*50*

A Pearson Correlation Coefficient measures 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

The formula to calculate a Pearson Correlation Coefficient, denoted *r*, is:

This tutorial provides a step-by-step example of how to calculate a Pearson Correlation Coefficient by hand for the following dataset:

**Step 1: Calculate the Mean of X and Y**

First, weâ€™ll calculate the mean of both the X and Y values:

**Step 2: Calculate the Difference Between Means**

Next, weâ€™ll calculate the difference between each of the individual X and Y values and their respective means:

**Step 3: Calculate the Remaining Values**

Next, weâ€™ll calculate the remaining values needed to complete the Pearson Correlation Coefficient formula:

**Step 4: Calculate the Sums**

Next, weâ€™ll calculate the sums of the the last three columns:

**Step 5: Calculate the Pearson Correlation Coefficient**

Now weâ€™ll simply plug in the sums from the previous step into the formula for the Pearson Correlation Coefficient:

The Pearson Correlation Coefficient turns out to beÂ **0.947**.

Since this value is close to 1, this is an indication that X and Y are strongly positively correlated.

In other words, as the value for X increases the value for Y also increases in a highly predictable fashion.

**Additional Resources**

An Introduction to the Pearson Correlation Coefficient

How to Find a Confidence Interval for a Correlation Coefficient