MS in Pure Maths to PhD in Statistics I currently am working on a MS in pure maths, but am interested in options for pursuing a PhD in a more applied field. Specifically I am interested in going on to graduate work in something like statistics. How hard would it be for me to go straight from an MS in pure math with only a very few courses in statistics to a PhD program in statistics?

I have some experience in probability with my research (random walks on finite groups). But outside of that, I am pretty inexperienced with applied math.
I think the main hurdle will not be the knowledge about statistics you'll bring. (As a trained mathematician you should be able to pick up new math quick enough.) The main hurdle could be to embrace a new kind of doing science and research.

In more applied math people sometimes think differently about problems than in pure math. Roughly speaking, one is much more open to adapt assumptions and requirements for some problems such that they become more simple theoretically, more suited computationally or otherwise more convenient. Since one usually works with things that are related to the real world and hence, somehow uncertain and noisy, it is often not useful to stick to every assumption but use some freedom in modeling. I heard the saying "All models are wrong." Well, true but this should not make you hesitate to work with models.

I've seen people changing from pure math to applied math who never could adopt to these principles (but also cases where there were no problems). If you think that you won't have problems with issues like I described, then things will turn out fine, I think.