I enjoy the rare statistics textbook that can take its subject with a grain of salt:
The practitioner has heard that the [random field] should be ergodic, since “this is what makes statistical inference possible,” but is not sure how to check this fact and proceeds anyway, feeling vaguely guilty of having perhaps overlooked something very important.
—Geostatistics: Modeling Spatial Uncertainty, by Chilès and Delfiner.
It’s a familiar feeling!
As Chilès and Delfiner wryly suggest, we statisticians could often do a better job of writing for beginners or practitioners. We should not just state the assumptions needed by our tools, but also explain how sensitive results are to the assumptions, how to check these assumptions in practice, and what else to try if they’re not met.
For this reason, I really enjoy reading stat textbooks like “What Is a P-Value Anyway?” by Andrew Vickers.
Vickers writes as if he is having a conversation about stats with the reader. He explains the value of the p-value, but also demonstrates its limits and when to even abandon hypothesis testing entirely.
Although I am a believer in knowing the rules before you break the rules, we could do a better job of explaining when the rules become pliable.
Agreed.
I hadn’t heard of Vickers’ book before, but it sounds like a great resource to recommend for beginners. I will look for a copy — thanks for pointing it out!