Kendall’s Tau is a rank-based correlation coefficient used in statistical analysis to describe the direction and strength of association between two ordered variables. It is also called Kendall’s rank correlation coefficient, and it is especially useful when a researcher wants to understand whether two sets of observations tend to follow the same order.
The idea behind the coefficient is easier than the notation sometimes suggests. Kendall’s Tau compares pairs of observations. If two students, patients, essays, judges’ scores, survey responses, or laboratory records appear in the same order on both variables, the pair supports a positive association. If the order is reversed, the pair supports a negative association. The final coefficient summarises that balance.
This article explains what Kendall’s Tau is, how it differs from Pearson’s and Spearman’s correlation, when to use it, how the formula works, how to calculate it, how ties are handled, how to interpret the result, and how to report Kendall’s Tau in academic writing.
What Is Kendall’s Tau?
Kendall’s Tau is a measure of association for two variables that can be ordered. Instead of focusing on the exact distance between values, it asks whether the observations keep a similar order across both variables. This makes it useful for rankings, ordinal scales, scores with many ties, and quantitative variables where the order is more important than the raw spacing.
Imagine a teacher ranks six student essays by structure and also ranks the same essays by clarity. If essays that receive high structure ranks also tend to receive high clarity ranks, Kendall’s Tau will be positive. If essays ranked highly for structure tend to receive low clarity ranks, the coefficient will be negative. If the two rankings are mixed without a steady pattern, the coefficient will sit closer to zero.
Kendall’s Tau definition
Kendall’s Tau is a statistic that measures ordered association between two variables by comparing all possible pairs of observations. A pair is concordant when the two observations appear in the same order on both variables. A pair is discordant when the order is reversed. Kendall’s Tau is based on the difference between these two counts.
The coefficient usually ranges from -1 to +1. A value near +1 means that the two variables show very similar ordering. A value near -1 means that one ordering is close to the reverse of the other. A value near 0 means that the ordered pairs do not show a clear increasing or decreasing pattern.
What Kendall’s Tau tells the reader
Kendall’s Tau gives two pieces of information at once. The sign gives the direction of the association. A positive coefficient means that higher values or ranks on one variable tend to go with higher values or ranks on the other. A negative coefficient means that higher values on one variable tend to go with lower values on the other.
The size of the coefficient shows how consistently the pairs follow that direction. A coefficient of -0.70 and a coefficient of +0.70 are similar in strength, but they describe opposite directions. The first suggests a mostly reversed order. The second suggests a mostly shared order.
Pairs instead of distances
The defining feature of Kendall’s Tau is its pair-by-pair logic. The coefficient does not begin by calculating means or standard deviations. It begins by asking how every observation compares with every other observation. If there are 10 observations, there are 45 unique pairs. If there are 20 observations, there are 190 pairs.
This pair comparison gives Kendall’s Tau a clear interpretation. It is closely connected to the probability that two randomly chosen observations will be ordered in the same way rather than in opposite ways. For many readers, that interpretation is easier to understand than a formula based only on rank differences.
Sample coefficient and population association
In most research reports, Kendall’s Tau is calculated from a sample. The sample coefficient describes the data that were observed and may also be used to estimate the ordered association in a wider population. These are not the same claim. A coefficient from one sample can change when a new sample is drawn from the same population.
This distinction connects Kendall’s Tau to inferential statistics. If the coefficient is used only to describe the sample, it is descriptive. If the researcher tests whether the population association differs from zero, or reports a confidence interval, the analysis has moved into inference.
Assumptions of Kendall’s Tau
Kendall’s Tau is often introduced as a flexible alternative to Pearson’s correlation. That flexibility is real, because Kendall’s Tau does not require a straight-line relationship between raw numerical values. Still, it is not a coefficient to use without checking the data structure. The variables must be paired, ordered, and suitable for an association measured through ranks or order comparisons.
Paired observations
Kendall’s Tau requires paired observations. Each case must have a value on both variables. If a student has a motivation rating but no exam rank, that case cannot be compared in the ordinary calculation unless missing data are handled through a planned method.
