How to Report Correlation Results in APA Format

Correlation coefficients need exact notation and degrees of freedom. Learn the APA standard for Pearson, Spearman, and correlation matrices with worked examples and common pitfalls.

What You Need to Know

Always report r or rs with the degrees of freedom (which equals n − 2, not n), the observed correlation value, and the p-value. Include the sign: r = −.35 is different from r = .35. Avoid labelling small or medium effects as "weak" or "strong" without discipline-specific context.

§1 Pearson Correlation in APA Format

A Pearson correlation coefficient measures the linear relationship between two continuous variables. When you report one, you state the coefficient, its degrees of freedom, and the p-value.

Notation

r(df) = .XX, p = .XXX
r
Pearson product-moment correlation coefficient (always between −1 and +1).
df
Degrees of freedom, calculated as n − 2, where n is the number of paired observations.
p
The two-tailed p-value from the t-distribution, indicating the probability of seeing a correlation this large if the true correlation were zero.

Why is df = n − 2?

The correlation test uses a t-statistic with n − 2 degrees of freedom because you are estimating two parameters (the means of both variables) from the data. Many students mistakenly report n instead of n − 2. The correct formula is always df = n − 2.

Worked Example: Significant Pearson Correlation

Scenario: You collect data on study hours and final exam scores from 52 students. You compute Pearson's r and find r = .628. The p-value is .001.

How to write it:

Study hours and final exam score were strongly positively correlated, r(50) = .628, p = .001.

Note the details:

  • Degrees of freedom: 50 = 52 − 2.
  • The p-value is reported to 3 decimal places.
  • The coefficient is reported to 3 decimal places (two digits after the decimal is common practice).
  • We describe the correlation as "positive" because r > 0.
  • We avoid saying "strong" without justification—context matters. In education, r = .628 is often considered moderate to strong; in other fields, it may be smaller.

§2 Spearman Rank Correlation in APA Format

When data are ordinal or if the assumption of linearity is violated, use Spearman's rank correlation (ρ, the Greek letter rho). The APA notation differs slightly from Pearson's, using either rs or ρ.

Notation

rs(df) = .XX, p = .XXX
or: ρ(df) = .XX, p = .XXX
rs or ρ
Spearman rank correlation coefficient (also between −1 and +1).
df
Degrees of freedom, calculated the same way: n − 2.
p
The two-tailed p-value under the null hypothesis that the rank correlation is zero.

Worked Example: Spearman Correlation

Scenario: You survey 40 participants about their job satisfaction (ordinal scale: 1–10) and their years in the current role. You compute Spearman's ρ and find ρ = .413. The p-value is .008.

How to write it:

Job satisfaction and tenure were moderately positively correlated, rs(38) = .413, p = .008.

Alternative notation (using ρ):

Job satisfaction and tenure were moderately positively correlated, ρ(38) = .413, p = .008.

Note the details:

  • Degrees of freedom: 38 = 40 − 2.
  • Both rs and ρ are acceptable in APA style; check your discipline's convention.
  • The interpretation process is the same: report the sign, magnitude, and p-value.

§3 Common Mistakes in Reporting Correlations

Mistake Wrong Example Correct Example
Reporting n instead of df r(52) = .628, p = .001 r(50) = .628, p = .001
Confusing r with r² "r explained 39.5% of variance" "r² = .395, so 39.5% of variance was explained"
Omitting the sign of r r(50) = .628 (when it is actually negative) r(50) = −.628
No p-value r(50) = .628 r(50) = .628, p = .001
Calling r = .30 "strong" without context "A strong correlation of r = .30" "A moderate correlation of r = .30 (by Cohen's conventions for social science)"
Inconsistent decimal places r(50) = .63, p = .0009 r(50) = .628, p = .001

§4 Reporting a Correlation Matrix

When you present correlations between multiple variables, use a correlation matrix table. Rows and columns are the variables; cells contain the correlation coefficient and its p-value.

Example Correlation Matrix

Variable 1. Age 2. Income 3. Job Satisfaction
1. Age — .71* .38**
2. Income .71* — .52**
3. Job Satisfaction .38** .52** —

Note. N = 185. * p < .05. ** p < .01. All correlations are two-tailed.

