Spearman Rank Correlation Visualizer

See how converting data to ranks changes a correlation — and when Spearman's rho tells a different story than Pearson's r.

Your data

Paired (x, y) values — one pair per line

Raw data

Ranks of the data

Spearman's ρ

0.8

Pearson's r (raw data)

0.8

ρ and r are close, which is typical when the underlying relationship is already close to linear.

Approximate significance: two-tailed p ≈ 0.1041 (t = ρ√[(n−2)/(1−ρ²)], df = 3) — the standard large-sample approximation. For n = 5 with no ties, the exact critical values are 0.900 (α=0.1), 1.000 (α=0.05), 1.000 (α=0.02).

How to use this tool

Paste your own (x, y) pairs, one per line, or pick a preset.
Compare the raw-data scatter plot with the rank scatter plot next to it.
Read off Spearman's rho and Pearson's r side by side.
Check the approximate significance, or look up the exact critical value for small, tie-free samples.

Formula Reference

Spearman's rho

the Pearson correlation coefficient computed on the ranks of x and y

No-tie shortcut

ρ = 1 − 6Σd² / [n(n² − 1)], where d is the difference between paired ranks

Approximate significance

t = ρ√[(n − 2) / (1 − ρ²)] with n − 2 degrees of freedom

ArticleSpearman's Rank Correlation ArticlePearson Correlation CalcCorrelation Calculator ToolScatter Plot & Correlation Visualizer TableSpearman Critical Values GlossaryGlossary: Spearman's Rank Correlation

Frequently Asked Questions

Why does the 'Perfect monotonic, not linear' preset give ρ = 1 but r < 1?+

Ranking a strictly increasing curve like y = x² always produces a perfectly straight-line rank relationship, since the ranks rise together in exactly the same order. Pearson's r on the raw values is lower because the curve itself is not a straight line, even though it never changes direction.

How does this tool handle tied values?+

Tied values share the average of the ranks they would otherwise occupy, and rho is then computed as the ordinary Pearson correlation of those average ranks — mathematically equivalent to the standard tie-corrected Spearman formula, and exact rather than approximate.

Why is the significance labeled 'approximate'?+

The p-value shown uses the same large-sample t-approximation most statistics software defaults to. For small, tie-free samples the exact distribution differs slightly — use the linked exact critical values table for coursework that requires an exact answer.

What does it mean when rho and r are very different?+

A large gap usually means the relationship is monotonic (consistently increasing or decreasing) but curved rather than straight — Spearman's rho only cares about the order of the values, so it stays high, while Pearson's r drops because it measures how close the points are to a straight line.

Frequently Asked Questions

Why does the 'Perfect monotonic, not linear' preset give ρ = 1 but r < 1?+

How does this tool handle tied values?+

Why is the significance labeled 'approximate'?+

What does it mean when rho and r are very different?+