Correlation Comparison Calculator

Calculator Inputs

Input mode

Correlation method

Tail type

Alpha

Null difference on z scale

Results display target

Manual summary input

Correlation 1

Sample size 1

Correlation 2

Sample size 2

Raw paired datasets

Enter comma, space, or line-separated values. The selected method computes each correlation before comparison.

Dataset 1 X values

Dataset 1 Y values

Dataset 2 X values

Dataset 2 Y values

Example Data Table

Dataset	Variable X	Variable Y	Derived r	Sample Size
Marketing Spend vs Leads	12, 15, 18, 20, 24, 28, 31, 35	18, 20, 23, 27, 29, 34, 36, 39	0.9891	8
Email Sends vs Purchases	10, 12, 14, 16, 18, 21, 24, 27	14, 16, 17, 18, 21, 22, 25, 26	0.9807	8

Formula Used

This calculator compares two independent correlations. It first converts each correlation to Fisher’s z scale, then tests whether the transformed values differ more than sampling error predicts.

z(r) = 0.5 × ln((1 + r) / (1 - r))

SE = √(1 / (n₁ - 3) + 1 / (n₂ - 3))

Z = ((z(r₁) - z(r₂)) - Δ₀) / SE

CI for r uses Fisher z limits, then back-transforms with tanh(z).

For raw inputs, Pearson correlation uses covariance divided by the product of standard deviations. Spearman correlation ranks both variables first, then applies the Pearson formula to those ranks.

How to Use This Calculator

Choose manual mode if you already know both correlations and sample sizes.
Choose raw mode when you want the page to calculate each correlation first.
Select Pearson for linear relationships or Spearman for ranked monotonic relationships.
Set alpha and tail type according to your testing plan.
Press Compare Correlations to show results above the form.
Use the CSV button for tabular export and the PDF button for print-ready output.

FAQs

1. What does this calculator compare?

It compares two correlation coefficients to test whether one relationship is statistically stronger than the other across separate datasets or study samples.

2. When should I use Pearson correlation?

Use Pearson when both variables are numeric, reasonably continuous, and the relationship is approximately linear without severe outliers dominating the pattern.

3. When is Spearman a better choice?

Use Spearman when data are ordinal, heavily skewed, or better described by ranked monotonic movement rather than strict linear change.

4. Why does the calculator use Fisher z?

Fisher transformation makes correlation sampling behavior closer to normal, which supports a cleaner significance test and more stable interval estimates.

5. What does the p value mean here?

The p value estimates how surprising the observed difference would be if the transformed correlations were truly equal under the selected null assumption.

6. Can I compare dependent correlations with this page?

No. This implementation is designed for independent comparisons. Dependent correlations need specialized tests that account for shared variables and covariance.

7. Why are confidence intervals shown?

Confidence intervals show plausible ranges for each correlation and the difference estimate, helping you judge both precision and practical importance.

8. What if my lists have missing or text values?

Remove missing entries first and keep only numeric values. Each X list must match its paired Y list exactly in length.