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TOST — equivalence (proportions)

TOST for proportions declares two proportions equivalent when their difference falls within ±δ — the proportions analogue of the TOST equivalence test for means.

What is TOST — equivalence (proportions)?

Same TOST framework as tost (two one-sided tests); H₀ is that the proportion difference exceeds ±δ, H₁ is that it's inside. Both one-sided proportion z-tests must reject at α for equivalence to be declared at level α.

When should I use TOST — equivalence (proportions)?

Showing two treatments produce equivalent response rates within a pre-specified margin.
Bioequivalence-style comparisons on binary outcomes.

What data does it need?

Two binary columns + equivalence margin δ + α.

What does it report?

Larger of the two one-sided p-values + verdict.

What does it assume?

Independent samples.
Approximate normality of the proportion-difference distribution (n × p × (1 − p) ≥ ~5 per arm).

How do I interpret the result?

Equivalence is declared only when *both* one-sided tests reject — the reported p is the larger of the two and must be < α.