From what I have gathered in my first one and two-thirds semesters of graduate school, beginning a graduate program in statistics is a lot different than beginning a graduate program in mathematics. First, all students in their first year of the stats PhD program (at least at Iowa State) get lumped into one big group and take 5 of their first 6 classes together, but we all come from very diverse educational backgrounds. Only about half of us came straight from undergrad (and only some of us majored in statistics), some entered the working world for some time after getting a Bachelor’s and are returning for a Master’s and/or PhD, some have Master’s degrees in Math, some started a PhD or Master’s program elsewhere, and then transferred, etc. So, we all have differing levels of abilities when it comes to statistics.
Because we all come from different backgrounds, the first year of classes is meant to bring everyone to the same level of statistical knowledge. All of this core material is split into two different areas: theory and methods. The theory classes are probably more like a typical mathematics graduate class, because we learn theorems and have to prove things. The methods classes, however, are probably more like a typical engineering graduate class, because we learn formulas and are (nearly) constantly computing standard errors and p-values. (NB: I have never taken a math graduate course nor have I taken an engineering graduate course, so please, correct me in the comments if you think I’ve created them in my head incorrectly.)
Regardless, I usually like to think of the difference between theory and methods in a different way, as part of a larger metaphor for graduate school. I call this my “Wizard of Oz” metaphor. If you haven’t seen the Wizard of Oz, then you don’t know that the main character is a sweet Midwestern girl named Dorothy (played in my metaphor by statistics graduate students) who gets whipped up by a tornado and dropped off with her dog Toto (a stat grad student’s trusty laptop) in a mysterious land called Oz (played in my metaphor by graduate school) and has to find the Wizard of Oz (played by the amount of statistical knowledge needed to be successful and eventually get a degree) to get home (i.e. graduate). This metaphor repeats every semester, until you graduate, when you finally go back to Kansas. So, you work your way through every semester as if you were Dorothy traveling along the yellow brick road, and you pick up the Scarecrow (some heart), the Tin Man (some brains), and the Cowardly Lion (some courage) to help you on your journey, but you are plagued by the flying monkeys (self-doubt, over-thinking, over-stressing, etc.), the minions of the Wicked Witch (impostor syndrome) along the way.
Then you reach the castle, and you are confronted with the floating head: the thing you believe to be the wizard. You’re terrified and confused and see no way to get home. This is the methods part of statistics to me. The floating head is actually a jumble of p-values, sums of squares, F tests, t tests, degrees of freedom, SAS, and R, and you and your dog are shaking, and just spitting out the values the computer gives you, never really sure of what these numbers actually mean.
But then, you’re in theory class, and you’ve put the computer down, and you’re beginning to open up the curtain. You actually see what a likelihood ratio test does; you learn why the sample variance has a 1/(n-1) instead of a 1/n in front of it; you now actually know what they mean by “best unbiased estimator” and how to find it. The best part of theory for me is two-fold: first is that it gives me more solid ground to stand on in methods, and most of us will end up consulting or analyzing data in our careers, so that’s extremely important! The other part is that it’s kind of fun! The problems are like puzzles that you get to play with and finesse, and it is extremely rewarding to figure the puzzle out!
I guess what I’m trying to say is that the methods part of statistics always seems, especially to the outsider, like a big scary floating head that just spits out numbers and tells you whether or not something is significant. I started out as an outsider, not having majored in statistics, and having only ever taking AP Stats in high school, as well as only 2 trimesters of Probability and Statistics in undergrad, so I had this view for most of this year. But, I’m now beginning to discover that the beauty of statistics lies behind the curtain, controlling the floating head with all the numbers. The true beauty of statistics is that everything lies atop a solid foundation that is deep and unshakable.
That is, of course, unless you’re a Bayesian.