Editing Power (statistics) (section)

==Background==
{{main|Statistical hypothesis test}}
[[Statistical test]]ing uses data from [[Sampling (statistics)|sample]]s to assess, or make [[statistical inference|inferences]] about, a [[statistical population]]. For example, we may measure the yields of samples of two varieties of a crop, and use a two sample test to assess whether the [[mean values]] of this yield differs between varieties.

Under a frequentist hypothesis testing framework, this is done by calculating a test statistic (such as a [[t-statistic]]) for the dataset, which has a known theoretical [[probability distribution]] if there is no difference (the so called null hypothesis). If the actual value calculated on the sample is sufficiently unlikely to arise under the null hypothesis, we say we identified a statistically significant effect.

The threshold for significance can be set small to ensure there is little chance of falsely detecting a non-existent effect. However, failing to identify a significant effect does not imply there was none. If we insist on being careful to avoid false positives, we may create false negatives instead. It may simply be too much to expect that we will be able to find satisfactorily strong evidence of a very subtle difference even if it exists. Statistical power is an attempt to quantify this issue.

In the case of the comparison of the two crop varieties, it enables us to answer questions like:
* Is there a big danger of two very different varieties producing samples that just happen to look indistinguishable by pure chance?
* How much effort do we need to put into this comparison to avoid that danger?
* How different do these varieties need to be before we can expect to notice a difference?