Equivalence Test (TOST): Prove Two Methods Are Equivalent
What is the Equivalence Test?
Traditional hypothesis tests ask whether a difference exists, and a p-value above 0.05 only shows that the difference is not significant, not that it is equivalent. An equivalence test asks whether the difference is small enough to be acceptable, and is used to prove that two methods, batches or formulations are equivalent. It matters for analytical method replacement, process validation and bioequivalence studies, where demonstrating equivalence is far more meaningful than showing non-significance.
When to Use It
Use it when you must prove equivalence rather than just absence of a significant difference: replacing an analytical method, validating a new process against an established one, comparing two suppliers or batches, or demonstrating bioequivalence of generic drugs. It is also the correct tool when regulators or customers require an explicit equivalence claim.
How to Use It (Step by Step)
Enter the two samples (paired or independent), the equivalence bound Δ and the significance level α (default 0.05). The tool runs the two one-sided tests and outputs the mean difference, the 90% confidence interval and the verdict. If the sample size looks insufficient, use the sample size tool to estimate what is needed before collecting data.
Key Formulas / Example
TOST splits equivalence into two one-sided tests: reject that the difference is ≥ +Δ and reject that it is ≤ −Δ. Equivalence is declared when the (1−2α) = 90% confidence interval for the difference lies entirely inside (−Δ, +Δ). For example, bioequivalence typically uses Δ = ±20%, while analytical method comparability often uses ±10% to ±15%.