In statistics, we often use the Pearson correlation coefficient to measure the linear relationship between two variables. However, sometimes we’re interested in understanding the relationship between two variables **while controlling for a third variable**.

For example, suppose we want to measure the association between the number of hours a student studies and the final exam score they receive, while controlling for the student’s current grade in the class. In this case, we could use a **partial correlation **to measure the relationship between hours studied and final exam score.

This tutorial explains how to calculate partial correlation in Excel.

**Example: Partial Correlation in Excel**

Suppose we have a dataset that shows the following information for 10 students:

- Current grade in a class
- Hours spent studying for the final exam
- Final exam score

Use the following steps to find the partial correlation between hours studied and exam score while controlling for current grade.

**Step 1: Calculate each pairwise correlation.**

First, we’ll calculate the correlation between each pairwise combination of the variables:

**Step 2: Calculate the partial correlation between hours and exam score.**

The formula to calculate the partial correlation between variable A and variable B while controlling for variable C is as follows:

Partial correlation = (r

_{A,B}– r_{A,C}*r_{B,C}) / √((1-r^{2}_{A,B})(1-r^{2}_{B,C}))

The following screenshot shows how to use this formula to calculate the partial correlation between hours and exam score, controlling for current grade:

The partial correlation is **0.190626**. To determine if this correlation is statistically significant, we can find the corresponding p-value.

**Step 3: Calculate the p-value of the partial correlation.**

The test statistic *t *can be calculated as:

t = r√(n-3) / √(1-r

^{2})

The following screenshot shows how to use this formula to calculate the test statistic and the corresponding p-value:

The test statistic *t *is **0.51377**. The total degrees of freedom is n-3 = 10-3 = **7**. The corresponding p-value is **0.623228**. Since this value is not less than 0.05, this means the partial correlation between hours and exam score is not statistically significant.

You have a typo in your formula:

Partial correlation = (rA,B – rA,C*rB,C) / √((1-r2A,B)(1-r2B,C))

shd b

Partial correlation = (rA,B – rA,C*rB,C) / √((1-r2A,C)(1-r2B,C))