Seeing Theory: A Visual Introduction to Probability and Statistics

On a different thread this morning someone bemoaned the lack of statistical education - a sentiment that is widespread among people who have studied and worked with statistics and probability. It is really exciting to see pedagogical tools that help explain basic but important concepts like distributions and sampling. Great work.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#8

Post by shekharshan » Tue, Sep 29, 2020, 11:33 PM UTC

A couple of years ago I was just learning Python and was playing around with matplotlib. Running simulation of a dice roll 100, 1000, 10,000, 100,000, and 1,000,000 times started to show how the distribution starts to catch up with the expected 1/6th probability of each face. I was thinking how good it would be to teach young students this way.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#9

Post by qsort » Tue, Sep 29, 2020, 11:38 PM UTC

blululu wrote: post #7

On a different thread this morning someone bemoaned the lack of statistical education - a sentiment that is widespread among people who have studied and worked with statistics and probability. It is really exciting to see pedagogical tools that help explain basic but important concepts like distributions and sampling. Great work.

Agreed, this is extremely well-done. Even worse than the general lack of statistical education, I feel the teaching of statistics and probability suffers of the same problems as calculus/real analysis. Introductory statistics classes ramble at length about how random variables are functions from a probability space to a measurable space, but everyone who actually 'gets' the concept behind it eventually thinks in terms of realizations (i.e. much more similarly to what this tutorial does). Intuition without theory is shallow, but theory without intuition just leads to you eventually forgetting the theory.

Re: Seeing Theory: A Visual Introduction to Probability and Statistics

#10

Post by gbrown » Tue, Sep 29, 2020, 11:41 PM UTC

shekharshan wrote: post #8

A couple of years ago I was just learning Python and was playing around with matplotlib. Running simulation of a dice roll 100, 1000, 10,000, 100,000, and 1,000,000 times started to show how the distribution starts to catch up with the expected 1/6th probability of each face. I was thinking how good it would be to teach young students this way.

Definitely! Also, not just young students. If you can get over code-phobia, doing random experiments in a class can be really illustrative. When I teach hypothesis testing, I always teach it both from a simulation perspective and from a traditional perspective.

For one, by doing the simulation part directly it's easier to see the "under repeated sampling..." logic inherent in frequentist procedures. Additionally, it's possible to do simulation-based procedures where traditional methods break down (think: permutation tests).