This is certainly a challenging question. As Merriam and Tisdell (2016) write, “how long one needs to observe or how many people need to be interviewed are always difficult questions to answer, since the answers are always dependent on the particular study itself” (p. 246). However, as many qualitative methodologists have suggested, we can pay close attention to the insights being generated through continued data collection and analysis and monitor these for saturation. Our data are said to become "saturated" when we cease to find something new. This, of course, is a tricky concept in social science research as, presumably, there will always be something "new." However, when your analysis seems to no longer generate new codes and/or categories, you could argue that your data are saturated.

There's also effect size analysis or statistical power analysis. Take a look at

G*Power ( http://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html ) as a nice tool for this, as one example.

There's also the Resource Equation. It allows you to estimate what your sample sizes should be when other parameters are unknown. The formula is:

E = (the total number of experimental units) - (the number of treatment groups)

where E should be chosen to be between approximately 10 and 20

You may find the following article useful:

https://www.einstein.yu.edu/uploadedFiles/administration/animal-care-use-committee/Lab%20Animal%20Article%20Re%20Determining%20Sample%20Size.pdf

This is a very important question. It's a question of reaching "saturation": you should start analysing your corpus while collecting your data (observations, interviews, etc.). See what findings emerge (I tend to use thematic analysis). Then you should continue collecting your data while continuing to analyse them. Compare your new data to the exiting themes that you already found. Do it again and again untill "saturation": you can stop if you don't find some new themes, and only new examples to the same themes already found before.

Some basic papers:

Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77-101.

Strauss, A., & Corbin, J. (1994). Grounded theory methodology: An overview. In N.K. Denzin & Y.S. Lincoln (Eds.), Handbook of qualitative research (pp. 273-285). Thousand Oaks, CA: Sage.

Good luck (-:

Todd L'Herrou, Thanks indeed! your suggestion is helpful for quantitative analysis.

Reid Evans, Very helpful suggestions! Thanks indeed!

Sigal Barak-Brandes, Very helpful and practical suggestions and recommended readings! Thanks indeed!

Colleagues, it seems that in qualitative studies data collection/generation and analysis go side-by-side!.

Haji Karim Khan , you are welcome. But don't just think of it in terms of quantitative analysis. Remember, even in qualitative analysis, you are looking to see you have sufficient number to detect a difference or a pattern if one is present. You might not be expressing that in the same language, but some of the same principals apply. "Saturation" is useful only to the extent that you have resources (time / funding / people / access to subjects) to continue. But if you want to gain access to resources, you likely need to be able to estimate how much of those resources you need to detect some difference or pattern...