The pairing is what makes the pair comparison meaningful. Kendall’s Tau does not compare one list of values with an unrelated list. It compares two measurements from the same people, essays, classrooms, patients, schools, plants, survey responses, or other units of analysis.
Variables with meaningful order
Both variables should have an order that makes sense. This may be a ranked order, such as first through tenth; an ordinal scale, such as low, medium, and high; or a numerical order, such as test scores, time, age, or symptom score. The coefficient does not require equal distances between categories, but it does require that higher and lower positions mean something in the research context.
A nominal category code is not enough. If subject area is coded as 1 for biology, 2 for history, and 3 for art, those numbers do not create a meaningful order. Kendall’s Tau would not be suitable unless the categories had been transformed into an ordered variable for a clear reason.
A monotonic association pattern
Kendall’s Tau is designed for monotonic association. A monotonic pattern moves mainly in one direction. As one variable increases, the other tends to increase, or as one variable increases, the other tends to decrease. The pattern may be uneven or curved, but it should not repeatedly rise and fall.
A scatterplot or rank plot can help. If the points generally move upward or downward, Kendall’s Tau may give a fair summary. If the pattern rises, falls, and rises again, one coefficient may hide the structure of the data rather than clarify it.
Independence of observations
Each pair of observations should usually be independent of the others. If the same student appears several times, or many students come from the same classroom, ordinary Kendall’s Tau may treat related observations as if they were separate. This is especially important when a p-value or confidence interval is reported.
Independence is less about the formula and more about the study design. A coefficient can be calculated from repeated or clustered data, but the usual inferential reading may not fit. In that situation, the researcher may need a method that recognises repeated measurements, clustered cases, or another form of dependence in the data.
Ties and repeated values
Ties occur when two or more observations have the same value on one or both variables. They are common in rating scales, rubric scores, rounded measurements, and short ordinal scales. Kendall’s Tau can handle ties, but the version of the coefficient must be chosen carefully.
Kendall’s Tau-a is the simplest version and assumes no ties. Kendall’s Tau-b adjusts for ties and is widely used when both variables may contain repeated values. Kendall’s Tau-c is sometimes used for rectangular tables, especially when the numbers of categories differ. Many statistical packages report Tau-b by default because ties are common in practical data.
Unusual observations
Kendall’s Tau is usually less sensitive to extreme raw values than Pearson’s r because it works with order comparisons. A very large raw value becomes a high position in the ordering, rather than pulling a line through the scatterplot. This can be helpful when unusual values are real and should remain in the dataset.
Unusual observations should still be examined. A single case with a very unexpected rank pattern can influence the result, especially in a small sample. The researcher should check whether such observations are data entry errors, special cases, or meaningful parts of the population being studied.
When to Use Kendall’s Tau
Kendall’s Tau is appropriate when the research question asks whether two ordered variables tend to move together. It is often chosen when the data are ordinal, when ranks are central to the analysis, when there are many tied values, or when the researcher wants a coefficient with a clear pair-comparison interpretation.
The method fits many academic settings. An education researcher may compare teacher ratings and student self-ratings. A psychology researcher may examine two ordered questionnaire scales. A health researcher may study whether symptom severity categories increase with another clinical measure. A literature researcher may compare two judges’ rankings of texts. In each case, the analysis focuses on ordered association.
Use Kendall’s Tau for ordinal variables
Ordinal variables show order but do not guarantee equal distances between categories. A five-point agreement scale tells us that 5 is higher than 4, and 4 is higher than 3. It does not guarantee that the distance from 1 to 2 is the same as the distance from 4 to 5.
Kendall’s Tau is often suitable for this type of data because it does not depend on treating those distances as equal. It asks whether higher positions on one variable tend to go with higher or lower positions on another variable. That makes it a natural choice for ratings, rankings, ordered categories, and rubric levels.
Use Kendall’s Tau for monotonic patterns
Some relationships are clearly increasing or decreasing without forming a straight line. For example, reading comprehension may improve quickly with early practice and then improve more slowly after students have already practised a great deal. A straight-line coefficient may not describe that shape comfortably.
