I sorta disagree with the order in which things are taught. I don't particularly like that likelihood is taught before regression, when there's a really easy (a

I sorta disagree with the order in which things are taught. I don't particularly like that likelihood is taught before regression, when there's a really easy (and intuitive!) reason to learn it. I like the way that I was taught when I took biostats in graduate school. We fist covered t-test and ANOVA as a way to intuitively compare differences among groups. From that, we then generalized our approach, and learned that linear regression is a generalized form, which happens to have a closed form solution. From linear regression, we then learned about logistic regression and odds ratios, and about the log-link formulation. But drats! We don't have a closed form solution to calculating our Betas. But we can estimate a good set of them using likelihood! Statistics is often fraught with nuance, and I think the more we can convince to do more thinking about what we're trying to accomplish with a statistical analysis and how to prove it should have more emphasis over just "lets just make an alphabet soup out of our slide decks!". That's not to say you shouldn't have mathematical rigor, but mathematical rigor without an intuitive understanding is potentially giving the impression that more complex analysis == better analysis.