I'm considering to conduct a comparative case study (following Eisenhardt 1989) and need to control for industry effects (as to be able to generalize beyond a single industry). So, I'll select about 8-10 cases (companies) from x-number of industries: but how many industries do I need? Eisenhardt refers to a study by Pettigrew and argues that four to five different markets suffices to control for environmental variation. But what's the rationale? Why not 3 markets (less efforts required to describe outer context) or 6 markets (enhanced generalizability)?
Without actually looking at Pettigrew, my guess is that he/she knew (guessed?) something about the potential range of variation and ran some test calculations to see that four or five would be sufficient to express it. In other words, that would be the appropriate approach. It would be appropriate, and relatively easy, to repeat such a process for your specific study to understand how various hypothetical results would influence your conclusions, or potentially leave you unable to draw a clear conclusion. With modern computation tools, this is reusable effort because you can later simply replace your hypothetical values with your actual data. You will just be setting up the analysis tools earlier in the process, but it is almost all work you will need to do eventually.
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