I remember two classes in my college years that left me with a bitter taste for the rest of my life: genetics and statistics. Why?
Because the course content was to be memorized. For example, in genetics I was supposed to memorize the Chargaff rules, which
state that DNA contains equal amounts of adenine and thymine and equal amounts of guanine and cytosine (A = T and G = C). Why
memorize that rule if Chargaff himself did not know what it meant? Thanks to the deductive work of Watson and Crick, we now know
that DNA consists of hydrogen bonded A T pairs and G C pairs. So, why ask what the Chargaff rules are? Rather, we should ask what
Chargaff discovered, that was a critical piece in Watson and Crick's proposal for the structure of DNA.
The statistics class was even worse. For example, I memorized that if the sample is small, we use the t-test. But why?
No idea, just follow the rules.
Memorization becomes natural and easier to do once you understand your subject.
These chapters treat statistics as a branch of mathematics. Math is not easy.
You are not helping if you tell your students that math is easy. Math is hard and often not intuitive.
Seriously, can you visualize a 5-D object? Statistics is notoriously unintuitive.
Innocent people have been imprisoned because of faulty “statistical” arguments made by the prosecution
that the jury could not see through. So, to understand statistics you've got to understand the derivation
of its formulas, a process that is neither easy nor obvious.
My goal here is to understand the derivations. I will
often include interactive figures to help with understanding.