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Re: Profile Evaluation: PhD/Master's Degree
Your two Michigan advisors are much better placed to answer those questions than we are. Their recommendation letters carry enormous weight. Yes, the classes, grades, etc. matter too. While your advisers can't guarantee anything, they are the ones with experience getting people like you into graduate school. I'm not saying that you should do what they say without questioning it, but I'd put a lot of weight on their advice and no weight on definitive statements by people on an anonymous message board.
Here are some questions you can ask your advisers to help guide your decision process: what range of PhD programs they would expect you can get into this fall? Kind of think of this as a floor, ceiling, and best guesses at where you would get in. In their experience, how much would your admissions chances change if you did the MA first? Does this depend on what field you want to go into? How much is the benefit of the MA is in getting into a better program versus doing well in a program? Any classes you could take this summer, such as real analysis or a class in mathematical statistics?
Also, you can certainly apply to both MA and PhD programs and see what you get.