Kendall’s Tau can still capture the ordered movement. If students with more practice generally have higher comprehension scores, even along a curve, the coefficient may show a positive association. It does not estimate a curve, but it can summarise the ordered tendency.
Use Kendall’s Tau when pair interpretation is useful
The pair logic of Kendall’s Tau can be helpful when explaining results to readers who are not specialists. A positive coefficient means that, across the pairs in the data, concordant comparisons are more common than discordant comparisons. This is a direct and readable way to explain ordered association.
For instance, if a dataset compares students’ confidence ranks with performance ranks, Kendall’s Tau asks how often the more confident student in a pair also has the higher performance rank. The coefficient turns that repeated comparison into one number.
Plain reading: Kendall’s Tau summarises how often pairs line up in the same order compared with how often they appear in the opposite order.
Use Kendall’s Tau for association, not cause
Kendall’s Tau describes association. It does not show that one variable caused another. A positive coefficient between participation rank and final grade may fit the idea that participation supports learning, but the result could also reflect prior knowledge, confidence, feedback, attendance, teacher expectations, or other variables not included in the analysis.
Causal interpretation depends on the design rather than on the coefficient alone. Experiments, longitudinal evidence, clear temporal order, measurement quality, and careful control of alternative explanations all shape how far the interpretation can go.
Situations where another method may fit better
Kendall’s Tau is not the best answer for every relationship. If both variables are quantitative and the research question asks about a straight-line association between raw values, Pearson’s correlation may be more direct. If the research question asks about prediction or adjustment for several variables, regression analysis may be needed.
If one or both variables have only nominal categories, a table-based method may be more suitable. If the data are repeated, nested, or clustered, a model that matches that structure may be a better choice than an ordinary correlation coefficient.
Formula for Kendall’s Tau
The formula for Kendall’s Tau is built from pair comparisons. For every possible pair of observations, the calculation asks whether the order agrees across the two variables, disagrees, or contains a tie. Once those pairs have been counted, the coefficient summarises the balance of agreement and disagreement.
Concordant and discordant pairs
A pair is concordant when the observation that is higher on one variable is also higher on the other variable. A pair is discordant when the observation that is higher on one variable is lower on the other. If the observations have the same value on one of the variables, the pair contains a tie.
Suppose student A has a higher practice rank than student B and also a higher project rank. That pair is concordant. If student A has a higher practice rank but a lower project rank than student B, the pair is discordant. Kendall’s Tau repeats this comparison for all possible pairs in the dataset.
Kendall’s Tau-a formula
The simplest version is Kendall’s Tau-a. It is used when there are no ties. The formula is:
Formula: τa = (C – D) / [n(n – 1) / 2]
In this formula, C is the number of concordant pairs, D is the number of discordant pairs, and n is the number of paired observations. The denominator is the total number of unique pairs in the dataset.
The formula shows why the coefficient ranges from -1 to +1. If every pair is concordant, D is 0 and the coefficient becomes +1. If every pair is discordant, C is 0 and the coefficient becomes -1. If concordant and discordant pairs are nearly balanced, the coefficient moves toward 0.
Kendall’s Tau-b formula
In real data, ties are common. Kendall’s Tau-b adjusts for ties by changing the denominator. A common form is:
Formula: τb = (C – D) / sqrt[(C + D + Tx)(C + D + Ty)]
Here, Tx is the number of pairs tied only on the first variable, and Ty is the number of pairs tied only on the second variable. Statistical software may use equivalent notation, but the purpose is the same. Tau-b adjusts the calculation so ties do not distort the scale of the coefficient.
Kendall’s Tau-c
Kendall’s Tau-c is another tie-aware version, often used when the data are arranged in a rectangular table and the two variables have different numbers of ordered categories. It appears less often in introductory research reports than Tau-b, but it can be useful for ordered contingency tables.
For most beginner and intermediate research situations, the main decision is between Tau-a and Tau-b. When the dataset contains repeated ratings, repeated scores, or ordered categories with limited response options, Tau-b is usually the more practical choice.
