Correlation Calculator
Calculate Pearson r, Spearman rho, and R-squared. Visualize your data with a scatter plot and evaluate whether correlation implies causation.
Correlation Calculator
Accepts comma-separated (1.2, 3.4) or tab-separated values from spreadsheets
Correlation vs. Causation Checklist
A statistically significant correlation does not imply causation. Use this checklist to evaluate whether a causal claim is justified.
A credible causal claim requires a logical or biological mechanism through which the cause produces the effect — not just a statistical association.
If the relationship has been replicated across different populations, settings, and methodologies, it strengthens the case for causation.
For X to cause Y, X must occur before Y. Cross-sectional data alone cannot establish this — you need longitudinal or experimental evidence.
A gradient effect — where increasing the dose or intensity of X leads to a proportional change in Y — supports a causal interpretation.
Confounding variables, reverse causation, and selection bias are common threats. Strong causal claims require controlling for or eliminating these alternatives.
Randomized controlled experiments are the gold standard for causal inference. Observational studies can suggest associations but cannot definitively prove causation.
Causation Evidence Score
0 / 6
Cannot claim causation
How to Use This Correlation Calculator
Enter your data as X,Y pairs in the input field above, with one pair per line. You can use commas (e.g., "1.2, 3.4") or tabs to separate values, which means you can paste two columns directly from Excel or Google Sheets. Click Calculate to instantly compute the Pearson correlation coefficient, Spearman rank correlation, R-squared, p-value, and linear regression equation.
The tool generates a scatter plot with your data points and a trend line, so you can visually assess the relationship. Below the calculator, use the Causation Checklist to evaluate whether a causal claim is justified based on established criteria from research methodology.
Understanding Correlation Coefficients
The Pearson correlation coefficient (r) measures the linear relationship between two continuous variables. It ranges from -1 (perfect negative) to +1 (perfect positive), with 0 indicating no linear relationship. The Spearman rank correlation (rho) measures the monotonic relationship using ranked data, making it more robust to outliers and non-linear patterns.
R-squared tells you the proportion of variance in Y explained by X. A value of 0.64 means 64% of the variability in Y can be predicted from X. The p-value indicates whether the observed correlation is statistically significant — values below 0.05 are conventionally considered significant, meaning the correlation is unlikely to be due to chance alone.
Why Correlation Does Not Imply Causation
This is one of the most important principles in statistics and research. Two variables can move together for many reasons: a direct causal link, a shared confounding variable, reverse causation, or pure coincidence. For example, countries with higher chocolate consumption have more Nobel laureates — but chocolate does not cause Nobel prizes. Both are correlated with national wealth and education infrastructure.
The Causation Checklist in this tool is based on the Bradford Hill criteria and standard experimental design principles. It helps you systematically evaluate whether your correlation evidence is strong enough to support a causal claim. For rigorous causal analysis, consider running controlled experiments or using techniques like difference-in-differences, instrumental variables, or regression discontinuity designs.
Using Correlation Analysis in User Research
In product and user research, correlation analysis helps you identify relationships between user behaviors and outcomes. For example, you might correlate feature usage frequency with retention rates, or NPS scores with support ticket volume. These insights guide prioritization decisions — but remember that correlation alone should not drive product changes without understanding the underlying mechanism.
For deeper insights, pair quantitative correlation data with qualitative evidence from user interviews. Tools like Innerview help you analyze interview transcripts to uncover the why behind the statistical patterns, turning correlations into actionable product decisions.
Frequently Asked Questions
What is the difference between correlation and causation?
Correlation measures the statistical relationship between two variables — when one changes, the other tends to change in a predictable way. Causation means that one variable directly produces a change in the other. A strong correlation does not prove causation. For example, ice cream sales and drowning rates are correlated (both increase in summer), but ice cream does not cause drowning. Establishing causation requires experimental evidence, temporal precedence, a plausible mechanism, and the elimination of confounding variables.
What is Pearson r and how do I interpret it?
Pearson r (also called the Pearson correlation coefficient) measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 to +1. A value of +1 means a perfect positive linear relationship, -1 means a perfect negative linear relationship, and 0 means no linear relationship. Values between 0.7 and 1.0 (or -0.7 and -1.0) are generally considered strong correlations, while values between 0.3 and 0.7 are moderate, and below 0.3 are weak.
When should I use Spearman rho instead of Pearson r?
Use Spearman rho (rank correlation) when your data is ordinal (ranked), when the relationship between variables is monotonic but not necessarily linear, or when your data contains significant outliers. Spearman rho is more robust than Pearson r because it operates on ranks rather than raw values, making it less sensitive to extreme values and non-normal distributions. If both coefficients are similar, the relationship is likely linear. If Spearman is notably higher, the relationship may be monotonic but non-linear.
What does R-squared tell me that Pearson r does not?
R-squared (the coefficient of determination) is simply the square of Pearson r. While r tells you the direction and strength of a correlation, R-squared tells you the proportion of variance in Y that is explained by X. For example, if r = 0.80, then R-squared = 0.64, meaning 64% of the variability in Y can be explained by its linear relationship with X. The remaining 36% is due to other factors. R-squared is always between 0 and 1 and is especially useful when you want to communicate how much predictive power one variable has over another.
How many data points do I need for a reliable correlation?
As a general rule, you need at least 30 data pairs for a reasonably stable correlation estimate. With fewer than 10 pairs, correlation coefficients can fluctuate wildly and p-values are unreliable. For small samples (10 to 30), be cautious about drawing strong conclusions — the confidence interval around r will be wide. For critical decisions, aim for 50 or more data points. Also consider that outliers have a disproportionate effect on small samples, so always inspect your scatter plot visually before trusting the numbers.