Editing Power (statistics) (section)

== Applications ==
The main application of statistical power is "power analysis", a calculation of power usually done before an experiment is conducted using data from [[pilot studies]] or a literature review. Power analyses can be used to calculate the minimum [[sample size]] required so that one can be reasonably likely to detect an [[effect size|effect of a given size]] (in other words, producing an acceptable level of power). For example: "How many times do I need to toss a coin to conclude it is rigged by a certain amount?"<ref>{{cite web |url=https://www.statisticsdonewrong.com/power.html |title=Statistical power and underpowered statistics — Statistics Done Wrong |website=www.statisticsdonewrong.com |access-date=30 September 2019}}</ref> If resources and thus sample sizes are fixed, power analyses can also be used to calculate the minimum effect size that is likely to be detected.

Funding agencies, ethics boards and research review panels frequently request that a researcher perform a power analysis. An underpowered study is likely be inconclusive, failing to allow one to choose between hypotheses at the desired significance level, while an overpowered study will spend great expense on being able to report significant effects even if they are tiny and so practically meaningless. If a large number of underpowered studies are done and [[publication bias|statistically significant results published]], published findings are more likely false positives than true results, contributing to a [[replication crisis]]. However, excessive demands for power could be connected to wasted resources and ethical problems, for example the use of a large number of animal test subjects when a smaller number would have been sufficient. It could also induce researchers trying to seek funding to overstate their expected effect sizes, or avoid looking for more subtle interaction effects that cannot be easily detected.<ref>{{cite journal|title=Finding the right power balance: Better study design and collaboration can reduce dependence on statistical power|first1=Shinichi|last1=Nakagawa|year=2024|journal=PLOS Biology|first2=Malgorzata|last2=Lagisz|first3=Yefeng |last3=Yang|first4=Szymon M. |last4=Drobniak|volume=22 |issue=1 |pages=e3002423 |doi=10.1371/journal.pbio.3002423|doi-access=free |pmid=38190355 |pmc=10773938 }}</ref>

Power analysis is primarily a [[frequentist statistics]] tool. In [[Bayesian statistics]], hypothesis testing of the type used in classical power analysis is not done. In the Bayesian framework, one updates his or her prior beliefs using the data obtained in a given study. In principle, a study that would be deemed underpowered from the perspective of hypothesis testing could still be used in such an updating process. However, power remains a useful measure of how much a given experiment size can be expected to refine one's beliefs. A study with low power is unlikely to lead to a large change in beliefs.

In addition, the concept of power is used to make comparisons between different statistical testing procedures: for example, between a [[Parametric statistics|parametric test]] and a [[nonparametric test]] of the same hypothesis. Tests may have the same [[Size (statistics)|size]], and hence the same false positive rates, but different ability to detect true effects. Consideration of their theoretical power proprieties is a key reason for the common use of [[likelihood ratio test]]s.