Formula in words
In words, Kendall’s Tau asks whether ordered pairs agree more often than they disagree. The numerator, C – D, captures the direction and size of the balance. The denominator scales that balance so the result can be compared across datasets of different sizes.
This is also why the coefficient is not tied to the original units of measurement. A correlation between two ordered ratings is not measured in rating points. A correlation between rank order and test score is not measured in ranks or points. Kendall’s Tau is a standardised association measure.
Calculating Kendall’s Tau
Kendall’s Tau is usually calculated with statistical software, but a small hand calculation helps make the logic clear. The example below uses six students and two variables: practice rank and final project rank. There are no tied values, so the simple Tau-a formula can be used.
Suppose a teacher wants to know whether students who rank higher in practice work also tend to rank higher on a final project.
| Student | Practice rank | Final project rank |
|---|---|---|
| A | 1 | 1 |
| B | 2 | 3 |
| C | 3 | 2 |
| D | 4 | 4 |
| E | 5 | 6 |
| F | 6 | 5 |
Step 1: Find the total number of pairs
With six students, every student can be compared with every other student once. The number of unique pairs is:
Total pairs:
n(n – 1) / 2 = 6(5) / 2
Total pairs = 15
The calculation will therefore classify 15 pairs as concordant or discordant. Because the example has no tied values, every pair falls into one of those two groups.
Step 2: Compare each pair
Now compare students two at a time. Student A is ranked first on both variables, so A forms concordant pairs with every student below. Student B and student C create one discordant pair because B has a better practice rank than C, but C has a better final project rank than B.
The same comparison continues through the table. Most pairs keep the same general order. Two pairs reverse: B with C, and E with F. The counts are:
Pair counts:
Concordant pairs, C = 13
Discordant pairs, D = 2
Step 3: Insert the counts into the formula
The simple no-tie formula uses the number of concordant pairs, the number of discordant pairs, and the total number of pairs.
Calculation:
τa = (C – D) / [n(n – 1) / 2]
τa = (13 – 2) / 15
τa = 0.73
The result is approximately 0.73. In this small example, practice rank and final project rank show a strong positive ordered association. Students with higher practice ranks generally also have higher final project ranks, although the order is not perfect.
What the result says in the example
The coefficient does not say that practice caused the project rank. It also does not say that the difference between ranks is equal for every pair of students. It says that, in this dataset, the order of students on practice work is often similar to their order on the final project.
This is the kind of statement Kendall’s Tau supports well. It keeps the interpretation close to the data and avoids turning an ordered association into a stronger causal claim.
Calculating Kendall’s Tau with software
Most researchers calculate Kendall’s Tau with software such as R, Python, SPSS, Stata, Jamovi, JASP, or statistical calculators. The software usually reports the coefficient and may also report a p-value, sample size, and sometimes a confidence interval.
Software is useful, but it should not replace checking the data. Before interpreting the output, the researcher should confirm that the observations are paired correctly, missing values were handled as intended, the variables have meaningful order, and ties were treated by an appropriate version of the coefficient.
Handling Ties in Kendall’s Tau
Ties deserve their own attention because many real datasets contain repeated values. A classroom rubric may give several students the same score. A survey scale may give many respondents the same agreement category. A clinical scale may place several patients in the same severity level. These repeated values affect how pair comparisons are counted.
The presence of ties does not mean Kendall’s Tau has to be abandoned. It means the researcher should usually use a tie-aware version, especially Kendall’s Tau-b. The goal is to keep the coefficient readable while recognising that tied observations do not provide the same ordering information as distinct values.
Why ties occur
Ties often come from the measurement scale. A five-point response scale cannot create unique positions for hundreds of respondents. Rounded test scores can repeat. Ratings by judges can cluster at the same level. In these situations, repeated values are not necessarily errors. They reflect how the variable was measured.
Because Kendall’s Tau is based on order, tied values create a small complication. If two observations have the same value on one variable, that pair cannot be said to agree or disagree in the same way as two clearly ordered observations.
