Tutorial in R - Correlation - significance testing

Correlation

The difference between correlation and regression is the first doesn’t assign any dependency to either of the variables, and in the second a dependent variable (plotted on the Y axis) is assumed to change with changes in the independent varaible (plotted on the X axis).

R does have some functions for returning the correlation values between variables (eg. cor). The use of this function is shown in the chunk below. Note the use of the use=“complete” arguement is required to deal with the NAs in the dataset.

In the code below change the text in between the inverted commas to your directory and file name.

meas <- read.csv("~/ENG403/Weeks/5/meas.csv")
corres<-cor(meas[,8:10], use="complete")
print(corres)

           L          W          D
L  1.0000000 -0.6710455  0.1309648
W -0.6710455  1.0000000 -0.1384193
D  0.1309648 -0.1384193  1.0000000

#The following code allows me to access the variables with the maximum correlation and use in the text document.
av<-abs(corres[])
mv<-max(abs(corres[corres<1]))
mvid<-which(av[]==mv)[1]
if(mvid<ncol(corres))
  {cn=mvid[1]}else
  {cn=ncol-mvid[1]}
rn<-which(av[]==mv)[2]-ncol(corres)
lc<-corres[mvid[1]]
var1<-colnames(corres)[cn]
var2<-colnames(corres)[rn]

Apart from the values on the diagonal (which is the correlation of each variable on itself) the strongest relationship exists between W and L. The correlation coefficient (r) measures the strength of the relationship that exists between the two variables. Unfortunately there is no base test in r to test the significance level of the correlation coefficient. However th rcorr function in the Hmisc package does produce that output. The way this function requires the input columns is a little odd though!

print(cormat)

      [,1]  [,2]  [,3]
[1,]  1.00 -0.66  0.13
[2,] -0.66  1.00 -0.11
[3,]  0.13 -0.11  1.00

n
     [,1] [,2] [,3]
[1,]  209  209  194
[2,]  209  279  259
[3,]  194  259  261

P
     [,1]   [,2]   [,3]  
[1,]        0.0000 0.0687
[2,] 0.0000        0.0662
[3,] 0.0687 0.0662       

From the output can you interpret the correlations that are significantly significant?

EXERCISE

Experiment with the output for other types of correlation tests. What is the cov test?