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Correlation · COR-2D-S

Sample Size for Two Dependent Correlations Sharing One Variable

Compare correlations between X and Y and between X and Z when all three variables are measured in the same participants.

1. Information obtained from previous studies or pilot data

Use a population correlation from a previous study or pilot sample with a reasonably comparable population and measurement definitions.

This correlation is not tested, but is required to account for covariance between the two dependent correlations.

2. Inputs decided by the researcher for the new study

Shared-variable structure: compare ρXY with ρXZ. Together with ρYZ, the planned values must form a valid correlation matrix.

3. Results

Enter all three 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 HbA1c is more strongly correlated with fasting plasma glucose than with body mass index. Both correlations are measured in the same participants and share HbA1c as one variable, so they are dependent.

For this example, X is HbA1c, Y is fasting plasma glucose, and Z is body mass index. The correlation between fasting plasma glucose and body mass index is also required because it determines 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 sharing one index. It uses separate transformed-correlation covariance estimates under the pooled null hypothesis and the specified alternative, then searches for the smallest integer N meeting the target power.

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

Do not use this calculator for independent groups, correlations with no variable in common, Spearman or Kendall correlations, partially overlapping samples, clustered/repeated observations beyond the three measurements, or adjusted/partial correlations. It supports research planning and does not replace statistical consultation.

Method references

  1. Steiger JH. Tests for comparing elements of a correlation matrix. Psychological Bulletin. 1980;87:245–251.
  2. 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 Sharing One Variable (COR-2D-S).” Web calculator. NajibMY, 2026. Accessed August 1, 2026. https://najibmy.netlify.app/tools/sample-size/correlation/two-dependent-correlations-shared-variable/.