Specialty › Tests on summarized data

Compare two correlations (Fisher z)

Fisher's z test compares two independent correlations from typed-in r and n values, testing whether ρ₁ = ρ₂.

What is Compare two correlations (Fisher z)?

Pearson r is bounded in [−1, 1] and has a skewed sampling distribution near the extremes. The Fisher z-transformation z = ½·log((1+r)/(1−r)) approximately normalises the distribution; differences in z are then testable by a standard z-test with SE = √(1/(n₁−3) + 1/(n₂−3)).

For *paired* correlations (same subjects, different variable pairs), Steiger's z is the right test — not implemented here; use it when the two correlations are from the same sample.

When should I use Compare two correlations (Fisher z)?

Comparing correlations from two independent samples (different cohorts, different populations).

What data does it need?

r₁ + n₁ and r₂ + n₂.

What does it report?

Fisher-transformed difference + z + p + CI on the difference of Fisher zs (back-transform on request).

What does it assume?

Independent samples.
Approximately bivariate normal within each sample.

How do I interpret the result?

Confirm independence (different subjects) — using this test on paired correlations inflates type-I error.