parametric rank correlations: Kendall’s tau and Spearman’s (rho) rank correlation coefficient.

Correlation analyses measure the strength of the relationship between two variables.

Kendall’s Tau and Spearman’s rank correlation coefficient  assess statistical associations based on the ranks of the data.  Ranking data is carried out on the variables that are separately put in order and are numbered.

Correlation coefficients take the values between minus one and plus one.  The positive correlation signifies that the ranks of both the variables are increasing.  On the other hand, the negative correlation signifies that as the rank of one variable is increased, the rank of the other variable is decreased.

Correlation analyses can be used to test for associations in hypothesis testing.  The null hypothesis is that there is no association between the variables under study.  Thus, the purpose is to investigate the possible association in the underlying variables.  It would be incorrect to write the null hypothesis as having no rank correlation between the variables.

Kendall’s Tau: usually smaller values than Spearman’s rho correlation. Calculations based on concordant and discordant pairs. Insensitive to error. P values are more accurate with smaller sample sizes.

Spearman’s rho: usually have larger values than Kendall’s Tau.  Calculations based on deviations.  Much more sensitive to error and discrepancies in data.

The main advantages of using Kendall’s tau are as follows:

Spearman’s rank correlation coefficient is the more widely used rank correlation coefficient.

Symbolically, Spearman’s rank correlation coefficient is denoted by rs . It is given by the following formula:

rs = 1- (6∑di2 )/ (n (n2-1))

*Here di represents the difference in the ranks given to the values of the variable for each item of the particular data

This formula is applied in cases when there are no tied ranks.  However, in the case of fewer numbers of tied ranks, this approximation of Spearman’s rank correlation coefficient provides sufficiently good approximations.

Key terms:

Non-parametric test: it does not depend upon the assumptions of various underlying distributions; this means that it is distribution free.

Concordant pairs: if both members of one observation are larger than their respective members of the other observations

Discordant pairs: if the two numbers in one observation differ in opposite directions

Related Pages:

Taxes have the ability to elicit strong responses in many people, with some thinking they are too high, whilst others think they should be higher. A researcher conducted a simple study where they presented participants with the statement: "Tax is too high in this country", and asked them how much they agreed with this statement. They had four options how to respond: "Strongly Disagree", "Disagree", "Agree" or "Strongly Agree". These ordered responses were the categories of the dependent variable, tax_too_high. The researcher also asked participants to state whether they had a "low", "middle" or "high" income, where each of these categories had specified income ranges (e.g., a low income was any income under £18,000 per annum). The income level of participants was recorded in the variable, income.

Therefore, in the Variable View of SPSS Statistics two ordinal variables were created so that the data collected could be entered: income and tax_too_high. Next, the data from 24 participants was entered into the Data View of SPSS Statistics.

The Correlate > Bivariate... procedure below shows you how to analyse your data using Kendall's tau-b in SPSS Statistics when neither of the two assumptions in the previous section, Assumptions, have been violated. At the end of these four steps, we show you how to interpret the results from this test.

Since some of the options in the Correlate > Bivariate... procedure changed in SPSS Statistics version 27 and the subscription version of SPSS Statistics, we show how to carry out Kendall's tau-b depending on whether you have SPSS Statistics versions 27 or 28 (or the subscription version of SPSS Statistics) or version 26 or an earlier version of SPSS Statistics. The latest versions of SPSS Statistics are version 27 and the subscription version. If you are unsure which version of SPSS Statistics you are using, see our guide: Identifying your version of SPSS Statistics.

Kendall's is often used when data doesn't meet one of the requirements of Pearson's correlation. Kendall's is non-parametric meaning that it does not require the two variables to fall into a bell curve. Kendall's also does not require continuous data.

Not sure this is the right statistical method? Use the Choose Your StatsTest workflow to select the right method.

Kendall’s Tau is used to understand the strength of the relationship between two variables. Your variables of interest can be continuous or ordinal and should have a monotonic relationship. See more below.

Kendall’s Tau is also called Kendall rank correlation coefficient, and Kendall’s tau-b.

Every statistical method has assumptions. Assumptions mean that your data must satisfy certain properties in order for statistical method results to be accurate.

The assumptions for Kendall’s Tau include:

Let’s dive in to each one of these individually.

The variables that you care about must be continuous or ordinal. Continuous means that the variable can take on any reasonable value. Some good examples of continuous variables include age, weight, height, test scores, survey scores, yearly salary, etc. Kendall’s Tau is often used for correlation on continuous data if there are outliers in the data.

Ordinal variables are categories that have an inherent order. For instance, education level (GDE/Bachelors/Masters/PhD), income level (if grouped into high/medium/low) etc.

Your two variables should have a monotonic relationship. This means that the direction of the relationship between the variables is consistent. For instance, when one variable goes up, the other goes up (in general). In this case, a plot of the two variables would move consistently in the up-right direction. The relationship would also be monotonic if when one variable goes up, the other goes down (in general). In this case, the plot of the two variables would move consistently in the down-right direction.

You should use Kendall’s Tau in the following scenario:

Let’s clarify these to help you know when to use Kendall’s Taup

You are looking for a statistical test to look at how two variables are related. Other types of analyses include testing for a difference between two variables or predicting one variable using another variable (prediction).

Your variables of interest must be either continuous or ordinal. Continuous means that your variables of interest can basically take on any value, such as heart rate, height, weight, number of ice cream bars you can eat in 1 minute, etc. Kendall’s Tau is often used on continuous data when the data have outliers.

Ordinal variables are categories that have an inherent order. For instance, education level (GDE/Bachelors/Masters/PhD), income level (if grouped into high/medium/low) etc.

If your data are continuous and do not have outliers, you should probably use Pearson Correlation instead. If one of your variables is continuous and the other is binary, you should use Point Biserial Correlation. And if your variables are categorical, you should use the Phi Coefficient or Cramer’s V.

Kendall’s Tau can only be used to compare two variables.

Variable 1: Hours worked per week.Variable 2: Income.

In this example, we are interested in investigating the relationship between a person’s average hours worked per week and income. To begin, we collect these data from a group of people.

Depending on the population, one or both of these variables is likely skewed, or does not fit a bell curve. For this reason, we use Kendall’s Tau instead of Pearson Correlation. We double check that the other assumptions of Kendall’s Tau are met.

The analysis will result in a correlation coefficient (called “Tau”) and a p-value. Tau values range from -1 to 1. A negative value of Tau indicates that the variables are inversely related, or when one variable increases, the other decreases. On the other hand, positive values indicate that when one variable increases, so does the other.

The p-value represents the chance of seeing our results if there was no actual relationship between our variables. A p-value less than or equal to 0.05 means that our result is statistically significant and we can trust that the difference is not due to chance alone.

Q: What is the difference between Spearman’s Rho and Kendall’s Tau?A: Spearman’s Rho and Kendall’s Tau are very similar tests and are used in similar scenarios. We recommend using Kendall’s Tau first and Spearman’s Rho as a backup.

Q: How do I run Kendall’s Tau in SPSS or R?A: StatsTest is focused on helping you pick the right statistical method every time. There are many resources available to help you figure out how to run this method with your data:SPSS article: https://statistics.laerd.com/spss-tutorials/kendalls-tau-b-using-spss-statistics.phpSPSS video: https://www.youtube.com/watch?v=dTUTvqY4f0ER article: http://www.r-tutor.com/gpu-computing/correlation/kendall-tau-bR video: https://www.youtube.com/watch?v=PC8HXz4P06c