Power and sample size calculation for neuroscience

Dear TalkStats,

I have searched the forum but cannot find the answer I am looking for, if you could help that would be great!

I am recording cells and their action potential frequency in two conditions (group 1 and group 2). (So it is a repeated measures.)

How do I calculate the required sample size in order to detect a significant difference between the conditions? What is the required power?

Is the equation:

\(n = \frac{16 \sigma^2}{\Delta^2}+1\)

where n is the sample size, \(\Delta\) is the expected mean difference and \(\sigma\) is the standard deviation of my sample?

Questions on this:
1. This is "the sample size that gives 80% power at the 0.05 level of significance (two-sided)". What does this mean?
2. \(\Delta\) is something I choose and also depends on the type of data. If they are independent samples, then its \(\Delta=\mu_1-\mu_2\). What if they are paired samples, how do I find the value of \(\Delta\)?
3. \(\sigma\) - this is the standard deviation of my variable under which condition? Group 1? Group 2?

Any help on this would be great!
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