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Let's say I'm a PhD student in a field, let's call it X, and my research is all based on taking the methods developed in field X and applying them to some other fields, let's call them Y, Z, and W. Let's further suppose that I do not make any contributions to the theory of X, I only apply it to Y, Z, and W. Is X the proper fit for me, or should I really pick my favorite of Y, Z, and W?

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A PhD is meant to extend the knowledge within a field. It's obvious that you can contribute knowledge to Y, Z, and W, at least if you apply the X methods to solve some research questions in these fields. It's less clear what you contribute to X.

You state that you don't contribute to the theory of X, but maybe you extend or generalize the X methods alongside applying them? If you do that, you could get a PhD in X. Otherwise, Y, Z, or W would seem to make more sense.

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If you are making most of your contributions to W, Y, or Z, then it probably makes most sense to get a PhD in those compared to a PhD in X. This is for the reasons given by silvado.

However, if you're already a PhD student in X (your first assumption), you have to consider whether it is worth switching to W, Y, or Z. From what you've written, your department or advisor seems fairly flexible in terms of allowing you to work in different areas. Would switching to W,Y, or Z mean switching advisors or departments? Would it mean that your funding might change (e.g., if your funding is tied to a particular field)? It seems like if your research on W,Y, and Z is viewed positively by your department/advisor, there would have to be a substantial reason to switch away from that department/advisor, since the switch might result in less flexibility.

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If you are applying X to Y, you can easily be in either a department of Y (where you are making a difference) or in a department of X (where you will no doubt be contributing through the adaptation of the techniques to problems in Y). The biggest factor, I think, would be where you can find the best match between yourself and an advisor and departmental culture.

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