Power, by definition, is the ability to find a statistically significant difference when the null hypothesis is in fact false, in other words power is your ability to find a difference when a real difference exists. The power of a study is determined by three factors: the sample size, the alpha level, and the effect size.

Most of the time when a researcher is concerned about issues regarding power it is when a study if first being proposed prior to collection of any data. In this situation, the investigator wants to determine what an appropriate sample size would be or justify a proposed sample size. In order to answer this question, the researcher needs to know the other two parts of the equation: alpha level and effect size. Determining an alpha level is usually a pretty easy task, figuring out the effect size is another matter.

Cohen, regarded as the deity of power analysis, (1977, 1988) justifies these levels of effect sizes.

Effect size Index | Small | Medium | Large | |

t-test on Means | d | 0.20 | 0.50 | 0.80 |

t-test on Correlations | r | 0.10 | 0.30 | 0.50 |

F-test ANOVA | f | 0.10 | 0.25 | 0.40 |

F-test regression | f^{2} |
0.02 | 0.15 | 0.35 |

Chi-Square Test | w | 0.10 | 0.30 | 0.50 |

There are a number of web resources related to statistical power analyses

- StatPages.net - This site provides links to a number of online power calculators.
- G-Power - This site provides a downloadable power analysis program that runs under DOS. A Macintosh version is also available. The authors also provide online documentation and a brief tutorial on power analysis.
- Power analysis for ANOVA designs - an interactive site that computes that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design. This particular program can be found elsewhere on the web.
- PASS 2008 - a commercial site that allows you to download a 30 day trial version of their program. This is the software that I use. I don't think it's perfect, but I haven't come across anything that I think is better. Unlike many programs, PASS allows users to compute power for repeated measures designs.
- SPSS makes a program called SamplePower. I have only take a cursory look at it, and was disappointed that it didn't include repeated measures designs. However, one nice feature of the software is that it will output a complete report on your computer screen which you can then cut and paste into another document.