Rank correlation

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In statistics, rank correlation is the study of relationships between different rankings on the same set of items. It deals with measuring correspondence between two rankings, and assessing the significance of this correspondence.

Correlation coefficients

Two of the more popular rank correlation statistics are

1. Spearman's rank correlation coefficient (Spearman's ρ)
2. Kendall's tau rank correlation coefficient (Kendall's τ)

A rank correlation coefficient is in the interval [-1,1] where:

• If the agreement between the two rankings is perfect (i.e., the two rankings are the same) the coefficient has value 1.
• If the disagreement between the two rankings is perfect (i.e., one ranking is the reverse of the other) the coefficient has value -1.
• For all other arrangements the value lies between -1 and 1, and increasing values imply increasing agreement between the rankings.
• If the rankings are completely independent, the coefficient has value 0.

See also

• Kendall tau distance
• Spearman's rank correlation coefficient

v • d • e Statistics
Descriptive statistics	Mean (Arithmetic, Geometric) - Median - Mode - Power - Variance - Standard deviation
Inferential statistics	Hypothesis testing - Significance - Null hypothesis/Alternate hypothesis - Error - Z-test - Student's t-test - Maximum likelihood - Standard score/Z score - P-value - Analysis of variance
Survival analysis	Survival function - Kaplan-Meier - Logrank test - Failure rate - Proportional hazards models
Probability distributions	Normal (bell curve) - Poisson - Bernoulli
Correlation	Confounding variable - Pearson product-moment correlation coefficient - Rank correlation (Spearman's rank correlation coefficient, Kendall tau rank correlation coefficient)
Regression analysis	Linear regression - Nonlinear regression - Logistic regression