Compare Two Correlations Calculator
Test whether two independent correlations differ significantly. Enter each correlation and the sample size it came from.
Learn how to calculate it yourselfEnter your values
Results update as you type.
p-value (difference)
no significant difference
- z
- 1.368
Calculate it yourself
Compare independent correlations r₁ = 0.60 and r₂ = 0.20, each based on 30 observations.
Follow this worked example, then repeat the steps with your own numbers.
Transform both correlations
z₁ = ½ ln[(1 + 0.60)/(1 − 0.60)] ≈ 0.69315. z₂ = ½ ln[(1 + 0.20)/(1 − 0.20)] ≈ 0.20273.Find the standard error of the difference
SE = √[1/(30 − 3) + 1/(30 − 3)] ≈ 0.27217.Standardize the transformed difference
Z = (z₁ − z₂) ÷ SE ≈ 1.802.Use the standard normal distribution
Two-sided p = 2 × P(Znormal ≥ 1.802) ≈ 0.072.Use a normal probability table or spreadsheet function. Keep the transformed values unrounded until the last step.
The correlations must come from independent samples, with at least four observations in each. This formula does not test overlapping correlations from the same sample.
Check your answer in the calculatorUse your PaperSurvey.io results
Take correlations and sample sizes from independent groups into this calculator to compare their strengths.
How the test works
This test uses the Fisher r-to-z transformation to convert each correlation to a value that is approximately normally distributed, then compares the two using their sample sizes. It applies to two independent correlations, for example the same relationship measured in two separate groups of respondents.
Reading the result
A p-value below 0.05 means the two correlations differ by more than sampling noise would explain. A larger p-value means you cannot rule out that both groups share the same underlying correlation. Larger samples make the test more sensitive to real differences.
Frequently asked questions
Can I compare correlations from the same sample?
No. This calculator assumes the two correlations come from independent samples. Comparing overlapping correlations within one sample needs a different, dependent-samples test.
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