Key features:

  • The diagonal shows dashes or 1.00 (a variable always correlates perfectly with itself).
  • Matrix is symmetric (correlation of A with B = correlation of B with A).
  • Asterisks (* and **) indicate significance levels; the footnote defines them.
  • Sample size and significance convention (α = .05) appear in the note below the table.

§5 Reporting Non-Significant Correlations

If the p-value is greater than your chosen α (typically α = .05), you fail to reject the null hypothesis. Report it this way:

Age and job satisfaction were not significantly correlated, r(58) = .18, p = .161.

Notes:

  • Always report the actual p-value, even if it is non-significant.
  • Do not write "there is no correlation"—the test failed to detect one, but absence of evidence is not evidence of absence.
  • If p > .10, many researchers still describe the result as a "trend" if it is close to significance.

§6 Effect Size and Interpretation

Cohen's (1992) rough guidelines for effect size in social science are r ≈ .10 (small), .30 (medium), and .50 (large). However, these are rules of thumb and vary by discipline. A correlation of r = .30 might be considered large in some fields and modest in others. When you report a correlation, consider noting whether it aligns with your field's expectations:

Study hours and exam performance were significantly positively correlated, r(50) = .628, p < .001, which constitutes a strong effect by convention.

Avoid unqualified claims like "a strong correlation" unless you have defined strength in the context.

§7 Frequently Asked Questions

Do I report r or r²?

Report r in your main text. The correlation coefficient r tells you the direction and magnitude of the linear relationship. If you want to discuss explained variance, use r² (the coefficient of determination), but always report r itself first. For example: "r(50) = .628, p = .001; r² = .395, indicating that 39.5% of variance was shared."

How do I report a correlation matrix in APA format?

Use a table with variables on both rows and columns, correlations in cells, and asterisks to denote significance levels. Include a table note with sample size, the α level (e.g., α = .05), and footnotes explaining the asterisks. The diagonal should show dashes or 1.00. See §4 for a full example.

What is the degrees of freedom for a correlation test?

Degrees of freedom for a correlation test always equals n − 2, where n is the number of paired observations. This is because the test involves estimating two parameters (the means) and comparing the observed correlation to the null hypothesis under a t-distribution. Do not use n alone.

How do I report Spearman correlation versus Pearson?

Both use the format test(df) = .XX, p = .XXX. For Pearson, use r. For Spearman, use rs or ρ (rho). The degrees of freedom calculation is identical: n − 2. Choose Spearman when data are ordinal or when the linearity assumption fails.

How do I report a non-significant correlation?

Use the same format and always include the p-value. For example: "r(58) = .18, p = .161." Avoid saying "there is no correlation." Instead, write "was not significantly correlated" to clarify that the test failed to detect a relationship, not that one doesn't exist.

When should I report a one-tailed versus two-tailed p-value?

Two-tailed tests are standard unless you have a directional hypothesis stated before data collection. When you report, specify "two-tailed" in the table note or text if there is any ambiguity. For example: "All correlations reported are two-tailed." One-tailed tests are rare and require strong justification; consult your supervisor or methodology guide if unsure.

§8 Related Tools

CALCULATOR

Correlation Coefficient Calculator

Compute Pearson r, p-value, and confidence interval from raw data or summary statistics.

Open calculator → CALCULATOR

Spearman Rank Correlation Calculator

Calculate Spearman's ρ with degrees of freedom and significance testing.

Open calculator → CALCULATOR

Effect Size Calculator

Convert between r, d, odds ratio, and other effect size measures.

Open calculator → CALCULATOR

Linear Regression Calculator

Fit a line to data and report the slope, intercept, and model R².

Open calculator →

§9 Sources

  • American Psychological Association. (2020). Publication Manual of the American Psychological Association (7th ed.). APA.
  • Purdue University Online Writing Lab (OWL). APA Formatting and Style Guide.
  • Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.
  • Kline, R. B. (2004). Beyond significance testing: Reforming data analysis methods in behavioral research. American Psychological Association.