## What is a Pearson correlation?

A Pearson correlation, also known as a Pearson Product-Moment Correlation, is a measure of the strength for an association between two linear quantitative measures.

For example, you can use a Pearson correlation to determine if there is a significance association between the age and total cholesterol levels within a population. This is the example I will use for this guide.

## How to perform a Pearson correlation in SPSS

To perform a Pearson correlation in SPSS, you first need two variables of continuous data. Note, a Pearson correlation test is a parametric test. In other words, your data has to be normally distributed for the test to be valid. If you are unsure if your data is normally distributed, have a look at the normality testing in SPSS guide.

I have create a simple dataset containing 10 rows of data, each row signifies one person. I have two variables, the first being age (in years) and the other being blood total cholesterol levels (in mmol/L).

For this example we will have a null hypothesis as:

**“There is no correlation between participant ages and blood total cholesterol levels.”**

On the other hand, the alternative hypothesis would read:

**“There is a correlation between participant ages and blood total cholesterol levels.”**

## Performing the test

- Within SPSS, go to ‘
**Analyze > Correlate > Bivariate**‘.

A new window will open called **‘Bivariate Correlations’**. Here, you need to specify which variables you want to include in the analysis.

Drag both variables from the left window, to the right window called ‘**Variables**‘. In this case, both ‘**Age**‘ and ‘**Cholesterol**‘ will be moved across. Note, that you can drag more than two variables into the test, with each combination possible being tested for at the same time.

2. Ensure that ‘**Pearson**‘ is ticked under the title ‘**Correlation Coefficients**‘. Since we have not made any prior assumptions, we will also leave the ‘**Test of Significance**‘ as ‘**Two-tailed**‘.

3. Click the ‘**OK**‘ button to run the test.

## Output

By going to the SPSS Output window, there will be a new heading of **‘Correlations’** with a correlation grid displayed.

Within the grid, there are three pieces of information which are listed below.

- ‘
**Pearson Correlation**‘ – This is the Person Correlation Coefficient (**r**) value. These values range from 0 to 1 (for positive correlations) and -1 to 0 (for negative correlations). The larger the number, the stronger the linear association between the two variables i.e. a value of**‘1’**indicates a strong positive association and a value of ‘**-1**‘ indicates a strong negative association. A value of ‘**0**‘ indicates no such association. - ‘
**Sig. (2-tailed)**‘ – The P value for a two-tailed analysis. - ‘
**N**‘ – The number of pairs of data in the analysis.

## Interpretation

By looking at the results in the above table, it can be seen that the correlation between age and blood cholesterol levels gave a Pearson Correlation Coefficient (**r**) value of ‘**0.882**‘, which indicates a stong positive association between the two variables. Also, the P value of the association was ‘**0.001**‘, thus indicating a highly significant result. Therefore, I will reject the null hypothesis.

## Reporting

When reporting the results of a Pearson Correlation, it is useful to quote two pieces of data: the r value (the correlation coefficient) and the P value of the test. For the example above tis could read:

There was a strong positive association between participant ages and blood cholesterol levels (r = 0.882, P = 0.001).

IBM SPSS version used: 23