The Basics of Reporting Correlations in APA
Correlation analysis is one of the most widely used statistical techniques in the social and behavioral sciences. Whether you are examining the relationship between study hours and exam scores or investigating the association between stress and sleep quality, you need to report your findings in a standardized format.
APA 7th edition requires that correlation reports include the correlation coefficient, degrees of freedom (or sample size), and the p-value. Depending on the type of correlation, you may also report the coefficient of determination (r²) and a confidence interval. Getting these details right is essential for publication-ready manuscripts.
This guide covers Pearson r, Spearman r_s, point-biserial r_pb, correlation matrices, and the most common formatting mistakes researchers make.
Reporting Pearson Correlation
The Pearson product-moment correlation coefficient measures the strength and direction of a linear relationship between two continuous variables. It is the default correlation method when both variables are measured on an interval or ratio scale and the relationship is approximately linear.
APA Template
The standard APA format for reporting a Pearson correlation is:
r(df) = .XX, p = .XXX
Where df (degrees of freedom) equals N - 2. For example, with 50 participants, df = 48.
Key Formatting Rules
- No leading zero. Because r is bounded between -1 and +1, it cannot exceed 1.0. APA style therefore omits the leading zero: write r = .42, not r = 0.42. The same rule applies to p values.
- Two decimal places for r. Report the correlation coefficient to two decimal places (e.g., .42, not .4 or .4200).
- Exact p values. Report the exact p value to three decimal places (e.g., p = .003). Use p < .001 only when the value is below .001.
- Degrees of freedom in parentheses. Always include df = N - 2 immediately after the r.
Full Reporting Example
A Pearson correlation was computed to assess the relationship between weekly study hours and final exam scores. There was a statistically significant positive correlation between the two variables, r(48) = .42, p = .003. Students who reported more study hours tended to achieve higher exam scores. The coefficient of determination (r² = .18) indicated that study hours accounted for approximately 18% of the variance in exam scores.
Notice the structure: state the purpose of the analysis, report the statistical result, describe the direction of the relationship in plain language, and optionally provide the coefficient of determination for additional context.
When to Include r²
The coefficient of determination (r²) tells the reader what proportion of variance in one variable is explained by the other. Including r² is not strictly required by APA, but many journals expect it because it translates the abstract correlation coefficient into an intuitive percentage. An r of .42 may not immediately convey practical significance, but stating that 18% of the variance is shared makes the finding more concrete.
Interpreting Correlation Strength
Cohen (1988) proposed widely used benchmarks for interpreting the magnitude of correlation coefficients. These guidelines apply to the absolute value of r, regardless of sign.
| Absolute value of r | Interpretation | |------------------------|----------------| | .10 - .29 | Small | | .30 - .49 | Medium | | .50 or greater | Large |
A correlation of r = -.55 is a large negative correlation. The sign indicates direction (positive or negative), while the absolute value determines strength.
A word of caution. These benchmarks are conventions, not rigid cutoffs. Cohen himself described them as guidelines for situations where no better frame of reference exists. In some research domains, an r of .20 represents a meaningful and practically significant relationship, while in others, an r of .50 might be considered unremarkable. Always interpret your correlations in the context of prior research in your field.
For example, in personality psychology, correlations between personality traits and behavioral outcomes rarely exceed .30. An r of .25 in that context is a noteworthy finding. In physics or engineering, where measurement error is minimal, an r of .25 might indicate a weak and practically trivial relationship.
Reporting a Correlation Matrix (Table Format)
When you examine correlations among three or more variables, presenting them in a correlation matrix table is standard practice. APA format has specific conventions for these tables.
APA Correlation Table Template
Table 1
Means, Standard Deviations, and Intercorrelations for Study Variables
| Variable | M | SD | 1 | 2 | 3 | 4 | |----------|------|------|-------|-------|-------|---| | 1. Study hours | 14.20 | 5.80 | — | | | | | 2. Exam score | 78.50 | 12.30 | .42** | — | | | | 3. Class attendance | 0.82 | 0.15 | .38** | .51** | — | | | 4. Sleep quality | 3.60 | 0.90 | .12 | .08 | .21* | — |
Note. N = 50. M and SD represent mean and standard deviation, respectively.
* p < .05. ** p < .01.
Table Formatting Rules
Lower triangle only. A correlation matrix is symmetric — the correlation between variables 1 and 2 is the same as between 2 and 1. Reporting both halves is redundant. Present only the lower triangle (below the diagonal) and place a dash on the diagonal.
Asterisk notation. Use asterisks to indicate significance levels. The most common convention is one asterisk for p < .05 and two asterisks for p < .01. Some researchers add three asterisks for p < .001. Define all asterisks in a table note.
Include descriptive statistics. Adding the mean (M) and standard deviation (SD) columns to the same table gives readers everything they need to evaluate your correlations in a single location.
Variable numbering. Number the variables and use those numbers as column headers. This keeps the table compact and easy to read.
No leading zeros in the matrix. All r values within the table follow the same no-leading-zero rule.
Reporting Spearman Rank Correlation
The Spearman rank-order correlation (r_s or the Greek letter rho) is the non-parametric alternative to Pearson r. It measures the strength and direction of a monotonic relationship between two variables.
