I’ve been talking to a lot of statistics instructors about their introductory courses, particularly which topics they choose to include in the course. Pretty consistently, instructors can get to tests on two groups, for instance the two-sample t-test or the test of proportions in two groups. Some get to regression, fewer to ANOVA. Probably more instructors cover the “unequal variance” t-test than cover ANOVA. This is, I’ll argue, a misplaced priority. I’ll go further, to challenge the inclusion of any detail about the two-sample t-test or the test of two proportions. Leaving these out of your course can give you room to introduce a more fundamental and general method: regression.
I. Equal variance is silly a. pedagogically it’s a black box a. doesn’t increase power a. in practice, it’s not any more “correct” than the equal variance test. Both of them provide no place to consider covariates. d. The 2nd leading digit in a p-value, e.g. the 4 in p < 0.01458, is a fantasy creation, of no relevance in the actual world. (The remaining digits, e.g. 58, are just smoke and mirrors that wrongly mislead the reader into thinking a p-value is a precise calculation. Even the value of the first leading digit is hardly telling.) d. Including the unequal-variance t-test is like polishing your rear-view mirror in your car. You’ll get a better view in the mirror, but you’ll also be distracted from the road ahead and much more likely to get in an accident.
t and proportions are special case of regression
using Little Apps
covariates are not a paradox