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The basics of regression rely on, let's see, understanding the normal and t distributions (each of which is described in papers far beyond an undergraduate stat

The basics of regression rely on, let's see, understanding the normal and t distributions (each of which is described in papers far beyond an undergraduate statistics degree). Every stats program I know of teaches each of these concepts quite rigorously, and I can't imagine a stats program without them. I agree with your broader claim that to actually improve on existing techniques requires graduate education, but understanding existing techniques is well within the reach of most college students.

notafraudster 7y ago
I missed your reply contemporaneously. Of course undergrad stats programs introduce the normal/t distributions; but often in either a matter-of-fact way (the normal PDF is ...) or in a sort of intuitive way (think of t as a normal distribution, but punishing ourselves for the additional uncertainty of needing to estimate...), but rarely in a beginning to end way. I'm not critiquing this as pedagogy, although I think a lot of students get bombarded with poorly motivated distributions that aren't well connected to a broader problem class. But that being said, I think we teach students how to characterize distributions rather than how to prove or derive them from first principles. I don't think most undergraduate stats programs deal with the dart-board derivation of the normal distribution, or read Gosset's original t paper, and moment generating functions are rarely discussed. Here's an example of a fairly elementary question I don't think a stats undergrad would learn without self-guided study: You run a linear regression. One or more of your outcomes or regressors has a skewed distribution. Standard errors are often motivated under CLT claims of normal convergence. Suppose convergence is poor in your finite-sample. What are the consequences of this for your estimates and standard errors in terms of nominal coverage, bias, and consistency? It's possible an undergraduate class would cover Gauss-Markov and mention violations of normality, and maybe get into mitigations via transforming parameters... but to actually deep dive into the skills necessary to self-verify the kinds of consequences observed in the data you have? Nah. I mention this because it's a question that first came up to me in a graduate regression class and I was not well prepared for it, and now when I teach statistics undergrads I don't think they would be. Never mind any kind of analytic result, the notion of really digging in and running the kind of MC simulation required to get empirical results is typically a fourth year undergraduate topic.

notafraudster 7y ago

I missed your reply contemporaneously. Of course undergrad stats programs introduce the normal/t distributions; but often in either a matter-of-fact way (the normal PDF is ...) or in a sort of intuitive way (think of t as a normal distribution, but punishing ourselves for the additional uncertainty of needing to estimate...), but rarely in a beginning to end way. I'm not critiquing this as pedagogy, although I think a lot of students get bombarded with poorly motivated distributions that aren't well connected to a broader problem class. But that being said, I think we teach students how to characterize distributions rather than how to prove or derive them from first principles. I don't think most undergraduate stats programs deal with the dart-board derivation of the normal distribution, or read Gosset's original t paper, and moment generating functions are rarely discussed. Here's an example of a fairly elementary question I don't think a stats undergrad would learn without self-guided study: You run a linear regression. One or more of your outcomes or regressors has a skewed distribution. Standard errors are often motivated under CLT claims of normal convergence. Suppose convergence is poor in your finite-sample. What are the consequences of this for your estimates and standard errors in terms of nominal coverage, bias, and consistency? It's possible an undergraduate class would cover Gauss-Markov and mention violations of normality, and maybe get into mitigations via transforming parameters... but to actually deep dive into the skills necessary to self-verify the kinds of consequences observed in the data you have? Nah. I mention this because it's a question that first came up to me in a graduate regression class and I was not well prepared for it, and now when I teach statistics undergrads I don't think they would be. Never mind any kind of analytic result, the notion of really digging in and running the kind of MC simulation required to get empirical results is typically a fourth year undergraduate topic.