The classic randomization procedure in Fathom has three collections:
- a “source” collection, from which you sample to make
- a “sample” collection, in which you define a statistic (a measure in Fathom-ese), which you create repeatedly, creating
- a “measures” collection, which now contains the sampling distribution (okay, an approximate sampling distribution) of the statistic you collected.
This is conceptually really difficult; but if you can do this (and understand that the thing you’re making is really the simulation of what it would be like if the effect you’re studying did not exist—the deeply subjunctive philosophy of the null hypothesis, coupled with tollendo tolens…much more on this later), then you can do all of basic statistical inference without ever mentioning the Normal distribution or the t statistic. Not that they’re bad, but they sow confusion, and many students cope by trying to remember recipes and acronyms.
My claim is that if you learn inference through simulation and randomization, you will wind up understanding it better because (a) it’s more immediate and (b) it unifies many statistical procedures into one: simulate the null hypothesis; create the sampling distribution; and compare your situation to that.
Ha. We’ll see. In class, we have just begun to look at these “three-collection” simulations. I made a video demonstrating the mechanics, following the one on one- and two-collection sims described in an earlier post. They are all collected on YouTube, but here is the new one.