# Pearson's r

## Correlation between two continuous variables

Pearson's

*r*correlation is used to assess the relationship between**two continuous variables**. Pearson's*r*is the most popular correlation test. Pearson's*r*should not be run on data that has outliers. Before running a Pearson's*r*, be sure to check for the normality of the two continuous variables using skewness and kurtosis statistics. Outliers can grossly inflate or deflate a Pearson*r*correlation. The**coefficient of determination**is calculated as a measure of effect size for Pearson's*r*correlation and is simply the*r*value, squared.The Venn diagram below depicts the correlation of two continuous variables. Pearson's r is the correlation test used when testing the relationship between two continuous variables.

### The steps for conducting a Pearson's r correlation in SPSS

1. The data is entered in a within-subjects fashion.

2. Click

3. Drag the cursor over the

4. Click on

5. Click on the first continuous outcome variable to highlight it.

6. Click on the

7. Click on the second continuous outcome variable to highlight it.

8. Click on the

9. Click

2. Click

**.**__A__nalyze3. Drag the cursor over the

**drop-down menu.**__C__orrelate4. Click on

**.**__B__ivariate5. Click on the first continuous outcome variable to highlight it.

6. Click on the

**arrow**to move the variable into the**Variables:**box.7. Click on the second continuous outcome variable to highlight it.

8. Click on the

**arrow**to move the variable into the**Variables:**box.9. Click

**OK**.### The steps for interpreting the SPSS output for a Pearson's r correlation

1. In the

If the

If the

**Correlations**table, match the row to the column between the two continuous variables. The**Pearson Correlation**is the actual correlation value that denotes magnitude and direction, the**Sig. (2-tailed)**is the*p*-value that is interpreted, and the**N**is the number of observations that were correlated.If the

*p*-value is**LESS THAN .05**, then researchers have evidence of a statistically significant**bivariate association**between the two continuous variables.If the

*p*-value is**MORE THAN .05**, then researchers have evidence that there is not a statistically significant association between the two continuous variables.**Higher r coefficients**denote a**stronger magnitude of relationship**between variables.**Smaller r coefficients**denote**weaker relationships**.**Positive correlations**denote a relationship that**travels at the same trajectory**. As one value goes up, then the other value goes up. Also, as one value goes down, then the other value goes down too.**Negative correlations**denote a relationship that**travels in different directions**. As one value goes up, the other value goes down. Also, as one value goes down, then the other value goes up.Click on the

**Download Database**and**Download Data Dictionary**buttons for a configured database and data dictionary for Pearson's*r*correlation.**Click on the****Adjusing for Multiple Comparisons**button to learn more about Bonferroni, Tukey's HSD, and Scheffe's test. Click on the**Validation of Statistical Findings**button to learn more about bootstrap, split-group, and jack-knife validation methods.## Hire A Statistician - Statistical Consulting for Professionals

**DO YOU NEED TO HIRE A STATISTICIAN?**

Eric Heidel, Ph.D. will provide statistical consulting for researchers, professionals, and organizations at $100/hour. Secure checkout is available with Stripe, Venmo, Zelle, or PayPal.

- Statistical Analysis
- Research Design
- Sample Size Calculations
- Diagnostic Testing and Epidemiological Calculations
- Survey Design and Psychometrics