Ties on one variable
Suppose two students have the same participation rating but different project ranks. Their order on participation is tied, so the pair cannot fully support either a concordant or discordant comparison. Tau-b adjusts the denominator to account for such pairs.
This adjustment is important because frequent ties reduce the amount of ordering information in the data. A coefficient based on many tied values should be interpreted with that measurement limitation in view.
Ties on both variables
Some pairs are tied on both variables. For example, two respondents may give the same answer on two survey scales. Such pairs do not show one observation above or below the other on either variable. They therefore add less information to an ordered association than fully distinct pairs.
Different software packages may display tied-pair details differently, but the purpose is the same. The calculation separates concordant pairs, discordant pairs, and tied pairs so the final coefficient reflects the available ordered information.
When ties are frequent
Frequent ties do not automatically invalidate Kendall’s Tau. They do, however, change how the result should be read. A coefficient based on two five-point scales can be informative, but the reader should remember that the variables offer only a limited number of ordered positions.
If both variables have very few categories, a table can sometimes show the pattern more clearly than a single coefficient. In a report, Kendall’s Tau can still be useful, especially when it is combined with a table of counts or a short explanation of the measurement scale.
Reporting the version used
When the data contain ties, the methods section should name the version of Kendall’s Tau used. A sentence such as “Kendall’s Tau-b was used because the ordinal variables contained tied values” is often enough. This tells the reader that the calculation matched the data rather than relying on the simple no-tie version.
If software was used, the researcher can also report the software package and version when appropriate. This is especially helpful in technical work where exact p-values, small samples, or many ties are central to the analysis.
Interpreting Kendall’s Tau
Interpreting Kendall’s Tau begins with the sign, the size, the sample, and the research context. The sign tells the direction. The size tells how consistently the ordered pairs follow that direction. The context tells how the coefficient should be read in relation to the variables, the design, and the measurement scale.
Direction of the association
A positive Kendall’s Tau means that higher values on one variable tend to appear with higher values on the other. A negative Kendall’s Tau means that higher values on one variable tend to appear with lower values on the other. A value near zero means that the pairs do not show a clear ordered pattern.
Direction should be written in words, not left as a sign. Instead of writing only “τ was positive,” explain which variables tend to move together. For example: students with higher reading-confidence ranks tended to have higher comprehension-score ranks.
Strength of the association
Many introductory guides use labels such as weak, moderate, and strong. These labels can help beginners, but they should not be applied without context. A coefficient of 0.30 may be useful in one field and modest in another. Measurement quality, sample size, field expectations, and study design all shape interpretation.
| Value of Kendall’s Tau | General reading | Plain interpretation |
|---|---|---|
| Close to +1 | Strong positive ordered association | Most pairs appear in the same order on both variables. |
| Close to -1 | Strong negative ordered association | Most pairs appear in opposite order across the variables. |
| Close to 0 | Little ordered association | Concordant and discordant pair patterns are nearly balanced. |
Statistical significance
A significance test for Kendall’s Tau usually evaluates whether the population association is zero. This belongs to hypothesis testing. A small p-value suggests that the observed ordered association would be unusual if the population association were truly zero, assuming the test conditions are reasonable.
The p-value should not replace the coefficient. A small coefficient can become statistically significant in a large sample. A larger coefficient can be uncertain in a small sample. The coefficient, confidence interval, sample size, p-value, and design should be read together.
Confidence intervals
A confidence interval gives a range of plausible values for the population association. It is often more informative than a p-value alone because it shows both direction and uncertainty. A narrow interval suggests a more precise estimate. A wide interval suggests more uncertainty.
For example, a Kendall’s Tau of 0.42 with a confidence interval from 0.25 to 0.57 gives a different reading from the same coefficient with a confidence interval from -0.05 to 0.73. The point estimate is the same, but the second interval leaves much more uncertainty about the population pattern.
Association and causation
Kendall’s Tau is a correlation coefficient, and correlation does not prove causation. This point should be stated when there is any risk of overinterpretation. A positive association between two ordinal variables can be real and useful without showing that one variable produced the other.
