The power of any test of statistical significance will be affected by four main parameters:

- the effect size
- the sample size (
*N*) - the alpha significance criterion (
*α*) - statistical power, or the chosen or implied beta (
*β*)

All four parameters are mathematically related. If you know any three of them you can figure out the fourth.

## Why is statistical power important?

If you knew prior to conducting a study that you had, at best, only a 30% chance of getting a statistically significant result, would you proceed with the study? Or would you like to know in advance the minimum sample size required to have a decent chance of detecting the effect you are studying? These are the sorts of questions that power analysis can answer.

## How to calculate statistical power

Say we want to know the prospective power of our study and, by association, the implied probability of making a Type II error. In this type of analysis we would make statistical power the outcome contingent on the other three parameters. This basically means that the probability of getting a statistically significant result will be high when the effect size is large, the *N* is large, and the chosen level of alpha is relatively high (or relaxed).

For example, if I had a sample of *N* = 100 and I expected to find an effect size equivalent to *r* = .30, a quick calculation would reveal that I have an 57% chance of obtaining a statistically significant result using a two-tailed test with alpha set at the conventional level of .05. If I had a sample twice as large, the probability that my results will turn out to be statistically significant would be 86%.

Or let’s say we want to know the minimum sample size required to give us a reasonable chance (.80) of detecting an effect of certain size given a conventional level of alpha (.05). We can look up a power table or plug the numbers into a power calculator to find out.

For example, if I desired an 80% probability of detecting an effect that I expect will be equivalent to *r* = .30 using a two-tailed test with conventional levels of alpha, a quick calculation reveals that I will need an *N* of at least 84. If I decide a one-tailed test is sufficient, reducing my need for power, my minimum sample size falls to 67.

For more, see my book* Statistical Power Trip…*