# MASH : Maths and Stats Help

### Pearson's "r" Correlation

#### Introduction

A Pearson's 'r' correlation compares the relationships between two variables. Common examples include height and weight, IQ and Test Score, and Strength and Speed.

This test may also be referred to as the Pearson's product moment correlation coefficient.

It is considered a parametric test and therefore is only suitable for parametric data. To check if your data is parametric, please check out the dedicated guide: Parametric or Not Guide (PDF)

If either one of your variables that you would like to test is non-parametric you could consider the Spearman's 'rho' Correlation

#### Test Procedure

1. Click Analyze > Correlate > Bivariate 2. Within the 'Bivariate Correlations' window, select the two variables you intend to analyse and move them to the 'Variables' box using the blue arrow. 3. Select Continue, then OK

#### Results SPSS will generate one Correlations table:

##### Correlations

This table shows the three statistics we need to report when running a Pearson's 'r' correlation; the Correlation Coefficient (Pearson Correlation), the significance/ p-value (Sig (2-tailed)), and the sample size (N)

## Reporting the Results in APA Formatting

Alongside interpreting the p-value for significance, you will also need to interpret the strength and direction of the relationship. To do this you would use a correlation strength table. We have an example of this in the PDF below, however, we recommend using a table from a textbook (check either your reading list or the book recommendations we have on our site).

The relationship between an ostrich's height and speed was assessed. A Pearson's Correlation indicated a moderately strong, positive, significant relationship, = .65, p < .001, N = 174.

Pearsons's 'r' Correlation may also be reported with the degrees of freedom rather than the sample size. For a Pearson 'r' Correlation, the formula is (df = n – 2) degrees of freedom = sample size - 2. The degrees of freedom are reported in brackets such as the example below:

The relationship between an ostrich's height and speed was assessed. A Pearson's Correlation indicated a moderately strong, positive, significant relationship, r (172) = .65, p < .001.