I have a question about how one can interpret the inputs and result of a power analysis on paired data.
Would it be incorrect to call it: one possible method of calculating the minimum required sample size to detect a change (%) in a population mean, from one point in time to another (?). As in, what sample size would I need to detect a 30% change in the population mean in a future survey?
Using the Cohen's D effect size formula as an example for my power analysis; if "M" is the sample mean and "σ" is the sample standard deviation (together they = an estimate of the current population mean), can "µ" be considered the future population mean (the 30% change in the current mean, without sample error)? This is for a "before and after" repeated measures design (i.e "paired" data).
Would it be wrong to then conclude:
# Effect size, Cohen's D: d=(M-μ)/σ
# M=1, σ=0.5, µ=0.7
# 0.6 = (1-0.7)/0.5
# ...or -0.6 = (1-1.3)/0.5 (for two-sided test)
> pwr.t.test(d = 0.6,
+ power = 0.8000,
+ n = NULL,
+ type = "paired",
+ alternative = "two.sided",
+ sig.level = 0.05)
Paired t test power calculation
n = 23.79452
d = 0.6
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: n is number of *pairs*
Conclusion: A sample size of 24 would be sufficient to detect a +/-30% change (2-tailed test) from the current population mean in future surveys, with 80% probability and alpha=0.05 .
Is it incorrect to define a power analysis on paired data this way?
I'm guessing this is incorrect wording. The power analysis isn't for detecting changes from one point in time to another, but for testing the accuracy of an estimate of a population parameter via taking a sample, no?