I'm working on transitioning our undergrad introductory statistics course to one that
involves simulation-based ideas alongside parametric, theory-based models. At the risk of
sounding naïve, I would like your opinion on the following: With the advent of computers
that make simulation-based p-value calculations fast and easy, and for those of you that
teach this idea in parallel with theory-based p-values, how do you explain the motivation
for even using theory-based p-values to your students?
In other words, parametric models require assumptions that may not be met. If we can use
simulation to obtain a reliable p-value without worrying about these assumptions, then why
bother with a t-test (e.g.) for a p-value at all? It seems like a historical argument
("It's been done and probably will continue to be done for quite some time")
is one, but... I'm left feeling like I have to tell my students to conduct these
theory-based tests "just because."
Thanks for your thoughts.
Megan