It's usually straightforward to do a
Power Analysis to compute the
minimum sample size, especially in R which is my preferred statistical computing environment.
However, I am being asked to conduct a Power Analysis that's a little different than anything I've done or which I can find reference to online. I'm wondering if what I'm being asked for is even possible/valid.
The project basically has two
unequal groups of states and the hypothesis is that these two groups are significantly different in terms of an outcome variable (which is the duration of phone calls to customers). The "control" group consists of 40 states and produced about 2,500 observations. The "test" group has about 10 states and 500 observations.
Initially, I found group
pooled standard deviation, which I used to calculate an
Effect Size. Then I used a package called
R and found that I needed a minimum sample size of about 135 observations per group, given .05 significance and .8 power.
However, they rejected my answer because they want one group to be much bigger than the other like it is now, and they are expecting either two different minimum numbers of observations per group or a minimum % of the population in terms of numbers of states or observations that have to go into their "test" group.
I see Power Analyses for two sample t-tests (i.e. the R function
pwr.t2n.test), but I'd have to specify at least one of the sample sizes whereas they want me to tell them the minimal sample size for both groups (either as numbers or percentages) and this function doesn't reflect the differences in standard deviations for the two groups.
Is this possible or do I just tell them that's not how it works (i.e. the best I can do is tell them that given one of the sample sizes and a pooled standard deviation the second group has to be at least a certain size)?