> Much of the power of statistics is in common sense, amplified by appropriate mathematical tools, and refined through careful analysis.
I hate to be contrarian, but even though I have a degree in statistics, I feel like much of statistics/probability actually violates common sense. In fact, it's probably the most unintuitive field that I'm familiar with.
Many of the readers will probably be familiar with the Monty Hall problem or the Birthday problem, but imo, the entire field of statistics/probability is about equally unintuitive/violating of common sense.
A classic example would be that if you have a test (say for cancer) with a false positive rate of “””only””” 5%, and your disease has an incidence of say 1 in 1000.
Let’s say that you get a positive diagnosis for the disease, and you ask someone the question:
What is the probability you actually have the disease?
Most people will say 95% or 99%, but your actual probability of having the disease in this example is <2%
Unfortunately that well-worn example usually only proves that "false positive" as a technical term fails to match people's intuitions. The underlying problem about the base rate is important to teach, but it's easy for well-meaning people to try and teach the base rate lesson but fail by instead teaching a bullshit gotcha about the definition of "false positive."
I hate to be contrarian, but even though I have a degree in statistics, I feel like much of statistics/probability actually violates common sense. In fact, it's probably the most unintuitive field that I'm familiar with.
Many of the readers will probably be familiar with the Monty Hall problem or the Birthday problem, but imo, the entire field of statistics/probability is about equally unintuitive/violating of common sense.