Correlation · COR-2D-N

Sample Size for Two Dependent Correlations With No Variables in Common

Compare ρ_XY with ρ_WZ when X, Y, W, and Z are measured in the same participants.

1. Information obtained from previous studies or pilot data

These four correlations are not tested, but determine the dependence between the two tested correlations. Use values from a reasonably comparable population and measurement setting.

Correlation between X and W (ρXW)

Correlation between X and Z (ρXZ)

Correlation between Y and W (ρYW)

Correlation between Y and Z (ρYZ)

2. Inputs decided by the researcher for the new study

The complete set of six planned correlations must form a valid correlation matrix.

Anticipated correlation between X and Y (ρXY)

Anticipated correlation between W and Z (ρWZ)

Power (%)

Type I error, alpha (%)

Alternative hypothesis

Anticipated dropout/non-response (%)

3. Results

Enter all six correlations and the planning assumptions, then select Calculate sample size.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

Among adults with type 2 diabetes, a researcher wants to determine whether the correlation between HbA1c and fasting plasma glucose differs from the correlation between systolic blood pressure and urinary albumin-to-creatinine ratio. All four measurements are collected from the same participants, so the two correlations are dependent even though they have no variables in common.

For this example, X is HbA1c, Y is fasting plasma glucose, W is systolic blood pressure, and Z is urinary albumin-to-creatinine ratio. The four cross-correlations—ρ_XW, ρ_XZ, ρ_YW, and ρ_YZ—are also required because they determine the dependence between the two correlations being compared.

Formula and methodological note

The calculator uses Steiger's pooled Fisher-z-transformation Z-test for two dependent Pearson correlations with no indices in common. Separate covariance estimates under the pooled null and specified alternative are used in the power calculation.

The method assumes independent participants; four continuous, jointly normally distributed variables measured on every participant; linear relationships; Pearson correlations; and a prespecified comparison. The complete 4×4 correlation matrix must be positive semidefinite.

Do not use this calculator for independent groups, correlations sharing a variable, rank or partial correlations, partially overlapping samples, or clustered data. It supports research planning and does not replace statistical consultation.

Method references

Steiger JH. Tests for comparing elements of a correlation matrix. Psychological Bulletin. 1980;87:245–251.
Dunn OJ, Clark V. Correlation coefficients measured on the same individuals. Journal of the American Statistical Association. 1969;64:366–377.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Two Dependent Correlations With No Variables in Common (COR-2D-N).” Web calculator. NajibMY, 2026. Accessed August 1, 2026. https://najibmy.netlify.app/tools/sample-size/correlation/two-dependent-correlations-no-shared-variable/.