One way to quantify the relationship between two variables is to use the , which is a measure of the linear association between two variables.

It always takes on a value between -1 and 1 where:

• -1 indicates a perfectly negative linear correlation between two variables
• 0 indicates no linear correlation between two variables
• 1 indicates a 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-r²)

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 calculate a p-value for a correlation coefficient in Excel.

P-Value for a Correlation Coefficient in Excel

The following formulas show how to calculate the p-value for a given correlation coefficient and sample size in Excel:

For a correlation coefficient of r = 0.56 and sample size n = 14, we find that:

• t-score: 2.341478
• p-value: 0.037285

Recall that for a correlation test we have the following null and alternative hypotheses:

The null hypothesis (H₀): The correlation between the two variables is zero.

The alternative hypothesis: (Ha): The correlation between the two variables is not zero, e.g. there is a statistically significant correlation.

If we use a significance level of α = .05, then we would reject the null hypothesis in this case since the (0.037285) is less than .05.

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