Editing Power (statistics) (section)

==Factors influencing power==
[[File:Sample Sizes Effect on Power.png|thumb|An example of the relationship between sample size and power levels. Higher power requires larger sample sizes]]
Statistical power may depend on a number of factors. Some factors may be particular to a specific testing situation, but in normal use, power depends on the following three aspects that can be potentially controlled by the practitioner:

* the test itself and the [[statistical significance]] criterion used
* the magnitude of the effect of interest
* the [[sample size|size]] and [[Statistical dispersion|variability]] of the sample used to detect the effect

For a given test, the '''significance criterion''' determines the desired degree of rigor, specifying how unlikely it is for the null hypothesis of no effect to be rejected if it is in fact true. The most commonly used threshold is a probability of rejection of 0.05, though smaller values like 0.01 or 0.001 are sometimes used. This threshold then implies that the observation must be at least that unlikely (perhaps by suggesting a sufficiently large estimate of difference) to be considered strong enough evidence against the null. Picking a smaller value to tighten the threshold, so as to reduce the chance of a false positive, would also reduce power, increase the chance of a false negative. Some statistical tests will [[uniformly most powerful test|inherently produce better power]], albeit often at the cost of requiring stronger assumptions.

The '''magnitude of the effect''' of interest defines what is being looked for by the test. It can be the expected [[effect size]] if it exists, as a scientific [[hypothesis]] that the researcher has arrived at and wishes to test. Alternatively, in a more practical context it could be determined by the size the effect must be to be useful, for example that which is required to be [[clinically significant]]. An effect size can be a direct value of the quantity of interest (for example, a difference in mean of a particular size), or it can be a standardized measure that also accounts for the variability in the population (such as a difference in means expressed as a multiple of the standard deviation). If the researcher is looking for a larger effect, then it should be easier to find with a given experimental or analytic setup, and so power is higher.

The nature of the '''sample''' underlies the information being used in the test. This will usually involve the sample size, and the sample variability, if that is not implicit in the definition of the effect size. More broadly, the precision with which the data are measured can also be an important factor (such as the [[Reliability (statistics)|statistical reliability]]), as well as the [[design of experiments|design]] of an experiment or observational study. Ultimately, these factors lead to an expected amount of [[sampling error]]. A smaller sampling error could be obtained by larger sample sizes from a less variability population, from more accurate measurements, or from more efficient experimental designs (for example, with the appropriate use of [[Blocking (statistics)|blocking]]), and such smaller errors would lead to improved power, albeit usually at a cost in resources. How increased sample size translates to higher power is a measure of the [[efficiency (statistics)|efficiency]] of the test&nbsp;– for example, the sample size required for a given power.<ref name=Everitt2002>{{cite book |title=The Cambridge Dictionary of Statistics |last=Everitt |first=Brian S. |year=2002 |publisher=Cambridge University Press |isbn=0-521-81099-X |page=321}}</ref>