Editing Power (statistics) (section)

== Rule of thumb for t-test ==
Lehr's<ref>{{citation|surname1=Robert Lehr|periodical=Statistics in Medicine|title=SixteenS-squared overD-squared: A relation for crude sample size estimates|volume=11|issue=8|at=pp.&nbsp;1099–1102|issn=0277-6715|date=1992|language=German|doi=10.1002/sim.4780110811
|pmid=1496197 }}</ref><ref>{{Cite book|last=van Belle|first=Gerald|url=http://dx.doi.org/10.1002/9780470377963|title=Statistical Rules of Thumb, Second Edition|date=2008-08-18|publisher=John Wiley & Sons, Inc.|isbn=978-0-470-37796-3|series=Wiley Series in Probability and Statistics|location=Hoboken, NJ, USA|doi=10.1002/9780470377963 }}</ref> (rough) [[rule of thumb]] says that the sample size <math>n</math> (for each group) for the common case of a two-sided [[two-sample t-test]] with power 80% (<math>\beta = 0.2</math>) and [[significance level]] <math>\alpha = 0.05</math> should be:
<math display="block">n\approx16\frac{s^2}{d^2},</math>
where <math>s^2</math> is an estimate of the population variance and <math>d=\mu_1-\mu_2</math> the to-be-detected difference in the mean values of both samples. This expression can be rearranged, implying for example that 80% power is obtained when looking for a difference in means that exceeds about 4 times the group-wise [[standard error of the mean]].

For a [[one sample t-test]] 16 is to be replaced with 8. Other values provide an appropriate approximation when the desired power or significance level are different.<ref>Sample Size Estimation in Clinical Research From Randomized Controlled Trials to Observational Studies, 2020, doi: 10.1016/j.chest.2020.03.010, Xiaofeng Wang, PhD; and Xinge Ji, MS [https://journal.chestnet.org/action/showPdf?pii=S0012-3692%2820%2930458-X pdf]</ref>

However, a full power analysis should always be performed to confirm and refine this estimate.