# 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 superiority trial

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

The mean outcome is compared between two randomised groups. You should power the trial to be able to detect the smallest clinically important difference between these means.

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### Technical note

Calculation based on the formula:

`n = f(α/2, β) × 2 × σ2 / (μ1 − μ2)2`

where `μ1` and `μ2` are the mean outcome in the control and experimental group respectively, `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.

Adjustment for cross-overs based on formula: nadj = n × 10,000 / (100 - c1 - c2)2
where c1 and c2 are the percent cross-over in the control and experimental group respectively.

### References

Pocock SJ. Clinical Trials: A Practical Approach. Wiley; 1983.

Julious SA. Sample sizes for clinical trials with Normal data. Statist. Med. 2004; 23:1921-1986.