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In the placebo group value A is x %. You want to know if in the treatment group value is at least x + 10 %. How many people do you have to test? (Without getting into details about study design. :-)

Anyway, you don't think power analysis à la Cohen is useful?

If that is what you care about for some reason, you would set x+10% as the null hypothesis, right? Not sure what that scenario is supposed to have do with power.

Also, this isn't really about what I think, rather I would hope people check the Fisher 1955 ref and go from there.

What I think though is this whole idea of testing vague/vagrant hypotheses (eg the example we used here) is wrong in the worst way possible. The null hypothesis should be deduced from some theory, or at least correspond to what you care about. I have shared this paper on the site many times, I think it should be standard reading in high school: http://www.fisme.science.uu.nl/staff/christianb/downloads/me...

You cited Gigerenzer, Neyman, Pearson as if they opposed the concept of power. Fisher might be in a different boat but he also claimed that smoking doesn't cause lung cancer, so he probably wasn't always right. :-)

Sample size, effect size & power are related concepts in the context of power analysis -- see also Cohen's "A primer on power", which is available on the Internet. The concept of power has nothing to do with "degrees of evidence" or vague hypotheses.

>"You cited Gigerenzer, Neyman, Pearson as if they opposed the concept of power."

Sorry for the miscommunication. The point is that power is a Neyman/Pearson concept, Fisher said it didn't make sense. On the other hand a gradient of evidence is a Fisherian concept, Neyman/Pearson said that didn't make sense.

What people have been teaching as stats is a mismash of the two that makes sense to no one who thinks these types of things through. Gigerenzer reviews this strange phenomenon and offers some entertaining commentary, it is a decent starting point.

>"The concept of power has nothing to do with "degrees of evidence" or vague hypotheses."

Yes it does. To properly assess the probability of incorrectly failing to reject a hypothesis you need to know how likely the data would be under various rival hypotheses. This depends on the precision of the various hypotheses. This is explained by Fisher in my original ref.

You may also want to check out figure 2 of this paper which further illustrates the relationship between a statistical hypothesis and the research hypothesis: http://rhowell.ba.ttu.edu/Meehl1.pdf

> Ten years later, I wrote at greater length along similar lines (Meehl, 1978); but, despite my having received more than 1,000 reprint requests for that article in the first year after its appearance, I cannot discern that it had more impact on research habits in soft psychology than did Morrison and Henkel.

is the author using a null value to inform this perception?

Doesn't sound like it. It sounds like Meehl is giving an order of magnitude estimate. He is saying that it is his impression that both Morrison & Henkel's paper and his own seemed to have little effect on practice.

Clearly he doesn't think it had exactly zero effect, since it affected him!

assuming 1000 reprints somehow implies there should be a discernible 'impact on research habits' seems like an example of what your referenced Figure 2(o) calls 'Estimating parameters from sample'

(o) http://rhowell.ba.ttu.edu/Meehl1.pdf

You have it reversed.

"Estimating parameters from sample" (on the right) would be his observation that there was little discernible effect. Thinking that 1000 reprints of the paper would have a larger effect on practice would more correspond to "theory" (on the left), although that is a pretty vague one.

but where does the 1000 figure come from? it reads arbitrary

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