# 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 equivalence 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 equivalence trials. It only deals with the case where the true percentage 'success' in both control and experimental groups is assumed to be the same.

The percentage of patients that meet the primary outcome definition (e.g. percentage survived) is compared between two randomised groups. You must define a difference between these percentages, d, within which you will accept that the two treatments being compared are equivalent.

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### Technical note

Calculation based on the formula:

`n = 2 × f(α, β/2) × π × (100 − π) / d2`

where `π` is the true percent 'success' in both the control and experimental treatment groups, and

`f(α, β) = [Φ-1(α) + Φ-1(β)]2`

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

### Reference

Julious SA. Estimating Samples Sizes in Clinical Trials. CRC; 2009.