Matrix of Correlations and P-values

rcorr Computes a matrix of Pearson's r or Spearman's rho rank correlation coefficients for all possible pairs of columns of a matrix. Missing values are deleted in pairs rather than deleting all rows of x having any missing variables. Ranks are computed using efficient algorithms (see reference 2), using midranks for ties.

rcorr(x, y, type=c("pearson","spearman"))

# S3 method for class 'rcorr'
print(x, ...)

Arguments

x: a numeric matrix with at least 5 rows and at least 2 columns (if y is absent). For print, x is an object produced by rcorr.
y: a numeric vector or matrix which will be concatenated to x. If y is omitted for rcorr, x must be a matrix.
type: specifies the type of correlations to compute. Spearman correlations are the Pearson linear correlations computed on the ranks of non-missing elements, using midranks for ties.
...: argument for method compatiblity.

Value

rcorr returns a list with elements r, the matrix of correlations, n the matrix of number of observations used in analyzing each pair of variables, P, the asymptotic P-values, and type. Pairs with fewer than 2 non-missing values have the r values set to NA. The diagonals of n are the number of non-NAs for the single variable corresponding to that row and column.

Details

Uses midranks in case of ties, as described by Hollander and Wolfe. P-values are approximated by using the t or F distributions.

Author

Frank Harrell
Department of Biostatistics
Vanderbilt University
fh@fharrell.com

References

Hollander M. and Wolfe D.A. (1973). Nonparametric Statistical Methods. New York: Wiley.

Press WH, Flannery BP, Teukolsky SA, Vetterling, WT (1988): Numerical Recipes in C. Cambridge: Cambridge University Press.

Examples

x <- c(-2, -1, 0, 1, 2)
y <- c(4,   1, 0, 1, 4)
z <- c(1,   2, 3, 4, NA)
v <- c(1,   2, 3, 4, 5)
rcorr(cbind(x,y,z,v))
#>   x     y     z v
#> x 1  0.00  1.00 1
#> y 0  1.00 -0.75 0
#> z 1 -0.75  1.00 1
#> v 1  0.00  1.00 1
#> 
#> n
#>   x y z v
#> x 5 5 4 5
#> y 5 5 4 5
#> z 4 4 4 4
#> v 5 5 4 5
#> 
#> P
#>   x     y     z     v    
#> x       1.000 0.000 0.000
#> y 1.000       0.255 1.000
#> z 0.000 0.255       0.000
#> v 0.000 1.000 0.000