﻿ Key concepts: Statistical Power

# Key concepts: Statistical Power

## Definitions of power and beta

Even if the treatment really does affect the outcome, you might not obtain a statistically significant difference in your experiment. Just by chance, your data may yield a P value greater than 0.05 (or whatever value, alpha, you use as your cutoff).

Let's assume we are comparing two means with a t test. Assume that the two means truly differ by a particular amount, and that you perform many experiments with the same sample size. Each experiment will have different values (by chance) so each t test will yield different results. In some experiments, the P value will be less than alpha (usually set to 0.05), so you call the results statistically significant. In other experiments, the P value will be greater than alpha, so you will call the difference not statistically significant.

If there really is a difference (of a specified size) between group means, you won't find a statistically significant difference in every experiment. Power is the fraction of experiments that you expect to yield a "statistically significant" P value. If your experimental design has high power, then there is a high chance that your experiment will find a "statistically significant" result if the treatment really works.

The variable beta is defined to equal 1.0 minus power (or 100% - power%). If there really is a difference between groups, then beta is the probability that an experiment like yours will yield a "not statistically significant" result.

## How much power do I need?

The power is the chance that an experiment will result in a "statistically significant" result given some assumptions. How much power do you need? These guidelines might be useful:

If the power is less than 50% to detect some effect that you think is worth detecting, then the study is really not helpful.

Many investigators choose sample size to obtain a 80% power. This is arbitrary, but commonly used.

Ideally, your choice of acceptable power should depend on the consequence of making a Type II error.