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?
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