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corr - Linear or rank correlation

Syntax

RHO = corr(X)
RHO = corr(X,Y,...)
[RHO,PVAL] = corr(...)
[...] = corr(...,param1,val1,param2,val2,...)

Description

RHO = corr(X) returns a p-by-p matrix containing the pairwise linear correlation coefficient between each pair of columns in the n-by-p matrix X.

RHO = corr(X,Y,...) returns a p1-by-p2 matrix containing the pairwise correlation coefficient between each pair of columns in the n-by-p1 and n-by-p2 matrices X and Y.

[RHO,PVAL] = corr(...) also returns PVAL, a matrix of p-values for testing the hypothesis of no correlation against the alternative that there is a nonzero correlation. Each element of PVAL is the p-value for the corresponding element of RHO. If PVAL(i, j) is small, say less than 0.05, then the correlation RHO(i, j) is significantly different from zero.

[...] = corr(...,param1,val1,param2,val2,...) specifies additional parameters and their values. The following table lists the valid parameters and their values.

Parameter	Values
'type'	'Pearson' (the default) computes Pearson's linear correlation coefficient 'Kendall' computes Kendall's tau 'Spearman' computes Spearman's rho
'rows'	'all' (the default) uses all rows regardless of missing values (NaNs) 'complete' uses only rows with no missing values 'pairwise'computes RHO(i,j) using rows with no missing values in column i or j
'tail' — The alternative hypothesis against which to compute p-values for testing the hypothesis of no correlation	'both' — Correlation is not zero (the default) 'right' — Correlation is greater than zero 'left' — Correlation is less than zero

Using the 'pairwise' option for the 'rows' parameter may return a matrix that is not positive definite. The 'complete' option always returns a positive definite matrix, but in general the estimates are based on fewer observations.

corr computes p-values for Pearson's correlation using a Student's t distribution for a transformation of the correlation. This correlation is exact when X and Y are normal. corr computes p-values for Kendall's tau and Spearman's rho using either the exact permutation distributions (for small sample sizes), or large-sample approximations.

corr computes p-values for the two-tailed test by doubling the more significant of the two one-tailed p-values.

References

[1] Gibbons, J.D. (1985) Nonparametric Statistical Inference, 2nd ed., M. Dekker.

[2] Hollander, M. and D.A. Wolfe (1973) Nonparametric Statistical Methods, Wiley.

[3] Kendall, M.G. (1970) Rank Correlation Methods, Griffin.

[4] Best, D.J. and D.E. Roberts (1975) "Algorithm AS 89: The Upper Tail Probabilities of Spearman's rho", Applied Statistics, 24:377-379.

See Also

corrcoef, partialcorr, corrcov, tiedrank

cordexch

corrcov

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