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 | f2 | 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