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Spearman Rank Calculator

Calculate Spearman’s rank correlation from ranked data.

About Spearman Rank Calculator

Spearman’s correlation works on ranks rather than values, so it detects any monotonic relationship and is unaffected by outliers. It requires no assumption of normality. When a relationship is strong but curved, Spearman reports a high correlation while Pearson understates it substantially.

Formula

Spearman Rank

ρ = 1 − 6Σd² ÷ (n(n² − 1))

d
Difference between the two ranks for each pair
Spearman
Detects monotonic relationships, not just linear ones

Worked example

With the default values below, Spearman Rank Calculator returns Spearman’s Rho of 0.860140. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sum of squared rank differencesminimum 0
40
Number of pairsminimum 3
12

Results

Spearman’s Rho
0.860140
Strength of Association
Very strong
T Statistic
5.33273
Degrees of Freedom
10
Significance
Statistically significant

Step by step

  1. 1Values used
  2. 2Spearman Rank
  3. 3Spearman’s Rho= 0.860140
  4. 4Strength of Association= Very strong
  5. 5T Statistic= 5.33273
  6. 6Degrees of Freedom= 10
  7. 7Significance= Statistically significant

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Spearman Rank calculated?

ρ = 1 − 6Σd² ÷ (n(n² − 1)) Spearman’s correlation works on ranks rather than values, so it detects any monotonic relationship and is unaffected by outliers. It requires no assumption of normality.

Why does Spearman Rank matter?

When a relationship is strong but curved, Spearman reports a high correlation while Pearson understates it substantially.

What values do I need to enter?

This calculator takes 2 inputs: Sum of squared rank differences, Number of pairs. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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Spearman Rank Calculator – Calculate Spearman’s Rho