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Spearman correlation calculator

Rank-based correlation for ordinal data or non-linear monotonic relationships. Returns Spearman’s ρ with a t-approximation p-value.

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Your data

Two columns of equal length — values are paired by position. Ranks are computed automatically (ties get average ranks).

n = 0
n = 0
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When to use this

Spearman’s ρ (rho) is the rank-based cousin of Pearson’s r: it converts each variable to ranks and correlates the ranks. Use it when the data are ordinal (Likert ratings, class ranks, severity grades), when the relationship looks monotonic but curved (consistently increasing, just not in a straight line), or when outliers make Pearson’s r untrustworthy. Because only the order of values matters, a single extreme score cannot dominate the result — which makes Spearman a standard robustness check even for interval data.

Key assumptions

  • Paired observations that are independent across cases.
  • Both variables are at least ordinal — values can be meaningfully ranked.
  • The association of interest is monotonic (consistently rising or falling).
  • Ties are acceptable; this calculator assigns average ranks, the standard treatment.

Common mistakes

  • Interpreting ρ as a linear effect — it measures monotonic association, not slope.
  • Using Spearman when the relationship is non-monotonic (e.g. an inverted U); no correlation coefficient captures that.
  • Forgetting that with many ties (e.g. a 3-point scale) the p-value approximation becomes rough.

Frequently asked questions

Pearson or Spearman — which should I report?
If both variables are continuous, the relationship looks linear and there are no influential outliers, Pearson’s r is standard and slightly more powerful. Otherwise — ordinal scales, curved monotonic trends, outliers — report Spearman’s ρ. Running both is a useful sensitivity check: a large gap between them usually signals outliers or non-linearity.
How is the p-value computed?
Via the common t-approximation: t = ρ√((n−2)/(1−ρ²)) with n − 2 degrees of freedom, with ties handled by average ranks. For very small samples (n < 10) exact tables are slightly more accurate.

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