SPSS reports Pearson correlations as a matrix in which every coefficient appears twice, every variable is correlated with itself, and each cell stacks three different numbers. Once you know how the grid is built it takes seconds to read. This guide goes through it row by row with a three-variable worked example, lists the common misreadings, and gives the APA 7 write-up. The reporting format alone is in the Pearson correlation APA guide.
What SPSS gives you
Analyze > Correlate > Bivariate, with Pearson ticked, produces:
- Descriptive Statistics (if you ticked Means and standard deviations under Options): mean, SD and N of each variable.
- Correlations: the matrix. This is the result.
Recent SPSS versions can also add a confidence interval for each coefficient (look for a Confidence interval option in the Bivariate Correlations dialog). Older versions cannot, so the CIs in the write-up below were computed with the Fisher z method, which you can do by hand or in any CI calculator.
The worked example
Fifty undergraduates reported their average hours of sleep per night during exam week and their perceived stress (0 to 40), and their exam scores (0 to 100) were recorded. All three variables went into one Bivariate Correlations run.
Table 1: Descriptive Statistics
| Mean | Std. Deviation | N | |
|---|---|---|---|
| Sleep hours | 6.72 | 1.242 | 50 |
| Stress | 19.98 | 6.557 | 50 |
| Exam score | 65.98 | 10.640 | 50 |
The means and SDs for your descriptives table, and a check that N is what you expect for each variable.
Table 2: Correlations
| Sleep hours | Stress | Exam score | ||
|---|---|---|---|---|
| Sleep hours | Pearson Correlation | 1 | -.521** | .343* |
| Sig. (2-tailed) | .000 | .015 | ||
| N | 50 | 50 | 50 | |
| Stress | Pearson Correlation | -.521** | 1 | -.393** |
| Sig. (2-tailed) | .000 | .005 | ||
| N | 50 | 50 | 50 | |
| Exam score | Pearson Correlation | .343* | -.393** | 1 |
| Sig. (2-tailed) | .015 | .005 | ||
| N | 50 | 50 | 50 |
How the grid is built. Each variable has a row block and a column. The cell where a row block meets a column holds three numbers for that pair:
- Pearson Correlation: r, from −1 to 1. Sleep and exam score: r = .343, a moderate positive correlation. Stress and exam score: r = −.393, moderate and negative: more stress, lower scores.
- Sig. (2-tailed): the two-sided p value for that r. Sleep and exam score: .015.
- N: the number of people with values on both variables.
The diagonal is always 1. Every variable correlates perfectly with itself. Its Sig. cell is blank. Ignore it.
The matrix is symmetric. The cells above and below the diagonal are the same numbers: Sleep hours × Exam score (.343) and Exam score × Sleep hours (.343) are one correlation. Three variables give three correlations, not six.
The stars. With Flag significant correlations ticked (the default), SPSS adds ** to r when p < .01 and * when p < .05, and explains them in footnotes: "Correlation is significant at the 0.01 level (2-tailed)" and "Correlation is significant at the 0.05 level (2-tailed)". In APA text you report the exact p instead; stars belong only in a correlation table, with a note explaining them.
N when data are missing. By default SPSS uses pairwise deletion: each correlation uses everyone with both values, so N can differ from cell to cell. Report the N (or df) of each correlation, or switch to listwise deletion under Options so every cell uses the same people.
Reading the three pairs:
- Sleep hours and stress: r = −.521, Sig. = .000 (p < .001). Strong negative.
- Sleep hours and exam score: r = .343, Sig. = .015. Moderate positive.
- Stress and exam score: r = −.393, Sig. = .005. Moderate negative.
Misreadings that cost marks
- Writing p = .000. It means p < .001.
- Reporting the diagonal 1s, or each correlation twice. Read the lower (or upper) triangle only.
- Using N as the degrees of freedom. A correlation's df is N − 2: r(48), not r(50).
- Leading zeros. APA drops the zero for values that cannot exceed 1: r = .34, p = .015.
- Reading the stars as the p value. ** means p < .01, not p = .01. Report the exact Sig.
- Calling a correlation an effect. "More sleep caused higher scores" is not what r = .34 shows. Describe an association.
- Ignoring the scatterplot. r measures straight-line association only, and one outlier can make or break it. Plot the data (Graphs > Chart Builder > Scatter) before trusting the matrix. For ranked data or a curved but monotonic relationship, use Spearman's rho.
The APA 7 format template
There was a [weak/moderate/strong] [positive/negative] correlation between [variable 1] and [variable 2], r(df) = .XX, p = .XXX, 95% CI [.XX, .XX].
The write-up for this example
Pearson correlations were computed between sleep, stress and exam performance (N = 50). Students who slept more reported less stress, r(48) = −.52, p < .001, 95% CI [−.70, −.28], and obtained higher exam scores, r(48) = .34, p = .015, 95% CI [.07, .57]. Higher stress was associated with lower exam scores, r(48) = −.39, p = .005, 95% CI [−.60, −.13].
With three or more variables, a correlation table with means and SDs is often clearer than prose; the APA correlation table guide shows the layout.
Let KyroStat do the write-up for you
Already have the output? Paste the Correlations table from the SPSS Viewer into the box on the Pearson correlation reporting guide to get the APA sentence. Or upload the spreadsheet to KyroStat, which draws the scatterplots, checks linearity and outliers, and writes the APA sentences and the correlation table with the code behind them.
Also useful for the write-up (affiliate links): Proofreading for your thesis or paper (20% off with code PAP20): Paperpal
Frequently asked questions
Why does every correlation appear twice in the SPSS table? The matrix shows every variable against every other, so the cells above and below the diagonal mirror each other. Report each pair once.
What does "Correlation is significant at the 0.01 level (2-tailed)" mean? It is the footnote for the ** flag: that correlation's two-sided p is below .01. Report the exact p from the Sig. (2-tailed) row instead of the stars.
What are the degrees of freedom for a Pearson correlation? N − 2, using the N in that correlation's cell. With N = 50, report r(48).
Why is the N different in different cells? SPSS excludes missing values pairwise by default, so each correlation uses everyone with both values. Report each N or use listwise deletion.
Does SPSS give a confidence interval for r? Recent versions can, as an option in the Bivariate Correlations dialog. Otherwise compute it with the Fisher z transformation.
Which related guides might I need? Often these: linear regression output to predict one variable from another, partial correlation and Spearman's rho.