*30*

One way to quantify the relationship between two variables is to use theÂ Pearson correlation coefficient,Â which isÂ a measure of the linear association between two variables*.Â *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** = râˆš(n-2) / âˆš(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.

**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:Â**2.341478**p-value:Â**0.037285

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

**The null hypothesis (H _{0}):**Â The correlation between the two variables is zero.

**The alternative hypothesis: (Ha):**Â The correlation between the two variables isÂ *notÂ *zero, e.g. there is a statistically significant correlation.

If we use a significance level ofÂ Î± = .05, then we would reject the null hypothesis in this case since the p-value (0.037285) is less than .05. We would conclude that the correlation coefficient is statistically significant.