Correlation analysis and plotting in R

   Correlation is a statistical measured value (coefficient) that represents the relationship between two numerical variables. The correlation coefficient can be a positive or negative number in a range of -1 to 1, where the extremes (-1, 1) identify a full correlation and 0 represents no relationship. A positive value indicates that variables change in the same direction and a negative value indicates an inverse direction of variables that is if one variable increases the other one decrease.
Correlation methods

There are many correlation methods. Three widely used correlation types are:

• Pearson correlation evaluates the degree of linear relationship between normally distributed variables, and it is called the Pearson correlation coefficient, r.
• Spearman rank correlation identifies the strength of the relationship between two ranked variables. It is a non-parametric measure of rank correlation and called Spearman's correlation rank, rho.
• Kendall rank correlation assesses the level of relationship between two variables and called Kendall's tau, τ.  It is also a non-parametric rank correlation measure.

Let's see an example. You may use any quantitative data for this test. I use randomly generated sample data in this post.

set.seed(12)
a <- runif(100)*5
b <- sqrt(a)+runif(50)
c <- sqrt(a)+sin(a)
d <- c+rnorm(100)
 
data <- data.frame(a=a, b=b,c=c,d=d)
head(data)
          a        b         c           d
1 0.3468046 1.071878 0.9287955  0.29495733
2 4.0888760 2.863152 1.2102647 -0.06078913
3 4.7131087 2.626115 1.1709698  0.78701939
4 1.3469094 2.021082 2.1356061  2.65236189
5 0.8467406 1.596287 1.6693104  1.49134184
6 0.1694781 1.139260 0.5803452  0.58460319

To check the correlation of variables, we use cor() function in R.

cor(a,b)
[1] 0.8827953

cor(a,d)
[1] -0.09292306
cor(b,b)
[1] 1

We may check all data frame variables too. Output comes in a below matrix.

> cor(data)
            a            b            c           d
a  1.00000000  0.857666325 -0.182334309 -0.09292306
b  0.85766633  1.000000000  0.005663791 -0.05769570
c -0.18233431  0.005663791  1.000000000  0.48158862
d -0.09292306 -0.057695703  0.481588625  1.00000000

Correlation method can be specified in method argument of cor() function.

cor(a,b, method="pearson")
[1] 0.8576663
cor(a,b, method="kendall")
[1] 0.6824242
cor(a,b, method="spearman")
[1] 0.8672907

Testing correlation 

To check the correlation statistics and probability value (p-value) for two variables, we can use cor.test() function.

cor.test(a, b)

 Pearson's product-moment correlation

data:  a and b
t = 16.512, df = 98, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
 0.7952103 0.9021133
sample estimates:
      cor 
0.8576663 

cor.test(a, b, method="spearman")

 Spearman's rank correlation rho

data:  a and b
S = 22116, p-value < 2.2e-16
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.8672907 

cor.test(a, b, method="kendall")

 Kendall's rank correlation tau

data:  a and b
z = 10.06, p-value < 2.2e-16
alternative hypothesis: true tau is not equal to 0
sample estimates:
      tau 
0.6824242 

Plotting correlation matrix

There are many ways to plot a correlation matrix data. Here, I use levelplot() function of lattice package.

library(lattice)

cor_data <- cor(data)
print(cor_data)
            a            b            c           d
a  1.00000000  0.857666325 -0.182334309 -0.09292306
b  0.85766633  1.000000000  0.005663791 -0.05769570
c -0.18233431  0.005663791  1.000000000  0.48158862
d -0.09292306 -0.057695703  0.481588625  1.00000000

levelplot(cor_data)

Plotting with corrplot

Correlation data can also be plotted with a corrplot library.

> library(corrplot)

> corrplot(cor_data) 

or

> corrplot(cor_data,method="circle")

A method can be changed into "square", "ellipse", "number", "pie", "shade", and "color" type.

In this post,  a brief explanation of correlation and its usage in R is explained.