How to Report Spearman Correlation: Notation, AMA Format, and What Reviewers Check

Papers still turn up reporting Spearman's coefficient with the notation r, which is Pearson's symbol. The correct notation is ρ or r_s. Using r when the test actually run was Spearman signals a notation error to a statistically literate reviewer, and it can read as though the wrong test, not just the wrong symbol, was used.

When Spearman, not Pearson

If your data are ordinal, ranked, or fail a normality check, Spearman is the correctly routed coefficient rather than Pearson's. A separate guide walks through that decision in full, including a case where Pearson and Spearman answered the identical dataset 0.22 points apart. This post picks up after that decision has already been made: you have run Spearman, and now need to write it up correctly.

The correct notation

A complete Spearman result has four required elements: the coefficient ρ, a number between −1 and +1; the exact P value, never "P < 0.05" when you can write P = .006; the sample size N; and, increasingly expected by journals, a 95% confidence interval on ρ, computed via a Fisher z-transformation.² The major reporting guidelines ask for an effect estimate together with its precision rather than a bare test result: CONSORT's outcomes item calls for "the estimated effect size and its precision (such as 95% confidence interval)".⁴

A real result: stabilised glucose and long-term glucose control

Vanderbilt's diabetes screening cohort pairs a same-day stabilised glucose reading with glycosylated haemoglobin (HbA1c), a marker of average blood glucose over roughly the preceding three months, in 390 patients with both values recorded.¹ Both variables fail Shapiro-Wilk, so Spearman is the correctly routed coefficient here, not Pearson.

Example data: Vanderbilt University Department of Biostatistics public teaching datasets (hbiostat.org/data). Computed with scipy, not generated.

How to describe the strength, and why two conventions disagree

The word attached to a coefficient depends on which source you cite, and the two most commonly used conventions do not agree with each other. Schober and colleagues' 2018 tutorial, the standard reference in clinical and anaesthesia journals, gives these bands:²

By that table, the result above (ρ = 0.53) is described as a moderate correlation. But Cohen's older, more general convention for a correlation coefficient labels 0.10 as small, 0.30 as medium, and 0.50 and above as a large effect³, which is the convention StatsPlease's own effect-size classifier uses internally, and by that convention the identical 0.53 is a large effect. Neither labelling is wrong. They are different, both legitimate, conventions answering slightly different questions. Report the number first, name which convention you are quoting, and do not treat "strong" or "large" as an absolute description independent of its source.

Writing the AMA sentence

The American Medical Association (AMA) Manual of Style, the format standard for most clinical and surgical journals, keeps the leading zero in the coefficient (0.53, not .53), italicises the statistic symbols, and uses a capital P without a leading zero. Written in a results sentence: "Stabilised glucose was positively correlated with HbA1c (Spearman ρ = 0.53, 95% CI, 0.46–0.60, N = 390, P < .001)." Always name the test explicitly, Spearman ρ, not ρ alone, so the reader is not left to infer which correlation was run. If the P value is smaller than .001, write P < .001; never write P = .000, which is a rounding artefact, not a true value.

Your Methods section should state why Spearman was chosen: "Normality was assessed using the Shapiro-Wilk test. Because both variables departed significantly from a normal distribution, Spearman's rank correlation coefficient was used to evaluate the association."

This sentence is also where ChatGPT quietly fails you: ask an LLM to report a Spearman correlation and it will format a perfectly plausible sentence around a ρ it never computed from your data. The result above is computed with scipy, not generated; run the same pair through R or SPSS and the coefficient matches.

Frequently asked questions

Should I write r or rho for a Spearman correlation?

Rho, written as the Greek letter or as r with a subscript s. A bare r is Pearson's symbol. Writing r when the test you actually ran was Spearman is a notation error that signals to a reviewer that the wrong symbol, or possibly the wrong test, made it into the manuscript.

How do I interpret the strength of a Spearman correlation?

Report the coefficient itself first; the word you attach to it depends on which convention you cite. Schober et al.'s clinical bands (2018) label 0.40 to 0.69 as moderate and reserve strong for 0.70 and above. Cohen's older, more general convention labels 0.50 and above as a large effect. The same ρ can be described differently depending on which source you cite, so name your source.

Do I need to report a confidence interval for Spearman's rho?

The major reporting guidelines ask for an effect estimate together with its precision rather than a bare test result, and a confidence interval distinguishes a tight estimate from a wide one, which matters most when the sample size is small. A Fisher z-transformation is the standard way to compute it.

References

1. Vanderbilt University Department of Biostatistics. Public teaching datasets. https://hbiostat.org/data
2. Schober P, Boer C, Schwarte LA. Correlation Coefficients: Appropriate Use and Interpretation. Anesthesia & Analgesia. 2018;126(5):1763-1768. https://doi.org/10.1213/ANE.0000000000002864
3. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum Associates; 1988.
4. Schulz KF, Altman DG, Moher D; CONSORT Group. CONSORT 2010 Statement: updated guidelines for reporting parallel group randomised trials. BMJ. 2010;340:c332. https://doi.org/10.1136/bmj.c332