A Pearson correlation coefficient is used to quantify the linear association between two variables.
It always takes on a value between -1 and 1 where:
- -1 indicates a perfectly negative linear correlation.
- 0 indicates no linear correlation.
- 1 indicates a perfectly positive linear correlation.
To determine if a correlation coefficient is statistically significant you can perform a t-test, which involves calculating a t-score and a corresponding p-value.
The formula to calculate the t-score is:
t = r√
- r: The correlation coefficient
- n: The sample size
The p-value is calculated as the corresponding two-sided p-value for the t-distribution with n-2 degrees of freedom.
The following example shows how to perform a t-test for a correlation coefficient.
Example: Performing a t-Test for Correlation
Suppose we have the following dataset with two variables:
Using some statistical software (Excel, R, Python, etc.) we can calculate the correlation coefficient between the two variables to be 0.707.
This is a highly positive correlation, but to determine if it’s statistically significant we need to calculate the corresponding t-score and p-value.
We can calculate the t-score as:
- t = r√
- t = .707√
- t = 2.828
Using a T Score to P Value Calculator, we find that the corresponding p-value is 0.022.
Since this p-value is less than .05, we would conclude that the correlation between these two variables is statistically significant.