Tool · Research Methods

Equivalence testing calculator.

A null result is not the same as evidence of no effect. This tool implements two one-sided tests (TOST) to determine whether your result rules out effects large enough to matter — and how large a study you'd need to do so convincingly.

Set your equivalence bound (Δ) to the smallest effect that would be scientifically or substantively meaningful. If your confidence interval falls entirely within ±Δ, equivalence is established.

Step 1 Your result

Enter the observed effect and standard error from your study. Use the same units for both — raw coefficient, percentage points, or Cohen's d.

Observed effect (θ̂)

Standard error (SE)

Step 2 Equivalence bound

The smallest effect of scientific or practical importance — your "smallest effect size of interest" (SESOI). Any effect smaller than ±Δ is too small to matter. Same units as Step 1.

Bound (±Δ)

Cohen's d equivalent: —

Step 3 Planning a study

How many observations would a future study need to confidently declare equivalence? Enter the SD of your outcome to compute required N at θ = 0.

Outcome SD (σ)

Design

Two-sample One-sample / Paired

Step 4 Significance level

α (each one-sided test)

0.10 0.05 0.01

TOST at α = 0.05 uses the 90% CI. Equivalence is established when that interval falls entirely within ±Δ.

Equivalence diagram

Orange dot: observed effect. Thick bar: 90% CI (TOST interval). Thin bar: 95% CI (standard). Green band: equivalence region ±Δ.

Required sample size

Observations needed to declare equivalence at θ = 0 with your current Δ and σ. Computed using the exact TOST power formula.

Method. Two one-sided tests (TOST): Schuirmann, D.J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15(6), 657–680. Power formula and SESOI guidance: Lakens, D. (2017). Equivalence tests: A practical primer for t-tests, correlations, and meta-analyses. Social Psychological and Personality Science, 8(4), 355–362. Equivalence is established when the (1−2α)×100% CI falls entirely within ±Δ — equivalent to both one-sided tests rejecting at significance level α.