r - p-values of correlation coefficients

Question

I am using R and have a question on correlations.

A<-data.frame(A1=c(1,2,3,4,5),B1=c(6,7,8,9,10),C1=c(11,12,13,14,15 ))
B<-data.frame(A2=c(6,7,7,10,11),B2=c(2,1,3,8,11),C2=c(1,5,16,7,8))
cor(A,B)
# ? ? ? ? ? A2 ? ? ? ?B2 ? ? ? C2
# A1 0.9481224 0.9190183 0.459588
# B1 0.9481224 0.9190183 0.459588
# C1 0.9481224 0.9190183 0.459588

I wanted to obtain the p-value for each of the correlation coefficients in the matrix. Is this possible?

I tried using rcorr function from Hmisc package but obtain only a single p-value and not for each correlation.

A <- as.vector(t(A))
B <- as.vector(t(B))
rcorr(A, B)
     x    y
x 1.00 0.13
y 0.13 1.00

n= 15 


P
  x      y     
x        0.6425
y 0.6425       

Similarly, I also tried using "psych" package in R to do this but unable to.

Answer 1

You can apply rcorr directly on A and B if you convert them to matrices first :

library(Hmisc)
rcorr(as.matrix(A),as.matrix(B))

Which gives :

     A1   B1   C1   A2   B2   C2
A1 1.00 1.00 1.00 0.95 0.92 0.46
B1 1.00 1.00 1.00 0.95 0.92 0.46
C1 1.00 1.00 1.00 0.95 0.92 0.46
A2 0.95 0.95 0.95 1.00 0.97 0.16
B2 0.92 0.92 0.92 0.97 1.00 0.15
C2 0.46 0.46 0.46 0.16 0.15 1.00

n= 5 


P
   A1     B1     C1     A2     B2     C2    
A1        0.0000 0.0000 0.0141 0.0273 0.4361
B1 0.0000        0.0000 0.0141 0.0273 0.4361
C1 0.0000 0.0000        0.0141 0.0273 0.4361
A2 0.0141 0.0141 0.0141        0.0078 0.7981
B2 0.0273 0.0273 0.0273 0.0078        0.8125
C2 0.4361 0.4361 0.4361 0.7981 0.8125