The Pearson correlation coefficient can be used to measure the linear association between two variables.

This correlation coefficient always takes on a value between **-1** and **1** where:

**-1**: Perfectly negative linear correlation between two variables.**0**: No linear correlation between two variables.**1:**Perfectly positive linear correlation between two variables.

To determine if a correlation coefficient is statistically significant, you can calculate the corresponding t-score and p-value.

The formula to calculate the t-score of a correlation coefficient (r) is:

t = r√n-2 / √1-r^{2}

The p-value is calculated as the corresponding two-sided p-value for the t-distribution with n-2 degrees of freedom.

To calculate the p-value for a Pearson correlation coefficient in R, you can use the** cor.test()** function.

cor.test(x, y)

The following example shows how to use this function in practice.

**Example: Calculate P-Value for Correlation Coefficient in R**

The following code shows how to use the **cor.test()** function to calculate the p-value for the correlation coefficient between two variables in R:

**#create two variables
x <- c(70, 78, 90, 87, 84, 86, 91, 74, 83, 85)
y <- c(90, 94, 79, 86, 84, 83, 88, 92, 76, 75)
#calculate correlation coefficient and corresponding p-value
cor.test(x, y)
Pearson's product-moment correlation
data: x and y
t = -1.7885, df = 8, p-value = 0.1115
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
-0.8709830 0.1434593
sample estimates:
cor
-0.5344408
**

From the output we can see:

- The Pearson correlation coefficient is
**-0.5344408**. - The corresponding p-value is
**0.1115**.

Since the correlation coefficient is negative, it indicates that there is a negative linear relationship between the two variables.

However, since the p-value of the correlation coefficient is not less than 0.05, the correlation is not statistically significant.

Note that we can also type **cor.test(x, y)$p.value** to only extract the p-value for the correlation coefficient:

**#create two variables
x <- c(70, 78, 90, 87, 84, 86, 91, 74, 83, 85)
y <- c(90, 94, 79, 86, 84, 83, 88, 92, 76, 75)
#calculate p-value for correlation between x and y
cor.test(x, y)$p.value
[1] 0.1114995
**

The p-value for the correlation coefficient is **0.1114995**.

This matches the p-value from the previous output.

**Additional Resources**

The following tutorials explain how to perform other common tasks in R:

How to Calculate Partial Correlation in R

How to Calculate Spearman Correlation in R

How to Calculate Rolling Correlation in R