Kendall's Tau Correlation

Kendall's tau is a rank-based correlation coefficient that measures the strength and direction of a monotonic association between two variables from the balance of concordant and discordant pairs.

Kendall의 타우는 일치 쌍과 불일치 쌍의 균형을 이용해 두 변수 간 단조적 관련성의 강도와 방향을 측정하는 순위 기반 상관계수이다.

How do I measure the correlation between two ordinal variables or with a small sample and many ties?

서열변수 간의 상관이나 표본이 작고 동순위가 많은 경우의 상관은 어떻게 측정하나요?

Kendall's tau measures monotonic association from the proportion of concordant versus discordant pairs of observations. It fits ordinal variables, small samples or data with many tied ranks, where the tau-b version adjusts for ties.

When to use Kendall's Tau Correlation

• Two ordinal variables such as ranked preferences or Likert items
• Small samples where a rank-based coefficient is preferred
• Data with many tied values, using tau-b

When to use something else

• Both variables are continuous and roughly bivariate normal with a linear relationship: use Pearson correlation
• You want a rank coefficient comparable to Pearson in scale: use Spearman's rank correlation

Assumptions and requirements

• Paired observations
• Variables measured at least at the ordinal level
• Monotonic relationship
• Independent pairs

What the analysis reports

• Kendall's tau (tau-b or tau-c)
• p-value
• Confidence interval
• Correlation matrix for multiple variables

How to report it

There was a significant positive association between [variable 1] and [variable 2], τb = [value], p = [value].

Related methods

• Spearman's Rank Correlation
• Pearson Correlation
• Kendall's W

Run Kendall's Tau Correlation on Quorant