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I am going to conduct a study in which I'm going to compare the mathematical performance (means) of indigenous students to non-indigenous students in public-urban, private-urban, public-rural and private-rural schools. My problem is getting the required sample size for each variable (each variable has an unequal population). I've seen a similar study to mine in which the sample sizes for each variable is equal (n=20 to be specific, except for the indigenous students where n=18) and I'm not able to find out why 20 was chosen, as it is not stated. Is it necessary to have an equal sample size for each independent variable? Would n=30 samples for each variable be enough?

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    $\begingroup$ It sounds like you might be confusing the term "variable" with "group", "level", or "value". You have one independent variable, namely school type, which has four levels, namely public-urban, private-urban, public-rural, and private-rural. Your concern is that you have different numbers of subjects of each school type. Is that correct? $\endgroup$ – Kodiologist Sep 28 '17 at 14:24
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    $\begingroup$ Where does the "5" in the title come from? It sounds like you have 2 variables with 2 levels each--ie, 4 levels total. $\endgroup$ – gung Sep 28 '17 at 14:43
  • $\begingroup$ Yes sir @kodiologist. I'm sorry as I'm an absolute newbie. The total number of the indigenous students is 23 while in the other school types are almost 200 to 2000. We plan to use all 23 IPs as subjects. Do I need to have equal sizes for other school types? I plan to get 30 samples to other school types to make it almost equal to those IPs. Is that reasonable? Is there an author that says that it must be equal? $\endgroup$ – sammyyy Sep 29 '17 at 11:19
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It might depend on the statistical test you are using, but in general, slight differences between group sizes is not a big problem. You see them all the time in psychological or social science studies. The calculation of test-statistics differ, but assuming you are using a statistics program, the computer will be able to deal with it.

To your second question:

There is no way for me to say exactly how big your sample size should be, it depends among others on teh distribution of your population, the test you are using and the statistical power you are aiming for. If you know all needed variables, you can for example use online calculators to get an answer.

If you don't care about a statistical exact estimate and/or don't have the needed information (which is quite common), you maybe just want to know what sample size would be needed for your study to be comparable with those of your peers. In that case, it's best to do what you already did and look for similar experiments. From my own experience working with researchers doing quite similar studies to the one you are describing, n=30 per group seems to be quite common.

Ps: Take note of the comments below your question, regarding the terminology

Edited to make things clearer, based on whuber's commentary

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    $\begingroup$ There is no credible statistical basis for telling people that n=30 will be "safe." Statistical theory informs us that the sample size should depend on the nature and objectives of the study as well as the amount of variation that will be modeled with random variables. For formal hypothesis tests, it must at the very least depend on the needed test size (that is, confidence), power, and standardized effect size. $\endgroup$ – whuber Sep 28 '17 at 15:27
  • $\begingroup$ Of course you are right, that there is no statistical basis to say someone he is safe. But I don't think I did that. I hope he understands my commentary as "30 being safe, regarding to common practices of his research community" $\endgroup$ – Bobipuegi Sep 28 '17 at 15:31
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    $\begingroup$ That is precisely what I am objecting to: I think you are misleading the OP by twice suggesting 30 should work when you have no basis to support that claim other than a supposition about what his research community is and what they believe in. I want to make it very clear to any readers that these assumptions neither have any foundation in the evidence before us, nor are they justified statistically. $\endgroup$ – whuber Sep 28 '17 at 15:37
  • $\begingroup$ That is a bit like objecting the common 5% threshold for statistical significance just because there is no statistical reason for it.... the op seems to be asking for practical advice and I am giving it based on common samples sizes I observed in similar studies as the one he is describing. But yeah, I will edit my answer if it's not clear $\endgroup$ – Bobipuegi Sep 28 '17 at 15:44
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    $\begingroup$ To me this sounds like: "Someone told that 30 is sufficient to use normal approximations. Thus, 30 is fine for everything else, e.g. sample sizes or my age." Sample size obvisously depends on power considerations, effect sizes to be detected, the design etc. $\endgroup$ – Michael M Sep 29 '17 at 7:35

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