Compare › Equivalence

Non-inferiority test (means / proportions)

A non-inferiority test rejects the hypothesis that the new arm is worse than the reference by ≥ δ, concluding instead that it is no worse by more than that margin — for means or proportions.

What is Non-inferiority test (means / proportions)?

Non-inferiority is one-sided equivalence. The framing matters in trials where the new arm is expected to be similar but cheaper, safer, or easier to administer than the reference — you want to show it's not meaningfully worse, not that it's identical.

The clinical margin δ should be pre-specified and justified (usually based on a fraction of the reference vs placebo effect). The (1 − α) CI for the difference is the visual: if the CI's adverse boundary doesn't cross −δ, non-inferiority is declared.

When should I use Non-inferiority test (means / proportions)?

Comparative-effectiveness trials.
Generic-drug bioequivalence (with the specific FDA framing).
Cheaper / safer / simpler treatment vs gold-standard reference.

What data does it need?

Two columns (numeric for means, binary for proportions) + margin δ + α + direction.

What does it report?

One-sided test statistic + p + CI on the difference + verdict.

How do I interpret the result?

Pre-specify δ (and direction) in the protocol; choosing δ after seeing the data is a major source of bias in non-inferiority trials.