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Correlation · COR-2I

Sample Size for Test of Two Independent Correlations

Plan a test comparing correlation coefficients measured in two independent groups.

1. Information obtained from previous studies or literature

The preserved method accepts planning correlations from 0 to less than 1.

2. Information decided by the researcher

Use 1 for equal allocation.

Defaults to 10%. Enter 0 if no adjustment is required.

3. Results

Enter the two-correlation assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A researcher wants to compare the correlation between body mass index and systolic blood pressure in adults with type 2 diabetes versus adults without diabetes. Because the two correlations come from separate participant groups, they are independent.

Formula and methodological note

The calculator preserves the Fisher-z normal-approximation formula for comparing two independent correlations. The two planning correlations are transformed and combined with the selected Type I error, power, and allocation ratio.

The groups must be independent and measure the same pair of continuous variables using comparable definitions. The allocation ratio is group 2 divided by group 1. The preserved method restricts both correlations to non-negative values below 1.

Group 1 is rounded upward first and group 2 is derived from that rounded size. The total is then inflated for dropout/non-response. The method does not address dependent correlations, covariate adjustment, clustering, non-linearity, measurement error, or multiplicity.

Method references

  1. Fisher RA. On the probable error of a coefficient of correlation deduced from a small sample. Metron. 1921;1:3–32.
  2. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale: Lawrence Erlbaum Associates; 1988.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Comparison of Two Independent Correlations (COR-2I).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/correlation/two-correlations/.