Spearman's Rank Correlation: How to Run It Online and Report It in APA7
Spearman's rank correlation (rs) is Pearson's correlation computed on the ranks of the scores. It measures how consistently one variable rises or falls with another.
What is Spearman's Rank Correlation?
Spearman's rank correlation (rs) is Pearson's correlation computed on the ranks of the scores. It measures how consistently one variable rises or falls with another.
When to use it
Use it for ordinal data (such as 1–7 ratings), for skewed variables, when there are outliers, or when the relationship is consistently increasing or decreasing but not a straight line.
Example question: Is higher anxiety associated with poorer sleep quality on 1–7 rating scales?
Preparing your data
One row per participant, one numeric (or ordinal) column per variable. Ranks are computed for you.
Example dataset (simulated; first rows of 40): id, anxiety_rating (1 to 7), sleep_quality_rating (1 to 7).
| id | anxiety_rating | sleep_quality_rating |
|---|---|---|
| 1 | 6 | 3 |
| 2 | 5 | 5 |
| 3 | 5 | 4 |
| 4 | 1 | 7 |
| 5 | 5 | 2 |
| 6 | 7 | 1 |
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 Spearman's Rank 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 variables. Many tied ranks are common with short rating scales; the tool should handle them.
- 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 at least ordinal.
- The relationship is monotonic (consistently rising or consistently falling), which a scatterplot can show.
- Independent observations (one row per participant).
- With many tied values the coefficient is still valid, but the p-value is approximate.
Key numbers to look at
- rs from −1 to +1.
- p and sample size (N).
- Direction: positive means higher ranks on one variable go with higher ranks on the other.
- Number of ties if reported.
Effect size
Interpret rs like r: about .10 small, .30 medium, .50 large.
Benchmarks such as small, medium and large are conventions (Cohen, 1988), not rules. Interpret size in the context of your field.
Reporting Spearman's Rank Correlation in APA7 style
Template
Use degrees of freedom N − 2 in parentheses and no leading zero.
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
- Calling the result Pearson's r.
- Interpreting a Spearman coefficient as the strength of a straight-line relationship.
- Ignoring that ordinal scales with only a few levels contain many ties.
Related analyses and alternatives
- Pearson Correlation: If both variables are continuous and linear.
- Correlation: For an overview of correlation choices.
- Heatmap: To plot a matrix of correlations.
Not sure which analysis you need? Use the test chooser.
Frequently asked questions
When should I choose Spearman instead of Pearson?
Choose Spearman for ordinal data, clearly non-normal data, outliers, or monotonic but curved relationships.
What does monotonic mean?
As one variable increases the other never reverses direction: it consistently increases, or consistently decreases.
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.