# Power (sample size) calculators

## Calculate how big your clinical trial needs to be with our easy to use online calculators

There are several different sample size calculators - choose the correct one according to the type of clinical trial you are planning (superiority/equivalence/non-inferiority) and the nature of the primary outcome variable (binary/continuous).

A superiority trial is one where you want to demonstrate that one treatment or intervention is better than another (or better than no treatment/intervention). An equivalence trial is where you want to demonstrate that a new treatment is no better or worse than an existing treatment and non-inferiority is to show that a new treatment is not worse than an existing treatment.

These calculators are based on approximations to the Normal distribution and may not be suitable for small sample sizes. These calculators have been tested for accuracy against published papers.

## Binary outcome non-inferiority trial

A binary outcome has two categories, such as dead/alive, hospitalisation - yes/no, therapeutic success/failure and so on. This calculator is designed for binary outcomes in parallel group non-inferiority trials.

The percentage of patients that meet the primary outcome definition (e.g. percentage survived) is compared between two randomised groups. The null hypothesis is that the percentage for those on the standard treatment is better than the percentage for those on the experimental treatment by an amount d:

H0: πs ≥ πe + d

By rejecting H0, we accept the alternative hypothesis, that the percentage for those on the new treatment is πs − d or better:

H1: πs − d < πe

in other words, that the experimental treatment is better than the standard treatment or only slightly worse (by no more than d). We usually call the new treatment in this situation non-inferior.

You must define the non-inferiority limit (d) so that a difference bigger than this would matter in practice. You should normally assume that the percentage 'success' in both standard and experimental treatment groups is the same, unless you have good reason to believe that one treatment is in fact superior to the other.

%
%
%
You could say:

### Technical note

Calculation based on the formula:

`n = f(α, β) × [πs × (100 − πs) + πe × (100 − πe)] / (πs − πe − d)2`

where `πs` and `πe` are the true percent 'success' in the standard and experimental treatment group respectively, and

`f(α, β) = [Φ-1(α) + Φ-1(β)]2`

`Φ-1` is the cumulative distribution function of a standardised normal deviate.

### Reference

Blackwelder WC. "Proving the Null Hypothesis" in Clinical Trials. Control. Clin. Trials 1982; 3:345-353.