Pearson Correlation Calculator with APA 7 Results
Paste two columns and get Pearson’s r with its p-value and 95% confidence interval, Spearman’s rho, r², a scatter plot with the regression line, and the results sentence written in APA 7 style for your thesis.
Use one-tailed only if the direction was fixed before collecting data.
How to use this calculator
1. Paste your two variables. One value per line in X and Y, one pair per row. Copying two adjacent columns from Excel or SPSS into the X box works too: the calculator splits them.
2. Name them. The names you type are used in the APA sentence and on the plot, so write what your thesis calls them.
3. Pick the coefficient. Pearson for interval data with a roughly linear relationship; Spearman for ordinal data, non-normal distributions or outliers. Both are computed, the chosen one is marked as reported.
4. Check the scatter plot. A correlation coefficient assumes a straight-line relationship. If the plot bends or one point sits far from the rest, say so in your chapter.
5. Copy the APA sentence. It goes into your results chapter as it is. The full chapter, every hypothesis with tables, is what the Chapter 4 Interpreter writes from your SPSS output.
Pearson or Spearman?
Pearson’s r measures the strength and direction of a linear relationship between two interval or ratio variables: age and income, hours studied and exam score, scale totals that behave like continuous scores. It is sensitive to outliers, because a single extreme pair pulls the line towards itself.
Spearman’s rho (rₛ) is Pearson’s r computed on the ranks of the values. Use it when the variables are ordinal, when the distribution is clearly non-normal, when there are outliers, or when the relationship is monotonic but not linear. In SPSS both appear under Analyze → Correlate → Bivariate.
Both coefficients run from −1 to +1. Cohen (1988) suggested .10 as small, .30 as medium and .50 as large in the behavioural sciences, and those are the words the calculator uses. A correlation says nothing about causation, and a non-significant one with a small sample says little about anything: look at the confidence interval.
How the statistics are calculated
r = Σ(xᵢ − Mx)(yᵢ − My) / √(Σ(xᵢ − Mx)² Σ(yᵢ − My)²). Significance is tested with t = r √(n − 2) / √(1 − r²) on n − 2 degrees of freedom, which is what SPSS uses for the Sig. (2-tailed) column.
The 95% confidence interval uses Fisher’s z transformation: z = arctanh(r), standard error 1/√(n − 3), interval z ± 1.96 SE transformed back with tanh. r² is the proportion of variance in one variable shared with the other. Spearman’s rho uses average ranks for ties and the same t approximation for its p-value, matching SPSS. All values are checked against scipy to six decimals.
Assumptions to check first
Linearity. Look at the scatter plot. A U-shape or a plateau gives a small r even when the variables are strongly related; Spearman handles a monotonic curve, nothing handles a U.
Bivariate normality for Pearson, or at least no heavy skew and no outliers with small samples. With 30 or more pairs the test on r is robust. Check normality with a Shapiro-Wilk test when the sample is small.
Independence of pairs. Each row is one participant; the same person measured twice is a paired design, not a correlation between two people.
Range. A sample that covers only a narrow range of X, for example only top students, shrinks the correlation. Mention it in the limitations if it applies.
How to report a correlation in APA 7
State the coefficient, what was correlated, the descriptives, then r(df) = value, p, and the confidence interval. Statistics are italicised, r and p have no leading zero, two decimals for r and three for p unless it is below .001. For several variables report a correlation matrix as an APA table with the significant coefficients marked. The calculator writes the sentence; change the variable names to match your study.
A results chapter repeats this for every hypothesis and adds the tables, the descriptive statistics, the assumption checks and the reliability of each scale. See a real one in the Chapter 4 Interpreter demo.
Frequently asked questions
What does a negative r mean?
As one variable rises the other falls. The strength is the absolute value: r = −.45 is as strong as r = .45, only in the opposite direction.
Is r = .30 with p = .20 a “moderate correlation”?
The size is moderate by Cohen’s labels, but with that p-value and a small sample the confidence interval will include zero, so you cannot claim the population correlation is different from zero. Report both the size and the interval, and let the reader see the uncertainty.
How many pairs do I need?
To detect a medium correlation (r = .30) with 80% power at α = .05 you need about 85 pairs; a large one (r = .50) needs about 30. Fewer than 10 pairs and a single outlier can decide the result.
Pearson gives r = .60 and Spearman gives .40. Which one?
They disagree when the relationship is driven by a few extreme values. Look at the plot. If one or two points sit far away, Spearman is the honest number; report it and say why.