# Power of a statistical test

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I'm new here, so first of all Hi :)

I did some reading & searching but didn't find an answer direct enough to the issue that bothers me: there's something regarding the power of a statistical test, 1 minus beta, that doesn't add up for me. I'd appreciate any assistance, and if it's possible please provide reliable references.

1. It is known that one way to achieve greater power is by using a larger sample size, N.
2. However, an N too large will result in a higher probability to reject the null hypothesis even when there is no effect at all, which is obviously a bad thing.
3. Since a large N also increases the power, one may conclude that a power too large will also be considered as a bad thing.

So, what I'd like to know is whether there is some "recommended upper bound/limit" for the power, one that you shouldn't pass in order to reduce the chances of rejecting the null hypothesis even when there is no effect. Something like the conventional 0.05 for the value of the alpha (in some fields).

Thanks

"Although there are no formal standards for power, most researchers who assess the power of their tests use 0.80 as a standard for adequacy. "
wikipedia
wikia, The Psychology Wiki

"It is customary to set power at greater than or equal to 0.80, although some experts advocate 0.90 in clinical trials (Eng, 2003). As this is not a clinical trial, then it is appropriate to set power at 0.80."
Research considerations: power analysis and effect size (MedSurg Nursing, Feb, 2008, by Lynne M. Connelly)

"Power=0.80 is common, but one could also choose Power=.95 or.90." How to Calculate Sample Size & Power Analysis Information for Dissertation Students & Researchers (ResearchConsultation.com in memory of Dr. Jeffrey W. Braunstein)

"Often times, a power greater than 0.80 is deemed acceptable."
EPA Endocrine Disruptor Screening Program (EDSP) statistical documentation

"Cohen (1988) suggests that the conventional Type II error rate should be 0.20, which would set power conventionally at 0.80. A materially smaller power would result in an unacceptable risk of Type II error, while a significantly larger value would probably require a larger sample size than is generally practical (Cohen 1992). Setting [beta] at 0.20 is consistent with the prevailing view that Type I error is more serious. Since [alpha] is conventionally set at 0.05, Cohen suggested setting [beta] at four times that value (Cohen 1988, 1992)."
An Analysis of Statistical Power in Behavioral Accounting Research (Behavioral Research in Accounting, 01-JAN-01, by Borkowski, Susan C. ; Welsh, Mary Jeanne ; Zhang, Qinke Michael)

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2. However, an N too large will result in a higher probability to reject the null hypothesis even when there is no effect at all, which is obviously a bad thing.
That's a type I error and it is controlled by alpha. For a fixed alpha, increasing N increases the power of the test without increasing the chance of type I error, so what you mention here is not a problem.

Well I found that the best way to do it is through practice, similar to doing your http://theory-test-practice.co.uk" [Broken]

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The definition that I've seen for the power of a statistical test defines it as a function, not as a single number. So when the number .80 is mentioned for the power of a test, what is the definition of "power" in that context? What calculation produces this number? Is some particular "effect size" assumed?

Yes, Stephen Tashi, you are right. Power is best described by a "power curve" rather than by a single number. Those who say the power is 80%, for example, have a particular effect size in mind (and reallly ought to say what it is). The user might well be interested in different effect sizes.