The strength of a causal interpretation depends on design features such as sampling, measurement, timing, comparison groups, and control of alternative explanations. The coefficient supports a statement about ordered association, not a causal claim by itself.
Kendall’s Tau vs Spearman vs Pearson
Kendall’s Tau, Spearman’s rank correlation, and Pearson’s correlation all describe association between two variables, but they do not ask exactly the same question. The best choice depends on the variables, the shape of the relationship, and the claim the researcher wants to make.
Kendall’s Tau and Spearman’s rank correlation
Kendall’s Tau and Spearman’s correlation are both rank-based. They are often considered when the variables are ordinal or when the relationship is monotonic rather than strictly linear. The difference is in the logic of the calculation.
Spearman’s correlation first converts the variables into ranks and then measures association between those ranks. Kendall’s Tau compares pairs of observations and counts whether the order agrees or disagrees. Because of this pair logic, Kendall’s Tau often has a very direct interpretation, while Spearman’s coefficient may look more familiar to readers who already know Pearson’s r.
Kendall’s Tau and Pearson correlation
Pearson’s correlation uses the original numerical values and measures linear association. It works best when the research question is about a straight-line relationship between two quantitative variables. Kendall’s Tau works with order and can be suitable for ordinal variables, non-normal distributions, and monotonic relationships that do not form a straight line.
For example, if a researcher measures exact reaction times and exact accuracy scores and expects a straight-line pattern, Pearson’s r may be suitable. If a researcher compares two ordered rating scales with many tied values, Kendall’s Tau-b may fit the data more comfortably.
Comparison table
| Coefficient | Main idea | Often used for |
|---|---|---|
| Pearson’s r | Linear association using raw quantitative values | Two quantitative variables with an approximately straight pattern |
| Spearman’s rho | Correlation between ranks | Ordinal variables and monotonic patterns |
| Kendall’s Tau | Balance of concordant and discordant pairs | Ordered data, small samples, ties, and pair-based interpretation |
Choosing among the three
Start with the research question. If the question is about a straight-line relationship between two quantitative variables, Pearson’s r is usually the first coefficient to consider. If the question is about ordered movement, either Spearman’s rho or Kendall’s Tau may be suitable. If ties are frequent, or if the pair-comparison interpretation is useful, Kendall’s Tau-b is often a strong choice.
The choice should also be explained in the methods section. A reader should not have to guess why a rank-based coefficient was used. The explanation can be brief: the variables were ordinal, the relationship was monotonic, tied values were present, or the analysis focused on ordered association.
Reporting Kendall’s Tau in Academic Writing
A clear report of Kendall’s Tau should give the coefficient, the sample size, the version used when relevant, the p-value or confidence interval if inference was conducted, and a plain-language interpretation. The report should give the number and then show what that number means for the study.
What to include
In many reports, a Kendall’s Tau result includes the symbol τ, the value of the coefficient, the sample size, and the p-value. If ties were present, it is useful to say that Tau-b was used. If confidence intervals are available, they give helpful information about uncertainty.
- the two variables being analysed
- the version of Kendall’s Tau, especially Tau-b when ties are present
- the coefficient value
- the sample size used in the calculation
- the p-value, confidence interval, or both, when inferential results are reported
- a short interpretation of direction and strength
Example report sentence
A concise report might read:
A Kendall’s Tau-b correlation showed a positive association between reading-confidence rank and comprehension-score rank, τb = .46, n = 84, p < .001.
The sentence names the coefficient, the variables, the direction, the value, the sample size, and the p-value. A longer report could add a confidence interval and a sentence explaining that higher confidence ranks tended to appear with higher comprehension ranks.
Methods section wording
The methods section should explain why Kendall’s Tau was chosen. The wording does not need to be complicated. For example:
Kendall’s Tau-b was used because both variables were ordinal and contained tied values. The analysis examined whether higher ranks on one variable tended to correspond with higher ranks on the other.
This tells the reader that the method fits the measurement level and the presence of ties. It also keeps the interpretation connected to ordered association rather than a stronger claim.
