Comment by dwater
3 years ago
I teach post-grad stats classes in the US, with no real prerequisites besides a Bachelor's degree. Most but not all of my students have passed a college level stats class that covered these concepts, and maybe half of those did not retain a true understanding of these concepts by the time they got to my classroom. In my experience, math is the least like/most hated of the core subjects, and stats is one of the least liked/most feared math subjects.
What makes statistics seems so daunting to the average student over, say, discrete mathematics? I feel like statistics has so many immediately obvious real world use cases and useful analogies to help frame it (die rolls, etc).
As a person with a bachelor's in math who dislikes statistics, it's the one field I know where "gotcha" problems are more common in reality than in class. And they are nasty problems. It takes a lot of education until you can confidently say what simplifications are justified for your situation. And a lot of professional statisticians like to flex on newcomers for simple mistakes.
You're right that some education would help people with everyday situations. It'd be nice if schools had intro to probability and statistics as the only required math course for all students. Even just covering fractions for probabilities, mean/median/mode, and then memorizing basic tricks or terms to look up on Wikipedia/Wolfram throughout life.
The very idea underlying statistics (that we can learn something useful from a class of events by ignoring specifically that which makes them different from each other) is a very recent invention -- only a few hundred years old -- and it's still counter-intuitive to a lot of people.
Ask people to predict whether the Jones' have a dog and they'll start asking questions about the specifics of the Jones', like do they have children, do they live in the suburbs, have they always wanted a dog, etc. Then they try to construct a narrative based on "logical" conclusions.
When the right approach might be to ask "what's the background rate of dog ownership in the Jones' country of residence?" But that takes ignoring the specifics, and that doesn't come easily to people. It took several millennia for anyone to realise it could be useful.
> Ask people to predict whether the Jones' have a dog and they'll start asking questions about the specifics of the Jones', like do they have children, do they live in the suburbs, have they always wanted a dog, etc. Then they try to construct a narrative based on "logical" conclusions.
This is the core idea of Bayesian statistics.
You fall back to the background rate only if you have no ability to access more pertinent facts.
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Easy to get things wrong from the wrong intuition or understanding of the problem. Cross mathematic discipline etc. But I feel that most applications just need high school math.