When to Use Spearman
Use Spearman correlation when:
- One or both variables are measured on an ordinal scale (e.g., Likert ratings, rankings).
- The data contain significant outliers that would distort Pearson r.
- The relationship is monotonic but not linear (e.g., one variable increases as the other increases, but not at a constant rate).
- The normality assumption is violated and sample sizes are small.
APA Template and Example
The format is nearly identical to Pearson, but uses the subscript s to distinguish it:
r_s(df) = .XX, p = .XXX
Full example:
A Spearman rank-order correlation was computed to assess the relationship between customer satisfaction ratings and likelihood of repurchase. There was a strong positive correlation between the two variables, r_s(78) = .61, p < .001. Higher satisfaction ratings were associated with greater repurchase likelihood.
Some style guides use the Greek letter rho in place of r_s. Both conventions are acceptable, but be consistent throughout your manuscript.
Point-Biserial Correlation
The point-biserial correlation (r_pb) is used when one variable is continuous and the other is naturally dichotomous (having exactly two categories). Examples include correlating test scores with pass/fail status or examining the relationship between salary and gender.
APA Template and Example
r_pb(df) = .XX, p = .XXX
Full example:
A point-biserial correlation was computed to examine the relationship between gender (coded as 0 = female, 1 = male) and mathematics achievement scores. The correlation was statistically significant, r_pb(98) = .31, p = .002, indicating that male students scored higher on average than female students.
Computationally, the point-biserial correlation is identical to the Pearson r when one variable is dichotomous. The distinction is primarily conceptual. If a reviewer or journal does not require the r_pb label, reporting it as a standard Pearson r is also acceptable.
Non-Significant Correlations
A common mistake is omitting non-significant correlations from results sections. APA guidelines require that you report all planned analyses, regardless of whether they reached statistical significance.
Why Report Non-Significant Results
Non-significant findings contribute to the scientific record. They help prevent publication bias, inform future meta-analyses, and provide important context for interpreting the correlations that were significant.
Example
The correlation between daily caffeine intake and GPA was not statistically significant, r(48) = .12, p = .394. This suggests that caffeine consumption, at the levels observed in this sample, was not meaningfully related to academic performance.
The format is identical to a significant result. State the finding clearly, report the statistics, and provide a brief interpretation. Do not apologize for or dismiss non-significant findings.
In correlation matrices, non-significant correlations appear without asterisks. Never leave cells blank or replace non-significant values with "ns" — always report the actual coefficient.
Common Mistakes
Reporting r² Instead of r Without Clarification
Some researchers report r² (the coefficient of determination) as their primary statistic when they should be reporting r. The two convey different information. An r of .50 sounds moderate, but the corresponding r² of .25 tells you only 25% of variance is shared. If you report r², make sure the reader knows it is r² and not r, and consider reporting both.
Confusing Correlation With Causation in the Write-Up
Saying "study hours improved exam scores" implies a causal relationship that a correlation cannot establish. Use language that reflects association: "was associated with," "was related to," or "tended to co-occur with." Reserve causal language for experimental designs.
Not Reporting Degrees of Freedom
Writing "r = .42, p = .003" without degrees of freedom omits critical information. Degrees of freedom allow the reader to determine the sample size (N = df + 2) and evaluate the statistical power of the analysis. Always include them.
Using Leading Zeros for r and p Values
Because r is bounded by -1 to +1 and p is bounded by 0 to 1, neither can exceed 1.0 in absolute value. APA style requires omitting the leading zero: write r = .42, not r = 0.42, and p = .003, not p = 0.003.
Omitting Non-Significant Correlations From Tables
If you examined the correlation between two variables, report it in your matrix regardless of significance. Selective reporting of only significant correlations inflates the apparent pattern of results and constitutes a form of reporting bias.
Failing to Specify the Type of Correlation
If you used Spearman instead of Pearson, or point-biserial instead of standard Pearson, state this explicitly. Writing just "r = .45" when you computed a Spearman correlation is misleading because the reader will assume Pearson by default.
APA Correlation Reporting Checklist
Use this checklist before submitting your manuscript:
- [ ] Stated the purpose of the correlation analysis
- [ ] Specified the type of correlation (Pearson, Spearman, or point-biserial)
- [ ] Reported the correlation coefficient to two decimal places
- [ ] Included degrees of freedom in parentheses (df = N - 2)
- [ ] Reported the exact p value (or p < .001)
- [ ] Omitted leading zeros for r and p values
- [ ] Described the direction and strength of the relationship in words
- [ ] Reported all planned correlations, including non-significant ones
- [ ] Included effect size (r² or verbal interpretation using Cohen's benchmarks)
- [ ] Formatted correlation matrix with lower triangle only and asterisk notation
- [ ] Added a table note defining significance asterisks and sample size
- [ ] Used associational language (not causal) when describing results
Try StatMate's Free Correlation Calculator
Formatting correlation results by hand is tedious and error-prone. StatMate's Correlation Calculator automates the entire process.
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- Pearson r with exact p-value
- Coefficient of determination (r²)
- 95% confidence interval for r
- Scatter plot with regression line
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The output follows every APA 7th edition convention covered in this guide — correct decimal places, no leading zeros, degrees of freedom, and plain-language interpretation. You can copy the formatted text directly or export it to Word (.docx) with a single click.