I need to conduct a a priori sample size determinations for t-test with unequal means, but I don't know the sizes of the groups nor the ratio of both groups... Can I do a sample size determination without knowing these things? I based myself on the sample size I got from a normal t-test sample size determination to know the second sample size... Is this correct? Or is there another way?
Hello Indra,
Yes, you may do an a priori power analysis to determine what would be a suitable sample size for your study. You'll need to specify: (a) minimum desired power; (b) intended Type I error risk (alpha level); (c) directional vs. non-directional test; and (d) the minimum magnitude of difference that you consider to be non-ignorable, or noteworthy, and that you'd like your study to be capable of detecting, should it exist in the population (effect size: ES). Often, coming up with a defensible ES is the hardest part of this process.
You could: (a) use a panel of domain experts to arrive at a consensus ES; (b) review of similar, existing studies to see what sorts of observed ES values occur; (c) run a small pilot study to get an impression of what sort of effect might occur; or (d) pick a value out of thin air (not recommended!).
Here's a link that might get you started, with respect to the widely used program, g*power: https://www.psychologie.hhu.de/fileadmin/redaktion/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/gpower/GPowerManual.pdf
Good luck with your work.
Hi,
This article can give you a better insight into the apriori sample size calc.
http://canjsurg.ca/wp-content/uploads/56-3-207.pdf
I've read the question differently than David Morse and Bhogaraju Anand , so I have probably misunderstood something, but let me see if I understand this correctly. Is it that you have two groups and their respective populations are of very different sizes, say around 1000 and 1000000 (but you really don't know them with any precision), and you recognize that you likely need a smaller sample from the smaller group because of finite population corrections (e.g., Kalton, 2021, Intro to Survey Sampling)? If so, I don't know of power software that takes this into account, but there might be some. Might be easier to use simulation. Just adjust the standard error (with the finite correction) for a range of possible population sizes and this will give you a range for your guidance on sample size (which of course is all the power analysis is doing).
So the way I read the question the answer is NO, you need at least to have some guesses about the population sizes but it depends on how small the populations are. For most research even with finite populations they are large enough not to worry about the finite population correction AND for a lot of research you are making your inference about an infinite super-population anyway. But given your question, at least the way I have read it, you are worried about this so it may be an issue.
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