# Why is expected group difference necessary in power analysis?

Why do we need the expected group statistic (i.e. mean) difference when calculating the sample size?

The point of power analysis is to find the right sample size so that I can detect a difference. If I just picked a random but reasonable sample size and calculated the difference in means and let that be the expected difference in means to do power-analysis, wouldn't that number be wrong?

Is the expected difference that one uses to calculate the sample size needed to achieve a particular power the true population level difference (n=N) or the sample difference in means? (n

• Are you suggesting that the determination of sample size requires no knowledge of the applied subject matter and/or the objectives and that just someone with the right software is all that's necessary?
– JimB
Commented Oct 21, 2019 at 20:04
• No, I was just thinking maybe it was part of a optimization scheme that if one started with a small but easy sample size and then obtained the difference in means and then iteratively used the power analysis formulas, they would converge at the right sample size. I thought math people should be able to derive the truth independently of other fields.
– user263327
Commented Oct 21, 2019 at 20:21
• It requires subject matter knowledge which is NOT an intrinsic feature of a set of numbers. In fact a single set of data could be used by different folks with different objectives or the same folks with different objectives at different times.
– JimB
Commented Oct 21, 2019 at 20:25

## 1 Answer

Is the expected difference that one uses to calculate the sample size needed to achieve a particular power the true population level difference (n=N) or the sample difference in means? (n)

It's the population difference.

Think of a statistical hypothesis test as an attempt to find something - that something being evidence against the null hypothesis.

The sample size is how hard you are looking. The bigger the sample size, the harder you look (or longer you spend looking).

The effect size (the expected group statistic) is the size of the thing you are looking for. If I hid a football inside your house, it's going to be easier to find than a tennis ball, which will be easier than a golf ball, which will be easier than a marble.

Picking an appropriate effect size is at least partially arbitrary, but you should at least try to determine an effect size that would be interesting or useful. Picking it by choosing an arbitrary value means that you might as well just select an arbitrary value for the sample size.