I am taking an online statistics course and I understand how to calculate the necessary sample size for a hypothesis test.
I am using an online calculator like http://www.evanmiller.org/ab-testing/sample-size.html or python like this https://stackoverflow.com/questions/15204070/is-there-a-python-scipy-function-to-determine-parameters-needed-to-obtain-a-ta
From what I understand, this gives me the minimum sample size for each group - control and treatment.
However, if I am designing a test and I have a total sample size of 30,000; how do I calculate how large the control vs. the treatment group should be.
I understand that the treatment group needs to be the minimum sample size I calculated before and I am reading that generally the 50/50 split leads to the highest statistical power, but how can I show this with a calculation. I have been googling it unsuccessfully, so even a link to the correct approach would be greatly appreciated.
This is the closest I found https://janhove.github.io/design/2015/11/02/unequal-sample-sized, but I wasn't able to extract the correct formula.
I found this helpful cross-validated answer Is a large control sample better than a balanced sample size when the treatment group is small? ; but I am still unsure how to calculate the best ratio between control and treatment group if I have a given total sample size. (or how to prove that the 50/50 split has the highest statistical power)
I also found this great answer Treatment and Control group, the sample size, but it applies to a different industry. The hypothesis test I am designing is in the industry of online user behavior psychology.
Thank you very much in advance for any hint in the right direction (even just the correct terminology I can search for).