# 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.

## Continuous outcome non-inferiority trial

This calculator is designed for continuous outcomes (such as walking distance, blood pressure, white blood cell count) in parallel group non-inferiority trials.

The mean outcome is compared between the experimental and standard treatment groups.

The null hypothesis is that the experimental treatment is inferior to the standard treatment. We write this as the mean in the standard treatment group (μs) is better than the mean in the experimental treatment group (μe) by an amount d:

H0: μs ≥ μe + d

which can be re-written

H0: μe − μs ≤ -d

The alternative hypothesis is that the experimental treatment is non-inferior to the standard treatment:

H1: μe − μs > -d

You must choose the non-inferiority limit, d, to be the largest difference that is clinically acceptable, so that a difference bigger than this would matter in practice. This difference should also not be greater than the smallest effect size that the standard treatment would be reliably expected to have compared with control.

You could say:

### Technical note

Calculation based on the formula:

`n = f(α, β) × 2 × σ2 / d2`

where `σ` is the standard deviation, 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. Sample sizes for clinical trials with Normal data. Statist. Med. 2004; 23:1921-1986.