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The measurement of rank correlation
Introductory remarks
Kendall tau coefficient
Tau as a coefficient of concordance
Tau as a coefficient of disarray
Spearman’s rho
Conjugate rankings
Daniels’ inequality
The Durbin-Stuart inequality
Stragglers
Notes and references
Problems
Introduction to the general theory of rank correlation
The general correlation coefficient
Tau as a particular case
rS as a particular case
Product-moment correlation as a particular case
Proof of Daniels’ inequality
Proof of the Durbin-Stuart inequality
Spearman’s footrule
Notes and references
Tied ranks
Calculation of t
Calculation of rho
Application to ordered contingency tables
Notes and references
Problems
Tests of significance
The significance of t
P-values
Continuity correction for S
Ties
The significance of rS
Continuity correction for Σ d2
Tests in the non-null case
Applications to time-series data
Notes and references
Problems
Proof of the results of Chapter 4
Exact distribution of t in the null case
Tendency of t to normality in the null case
Distribution of rS in the null case
Joint distribution of t and rS
Corrections for continuity
The non-null case
More exact treatment in the non-null case
rS in the non-null case
Notes and references
The problem of M ranking
The significance of W
Continuity correction for W
Estimation
Friedman test for randomised complete block designs
Incomplete rankings
Notes and references
Problems
Proof of the results of Chapter 6
Notes and references
Partial rank correlation
Notes and references
Problems
Ranks and variate values
Concordances
Relation between ranks and variate values
Relation between t and parent correlation in the normal case
Relation between ρS and ρ in the normal case
Notes and references
Proof of the results of Chapter 9
Correlation between ranks and variate values
Concordance
Notes and references
Paired comparisons
Coefficient of agreement
Notes and references
Proof of the results of Chapter 11
Notes and references
Some further applications
Estimation of population consensus
Two group concordance
Comparison of n ranking with a criterion ranking
Uses of rank correlation in linear regression
Power and efficiency of rank correlation methods
Appendix tables
Probability function of S and t (Kendall)
Probability of Σ d2 (for rS)
Probability function of the standard normal distribution
Random rankings of 20 (random permutations of the first 20 natural numbers)
Probability function of S (for Kendall’s coefficient of concordance)
Significance points of S (for Kendalls coefficient of concordance)
Significance points of Fisher’s z distribution
Significance points of χ2
Probability function of d in paired comparisons
Probability function of Σ (for u)
Significance points of tXYZ (for Kendall’s partial rank correlation coefficients)