Linear or rank correlation
RHO = corr(X)
RHO = corr(X,Y)
[RHO,PVAL] = corr(X,Y)
[RHO,PVAL] = corr(X,Y,'name
',value
)
RHO = corr(X)
returns a pbyp matrix
containing the pairwise linear correlation coefficient between each
pair of columns in the nbyp matrix X
.
RHO = corr(X,Y)
returns a p1byp2
matrix containing the pairwise correlation coefficient between each
pair of columns in the nbyp1
and nbyp2 matrices X
and Y
.
The difference between corr(X,Y)
and the MATLAB^{®} function corrcoef(X,Y)
is
that corrcoef(X,Y)
returns a matrix of correlation
coefficients for the two column vectors X
and Y
.
If X
and Y
are not column vectors, corrcoef(X,Y)
converts
them to column vectors.
[RHO,PVAL] = corr(X,Y)
also returns PVAL
,
a matrix of pvalues 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.
[RHO,PVAL] = corr(X,Y,'
specifies
one or more optional name/value pairs. Specify name
',value
)name
inside
single quotes. The following table lists valid parameters and their
values.
Parameter  Values 

type 

rows 

tail — The alternative hypothesis against which to compute pvalues for testing the hypothesis of no correlation 

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 pvalues
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 pvalues
for Kendall's tau and Spearman's rho using either the exact permutation
distributions (for small sample sizes), or largesample approximations.
corr
computes pvalues
for the twotailed test by doubling the more significant of the two
onetailed pvalues.
[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, 24:377379.
corrcoef
 corrcov
 partialcorr
 tiedrank