Correlation: How to Run It Online and Report It in APA7
A correlation measures how strongly and in which direction two variables move together, on a scale from −1 to +1.
What is Correlation?
A correlation measures how strongly and in which direction two variables move together, on a scale from −1 to +1.
When to use it
Use it to describe the association between two variables when neither is manipulated. Pick Pearson for continuous, roughly linear data and Spearman for ordinal data, outliers or curved but consistently rising or falling relationships.
Example question: Do students who study more hours score higher on the exam?
Preparing your data
One row per participant and one column per variable. Each variable is a numeric column and both values for a person sit in the same row.
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 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 two or more numeric variables. Choose Pearson or Spearman if the tool offers both.
- 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 numeric (Pearson: interval or ratio; Spearman: at least ordinal).
- Observations are independent: one row per person, with no repeated measures.
- Pearson needs a roughly linear relationship and no extreme outliers: look at a scatterplot first.
- Correlation is not causation, and a restricted range of scores shrinks the coefficient.
Key numbers to look at
- Coefficient (r or rs): direction and strength.
- p-value: whether the coefficient differs from zero.
- Sample size and degrees of freedom (N − 2).
- 95% confidence interval of the coefficient, which shows its precision.
Effect size
The correlation coefficient is itself the effect size. Cohen's conventions: |r| = .10 small, .30 medium, .50 large. r2 is the share of shared variance.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Correlation in APA7 style
Template
Report r with no leading zero and the degrees of freedom in parentheses.
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
- Concluding that one variable causes the other.
- Running Pearson on clearly curved or outlier-driven data without looking at the scatterplot.
- Testing many correlations and reporting only the significant ones; correct for multiple tests or report all.
Related analyses and alternatives
- Pearson Correlation: For linear relationships between continuous variables.
- Spearman's rank Correlation: For ordinal data, outliers or monotonic curves.
- Linear Regression: To predict one variable from another.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
What is a strong correlation?
As a rough guide, .10 is small, .30 is medium and .50 is large, but what counts as strong depends on your field. Always interpret the size in context.
Does a significant correlation mean the relationship is important?
Not necessarily. With large samples tiny correlations are significant. Judge importance from the size of r and its confidence interval.
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.