Nonparametric Rank Correlation

Kendall's Tau & Spearman's Rho

Full step-by-step workings, significance tests, effect sizes, rank tables, and visualizations.
This calculator was built with AI assistance — please verify critical results independently before use.
Infographic comparing Kendall's Tau and Spearman's Rho — key differences, formulas, and interpretation guide
Kendall tau-b
\(\tau_b = \dfrac{C - D}{\sqrt{(n_0 - n_1)(n_0 - n_2)}}\)
Spearman rho
\(\rho = 1 - \dfrac{6\sum d_i^2}{n(n^2-1)}\)
z-test (Kendall)
\(z = \dfrac{C-D}{\sqrt{n(n-1)(2n+5)/18}}\)
t-test (Spearman)
\(t = \rho\sqrt{\dfrac{n-2}{1-\rho^2}},\;df=n{-}2\)
Variable X
Variable Y
Significance level
Data Summary
Correlation Results
Step-by-Step Workings
Visualization
Rank Table
Pair Analysis (Kendall)
APA Citation
Click to copy

How to Use This Calculator

1
Enter your data
Paste or type your values into the Variable X and Variable Y fields. Separate values with spaces, commas, or line breaks. Both variables must have the same number of observations (minimum 3).
2
Choose a significance level
Select your α threshold — 0.01, 0.05, or 0.10. The default is 0.05, which is standard for most research contexts.
3
Click Calculate
The calculator instantly returns Kendall's tau-b and Spearman's rho, alongside z- and t-statistics, one- and two-tailed p-values, and an effect size classification.
4
Review the step-by-step workings
Expand the Kendall's Tau or Spearman's Rho tabs to see every calculation broken down — concordant/discordant pairs, rank differences, and significance tests.
5
Explore the visualizations
Switch between the Scatter, Comparison, and Rank Plot tabs to visually inspect the relationship, compare both coefficients side by side, and see how ranks align across observations.
6
Copy the APA citation
Scroll to the bottom and click the citation box to copy a ready-to-use APA-formatted result string directly to your clipboard.

This calculator was built with AI assistance — please verify critical results independently before use.