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Suppose, I have a correlation coefficient of 0.6234 between Variables A and B, on a sample size of 20. My alpha threshold is 0.05. I want to do a power analysis on this result.

I found a calculator but it is asking for "Correlation p H1".

Does this refer to the correlation coefficient "r" (0.6234 as above) or the p value of r (which I have calculated as 0.00330, two tailed).

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It is probably asking you to indicate what you think the true correlation is. But let me ask you this: What is the purpose of this power calculation? –  Wolfgang Sep 10 '11 at 17:10
    
@Wolfgang. I am doing a post-hoc power analysis with this calculator. It is called GPower (version 3.1). –  Adhesh Josh Sep 11 '11 at 3:07
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That's what I suspected. What do you hope to find out with this post-hoc power analysis? And more importantly, what value did you use for $\rho$ under $H_1$ for this power analysis? –  Wolfgang Sep 11 '11 at 13:31
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1 Answer

up vote 6 down vote accepted

For power/sample size analysis, you have to fix either one or the other: You're generally interested in determining the sample size to achieve a given power, or you want to know the power of a test given a certain sample size. In both cases, the type I risk ($\alpha$) is also fixed at a given value (typically, 5%), and we can accommodate group imbalance, dropouts, etc.

Given the way statistical test of null hypothesis are framed (definition of a null hypothesis, $H_0$, and the alternative, $H_1$, yielding the acceptance and rejection regions), the calculator is asking you the expected correlation, $\rho$, under the alternative.

Now, be aware that computing power "after the fact" (so-called post-hoc power analysis) is clearly not a definitive solution if you are working with a planned design.

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(+1) Related to what chl says, the value of $\rho$ they request allows one to interpret the output of the power analysis as "If the true correlation is $\rho$ and the sample size is $n$, then we you have a power of ______ using this hypothesis test". It's the measure of effect size in this hypothesis test. Similar to how the mean difference and the standard deviations produce a measure of effect tests in two-sample $t$-tests. Also, your point about being cautious with post-hoc power analysis is important - lots of problems with that. –  Macro Sep 10 '11 at 20:31
    
@chi Thanks does this mean I use 0.6234. –  Adhesh Josh Sep 11 '11 at 3:05
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If you want to test against a population correlation known with certainty (e.g., $\rho=0.80$), then put this one in the box. (As @Macro said, it amounts to postulate that the (observed) effect size in the sample is equal to the effect size in the population.) If you leave it blank, it is assumed that your test is against a zero correlation. Using this calculator, I obtained 33.61% and 86.85%, respectively (two sided). If you haven't specified an alternative hypothesis, before seeing the data, then it is safe to use the latter. –  chl Sep 11 '11 at 9:30
    
@chi. Thanks! This is exactly what I was after. –  Adhesh Josh Sep 12 '11 at 12:07
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