Results section wording
The results section should avoid leaving the coefficient alone. A number without interpretation forces the reader to do the work. After reporting the coefficient, add a sentence that names the direction and connects it back to the variables.
For example: “The positive coefficient indicates that students with higher motivation ratings tended to receive higher project-quality ratings.” This sentence does not overstate the result. It stays close to the association that Kendall’s Tau measures.
APA-style note
In APA-style writing, statistical symbols are often italicised. Many journals also prefer exact p-values when possible, such as p = .018, unless the value is very small. Requirements vary by journal, course, and institution, so the final formatting should follow the relevant style guide.
For classroom reports, the most important point is clarity: name the coefficient, state the result, and explain the association in ordinary language.
Conclusion
Kendall’s Tau is a rank-based correlation coefficient that describes ordered association between two variables. It is built from pair comparisons, which gives it a clear interpretation: the coefficient summarises whether pairs of observations tend to appear in the same order or in the opposite order across two variables.
The method is useful for ordinal variables, rankings, monotonic relationships, and datasets with tied values. It is often reported as Kendall’s Tau-b when ties are present. Like all correlation coefficients, it describes association rather than cause and effect.
In practice, the strongest use of Kendall’s Tau combines a suitable research question, ordered variables, clear handling of ties, and a careful interpretation. The coefficient should be read with the study design, the measurement scale, the sample size, and any uncertainty shown by p-values or confidence intervals.
Sources and Recommended Readings
If you want to go deeper into Kendall’s Tau, the following scientific publications provide useful discussions of Kendall’s rank correlation coefficient, pair-based interpretation, ties, confidence intervals, and inference.
- Concerning Kendall’s tau, a nonparametric correlation coefficient – A Psychological Bulletin publication focused on Kendall’s Tau as a nonparametric correlation coefficient.
- Bayesian Inference for Kendall’s Rank Correlation Coefficient – An American Statistician article presenting a Bayesian approach to inference for Kendall’s rank correlation coefficient.
- Simultaneous inference for Kendall’s tau – A Journal of Multivariate Analysis article on simultaneous tests and confidence intervals for Kendall’s Tau.
- An algorithm and program for calculation of Kendall’s rank correlation coefficient – A Behavior Research Methods article on calculating Kendall’s rank correlation coefficient.
- Kendall’s tau for serial dependence – A Canadian Journal of Statistics article applying Kendall’s Tau to serial dependence.
FAQs on Kendall’s Tau
What is Kendall’s Tau?
Kendall’s Tau is a rank-based correlation coefficient that measures ordered association between two variables by comparing concordant and discordant pairs of observations. It usually ranges from -1 to +1.
When should I use Kendall’s Tau?
Use Kendall’s Tau when both variables have a meaningful order and the research question concerns monotonic association. It is often used for ordinal variables, rankings, rating scales, tied values, and ordered data that do not fit a linear Pearson correlation well.
What is Kendall’s rank correlation coefficient?
Kendall’s rank correlation coefficient is another name for Kendall’s Tau. It measures how consistently two variables preserve the same ordering across pairs of observations.
What is the difference between Kendall’s Tau and Spearman’s correlation?
Kendall’s Tau compares pairs of observations and counts whether their order agrees or disagrees. Spearman’s correlation converts values into ranks and calculates a correlation between those ranks. Both are useful for ordered and monotonic data.
What does a Kendall’s Tau of 0 mean?
A Kendall’s Tau of 0 means that the data do not show a clear ordered association. Concordant and discordant pair patterns are roughly balanced, although another kind of relationship may still exist.
Can Kendall’s Tau show causation?
No. Kendall’s Tau describes association between two variables. It does not show that one variable caused the other to change. Causal claims require support from the research design and wider evidence.
How do you report Kendall’s Tau?
A report usually includes the version of Kendall’s Tau, the coefficient, sample size, p-value or confidence interval when used, and a plain interpretation. For example: Kendall’s Tau-b showed a positive association between the two variables, tau-b = .46, n = 84, p < .001.
