In statistics, we often use the Pearson correlation coefficient to measure the linear association between two variables*.*

To determine if a correlation coefficient is statistically significant, we can perform a correlation test in which we calculate a t-score and corresponding p-value.

A correlation test uses the following hypotheses:

**H**: The correlation between the two variables_{0}**is not**statistically significant.**H**: The correlation between the two variables_{A}**is**statistically significant.

If the p-value of the test is less than some significance level (e.g. α = .05) then we can reject the null hypothesis and conclude that the correlation between the two variables is statistically significant.

The easiest way to perform a correlation test in SPSS is by using **Analyze** > **Correlate** > **Bivariate**.

The following example shows how to do so in practice.

**Example: How to Perform a Correlation Test in SPSS**

Suppose we have the following two variables in SPSS named **X** and **Y**:

Suppose that we would like to calculate the correlation between these two variables and perform a correlation test to determine if the correlation coefficient is statistically significant.

To do so, click the **Analyze** tab, then click **Correlate**, then click **Bivariate**:

In the new window that appears, drag both the **X** and **Y** variables into the **Variables** box:

Make sure that the box is checked next to **Pearson** under the list of **Correlation Coefficients**.

Then click **OK**.

The following output will appear:

The output shows a correlation matrix between X and Y.

From the output we can see the following values:

- Pearson correlation coefficient:
**.651** - p-value of Pearson correlation coefficient:
**.009**

Recall the hypotheses used in a correlation test:

**H**: The correlation between the two variables_{0}**is not**statistically significant.**H**: The correlation between the two variables_{A}**is**statistically significant.

Since the p-value in the output (**.009**) is less than .05, we reject the null hypothesis.

We have sufficient evidence to say that the correlation between the two variables is statistically significant.

**Note**: Since the Pearson correlation coefficient (**.651**) was a positive value, this indicates that there is a positive correlation between the two variables.

**Additional Resources**

The following tutorials provide additional information about correlation coefficients:

An Introduction to the Pearson Correlation Coefficient

What is Considered to Be a “Strong” Correlation?

The Five Assumptions for Pearson Correlation