Another thought I had is to replace statistics requirements with a rigorous (but not measure-theoretic) probability class or, preferably a semester of both. My

Another thought I had is to replace statistics requirements with a rigorous (but not measure-theoretic) probability class or, preferably a semester of both. My engineering program required probability, not statistics, so I never took a formal stats class. However, my probability class was excellent. If I need to figure out a statistical method now, I might not know what method or <letter>-test to use, but I google a description of the problem and am greeted with stats websites and papers that solve various cases of the problem that are totally understandable using undergrad probability. The intuition for doing so is that, as this article argues, the hard part is in determining the right probability model describing your experiment. Once you have a good model, running the statistical test is easy (whether there’s a tractable algorithm is another question, but if there’s no tractable way to estimate your parameters, I’d argue as a practitioner a model being too difficult computationally is a good heuristic for your experiment not being robust)