I wish they'd cover the sample space/parameter space distinction "harder", as it seems key to the numerous philosophical divides in the foundations of statistics & probability theory, and it seems like a very good candidate for colorful & animated visualization.
Also, note that the classic coin flipping example used there right in the beginning serves as an extremely bad & misleading analogy, see here for why:
I wish we'd stop using it in Stats & Physics 101, or at least add huge disclaimers to it, something like "Coins don't actually behave this way, not even mathematically idealized ones".
Coin flipping is a canonical example that has historical, theoretical, and practical relevance--it's definitely a bit much to call it "extremely bad & misleading". Mathematically idealized coins do behave in this way, because you have the freedom to define the probability of the events however you like (so long as you do not violate the axioms of probability).
Also, there are lots of (abstract) mathematical nuances to explore around coin flipping once you get into stochastic processes (there are special aspects of Bernoulli RVs with p=0.5).
Besides, sometimes an imperfect example is a better one--it can stimulate thought and discussion about how well concepts--like modeling a coin flip with a random variable--map to the real world.
Your ucsb link describes an unfair coin flipping protocol, and not the fair protocol commonly used in practice. In particular, it provides a "strategy" at the end to generate an unfair toss (which requires, e.g., that you be both the flipper and the chooser). Other studies, such as the famous You can load a die, bit you can't bias a coin investigate fair flipping protocols and argue that you cannot, in fact, bias a coin:
But seriously, all of these interactive visualizations are amazing. I wish they had this kind of stuff when I was an undergrad. I remember trying to plot the beta distribution for different alpha and beta parameters in MATLAB trying to get an intuition for it; just dragging the sliders around on the prior and watching it update as each data point comes in is a million times more accessible.
Great visualizations. Really liked the practical examples it had for every topic. Only problem I felt was, that there wasn't an underlying explanation why one thing followed another. And without understanding the problems you are solving, you can't really appreciate the hundreds of years worth of mathematical progress leading to these innovations.
Slightly off topic, but beautiful site. I love sites that change and update the content in a floating manner as you scroll... NYT website has had articles like this for the past few years..
Does anyone know of packages or libraries that can help you do this? Or do I just need to hack my own JavaScript?
"Scrollytelling" is the term you're looking for - The Pudding did a solid walkthrough of a few libraries [1], and I've found scrollama [2] to be a solid bare-bones library. This talk [3] is a few years old, but it's a good one for seeing some different approaches scrollytelling can take.
[+] [-] no_identd|7 years ago|reply
Some Hacker News Discussions of this:
1. https://news.ycombinator.com/item?id=13735714
2. https://news.ycombinator.com/item?id=13760353
I wish they'd cover the sample space/parameter space distinction "harder", as it seems key to the numerous philosophical divides in the foundations of statistics & probability theory, and it seems like a very good candidate for colorful & animated visualization.
Also, note that the classic coin flipping example used there right in the beginning serves as an extremely bad & misleading analogy, see here for why:
https://econ.ucsb.edu/~doug/240a/Coin%20Flip.htm
I wish we'd stop using it in Stats & Physics 101, or at least add huge disclaimers to it, something like "Coins don't actually behave this way, not even mathematically idealized ones".
[+] [-] jointpdf|7 years ago|reply
Also, there are lots of (abstract) mathematical nuances to explore around coin flipping once you get into stochastic processes (there are special aspects of Bernoulli RVs with p=0.5).
Besides, sometimes an imperfect example is a better one--it can stimulate thought and discussion about how well concepts--like modeling a coin flip with a random variable--map to the real world.
[+] [-] jackpirate|7 years ago|reply
https://www.stat.columbia.edu/~gelman/research/published/dic...
I have some blog posts on developing biased coins and dice, and the results show that any coin with a measurable bias is quite obviously not fair:
https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...
whereas you can undetectably bias dice at home with just a bit of water:
https://izbicki.me/blog/how-to-cheat-at-settlers-of-catan-by...
[+] [-] olooney|7 years ago|reply
What metaphor for a Bernoulli trial do you prefer?
[+] [-] hopler|7 years ago|reply
[+] [-] olooney|7 years ago|reply
http://setosa.io/conditional/
But seriously, all of these interactive visualizations are amazing. I wish they had this kind of stuff when I was an undergrad. I remember trying to plot the beta distribution for different alpha and beta parameters in MATLAB trying to get an intuition for it; just dragging the sliders around on the prior and watching it update as each data point comes in is a million times more accessible.
[+] [-] QML|7 years ago|reply
[1] http://varianceexplained.org/statistics/beta_distribution_an...
[+] [-] tekkk|7 years ago|reply
[+] [-] anonu|7 years ago|reply
Does anyone know of packages or libraries that can help you do this? Or do I just need to hack my own JavaScript?
[+] [-] spacecaps|7 years ago|reply
[1] https://pudding.cool/process/how-to-implement-scrollytelling...
[2] https://github.com/russellgoldenberg/scrollama
[3] http://vallandingham.me/scroll_talk/examples/
[+] [-] melling|7 years ago|reply
https://seeing-theory.brown.edu/index.html#4thPage
[+] [-] nobrains|7 years ago|reply
[+] [-] unknown|7 years ago|reply
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[+] [-] icodemuch|7 years ago|reply
[+] [-] talko|7 years ago|reply
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