Pearson Correlation: How to Run It Online and Report It in APA7
Pearson's r measures the strength and direction of a linear relationship between two continuous variables.
What is Pearson Correlation?
Pearson's r measures the strength and direction of a linear relationship between two continuous variables.
When to use it
Use it when both variables are continuous (interval or ratio), the relationship looks like a straight line in a scatterplot, and there are no extreme outliers.
Example question: Is the number of study hours linearly related to exam score?
Preparing your data
One row per participant, one numeric column per variable (for example hours and score).
Example dataset (simulated; first rows of 50): id, study_hours (hours per week), exam_score (0 to 100).
| id | study_hours | exam_score |
|---|---|---|
| 1.0 | 9.8 | 73.0 |
| 2.0 | 9.7 | 81.0 |
| 3.0 | 13.1 | 87.0 |
| 4.0 | 6.2 | 73.0 |
| 5.0 | 12.2 | 71.0 |
| 6.0 | 4.9 | 71.0 |
Download the full example CSV to practise. If the tool asks for a different layout, follow the instructions on its page.
How to run it on StatFas
- Open the Pearson Correlation tool. You do not need an account to run an analysis.
- Enter your data or upload your file, laid out as described in Preparing your data.
- Select your variables. Select the two numeric variables to correlate (or several for a correlation matrix).
- Choose any options the tool offers (for example the confidence level, a post hoc test or the error bar type) and run the analysis.
- Read the results on the page. Check the assumptions first, then the test statistic, the p-value and the effect size.
- To save your results, log in or create a free account. Every analysis stays free; the account is only needed to download.
Assumptions and checks
- Both variables are continuous and measured on at least an interval scale.
- The relationship is linear; check a scatterplot.
- No extreme bivariate outliers; one outlier can create or hide a correlation.
- Roughly bivariate normal data for small samples (for large samples the test is robust).
- Independent observations.
Key numbers to look at
- r: from −1 (perfect negative) through 0 (none) to +1 (perfect positive).
- p and 95% CI for r.
- r2: proportion of variance the variables share.
- n and df = n − 2.
Effect size
|r| ≈ .10 small, .30 medium, .50 large (Cohen, 1988). Report the confidence interval as well.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Pearson Correlation in APA7 style
Template
For a matrix of correlations, present an APA table with the lower triangle only and mark significance with a note.
Worked example (simulated data)
The numbers below were computed from the example CSV above, so you can reproduce them. They illustrate the format and are not real findings.
APA7 reminders: italicise statistical symbols (M, SD, t, F, p, r), report exact p-values to two or three decimals (use p < .001 for very small values), omit the leading zero for values that cannot exceed 1 (.45, not 0.45), and put degrees of freedom in parentheses. See the APA7 cheat sheet.
Common mistakes
- Using Pearson for ordinal rating data when Spearman is more appropriate.
- Ignoring outliers or non-linear patterns.
- Reporting the leading zero (write .45, not 0.45) and forgetting the degrees of freedom.
Related analyses and alternatives
- Spearman's rank Correlation: If data are ordinal, skewed or contain outliers.
- Linear Regression: To predict an outcome and control for other variables.
- Heatmap: To display many correlations at once.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What are the degrees of freedom for a correlation?
N − 2, where N is the number of complete pairs.
How do I get the confidence interval for r?
It is computed with the Fisher z transformation. Report it as 95% CI [lower, upper].
References
American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://doi.org/10.1037/0000165-000
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
This guide is for learning and for preparing results for your own reports. You remain responsible for choosing an appropriate analysis, checking its assumptions and interpreting the results. Follow the formatting rules of your journal or institution where they differ from APA7.