Computationally intensive methods warrant reconsideration of pedagogy in statistics

Computationally intensive methods of statistical inference do not fit the current canon of pedagogy in statistics. To accommodate these methods and the logic underlying them, I propose seven pedagogical principles: (1) Define inferential statistics as techniques for reckoning with chance. (2) Distinguish three types of research: sample surveys, in which statistics affords generalization from the cases studied; experiments, in which statistics detects systematic differences among the batches of data obtained in the several conditions; and correlational studies, in which statistics detects systematic associations between variables. (3) Teach random-sampling theory in the context of sample surveys, augmenting the conventional treatment with bootstrapping. Regarding experimentation, (4) note that random assignment fosters internal but not external validity, (5) explain the general logic for testing a null model, and (6) teach randomization tests as well ast,F, and χ². (7) Regarding correlational studies, acknowledge the problems of applying inferential statistics in the absence of deliberately introduced randomness.