Research ToolsEquivalence / Non-inferiority (TOST)

Equivalence / Non-inferiority Test (TOST, two means)

"P>0.05" does not mean "the two groups are equal." To prove practical equivalence (or non-inferiority) you must pre-set an acceptable equivalence margin ±Δ, then run two one-sided tests (TOST). For the difference of two independent means this tool gives the TOST p-value, the (1−2α) confidence interval and an equivalence/non-inferiority verdict. Computed locally; data never uploaded.

① Input

MeanSDn
Group 1
Group 2
Equivalence margin Δ (same units as data)
α

How to use & methodology

Why can't P>0.05 be read as 'the groups are equal'?

The conventional null hypothesis is 'no difference'; a non-significant result is only 'no evidence of a difference', which may just mean an underpowered sample. To claim equivalence you must use TOST: pre-set an acceptable margin Δ and prove the difference lies within it.

How do I set the margin Δ?

Δ is the largest difference that is clinically negligible. It must be set in advance from expert judgement, prior studies or regulatory guidance and written into the protocol; never chosen after seeing the data, or the conclusion is invalid.

Equivalence vs non-inferiority?

Equivalence requires the difference within ±Δ on both sides (the new treatment is neither much better nor much worse); non-inferiority only requires 'not worse than the control by more than Δ' and is one-sided. This tool supports all three modes.

Why a 90% interval?

A TOST at α=0.05 is equivalent to checking whether the 1−2α=90% confidence interval falls within the equivalence margin. This is the standard way the TOST and confidence-interval approaches agree.