# Teaching stats for statistical thinking

Published: September 10, 2020   |   Read time:

In the Fall 2020 semester, I am going to be the TA for my departments biostatistics module. It’s a graduate level course aimed at incoming grad students to get them familiar with some of the stats they will need throughout their graduate career. We will be touching on all the standard stuff, like hypothesis testing, general linear models, and experimental design.

But from working in biostats for the last few years, I’ve found that my usual conversations with others about stats is more often around the idea of statistical thinking. Less of “is the standard deviation $$\frac{1}{n}$$ or $$\frac{1}{n-1}$$?” and more of “why does it matter if I have equal numbers of control cases and test cases?”. Less of “what is the law of total variance?” and more of “what is the difference between a random variable and the value that I have?”. Less of “what does it mean if my $$p$$-value is 0.06?” and more of “what does uncertainty look like in this situation?”.

Like much of modern-day teaching in schools, all the fun and discovery and thinking has been taken out of it1. Statistics is a subject with deep connections to many areas of math, many of which are simply related to the question “how do I become less uncertain about the things I see?”. That central question is why it is so fundamental to scientific discovery.

I couldn’t care less about the specific formula for the $$t$$ distribution or what is the specific hypothesis testing framework I should be using for my particular scenario. What is important, especially for science, is that you go into your experiments with the knowledge that you’re going to see stuff that doesn’t make any sense. You need to find a way to become less uncertain about what you observe before you can learn anything from it.

As Ronald Fisher said in 1938 2:

To consult the statistician after an experiment is finished is often merely to ask him to conduct a post mortem examination. He can perhaps say what the experiment died of.

Being able to think ahead about what you might see after an experiment is important. Knowing how to design experiments to reduce the effect of noise is important. This knowledge doesn’t come from memorizing tables of formula or facts about certain distributions. It comes from understanding what the spirit of statistics is about and how to think in a statistical way.

## References

1. See Lockhart’s Lament about the poor state of mathematics “education”. Written in 2009, it’s still very much true today, and for more subjects than just math, unfortunately.

2. Presidential Address to the First Indian Statistical Congress, 1938. The entire address is worth reading.