Hello Abdi,
The first question is, are you more concerned about: (a) precision of any parameter estimates; or (b) statistical power associated with hypothesis testing resulting from the study?
If (a), then you should consult a text on sampling methods, such as William G. Cochran, Sampling techniques (3rd ed.). Wiley. See this link: https://archive.org/details/Cochran1977SamplingTechniques_201703
If (b), then you'll need to decide: (a) what kind of statistical test makes sense, given the design and nature of score(s) to be collected; (b) how small an effect (which could be a group/treatment difference) you'd like your study to be able to detect, if in fact it exists; and (c) how much risk you are willing to live with of being wrong in your test result, both type I (alpha level) and type II (beta, the arithmetic complement of power). Programs like the freely available G*Power (https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower) can facilitate finding the lower bound sample size which would satisfy your chosen conditions.
Good luck with your work.
You could use PowerUp!, which is a tool for computing the minimum sample size for experimental research, including quasi-experimental studies (Dong & Maynard, 2013). Here is the full citation.
Dong, N., & Maynard, R. (2013). Powerup!: A tool for calculating minimum detectable effect sizes and minimum required sample sizes for experimental and quasi-experimental design studies. Journal of Research on Educational Effectiveness, 6(1), 24–67. https://doi.org/10.1080/19345747.2012.673143
Good luck,
Epitools is also good and easy to use.
https://epitools.ausvet.com.au/samplesize
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