# You will probably like this. (p<.05)

March 2, 2017 11:42 AM Subscribe

Seeing Theory is an amazing interactive introduction to statistics and probability. Though the visualizations and interactive toys are really great, the concepts can get complicated quickly. If you are confused, you may be interested in the free Open Intro to Statistics textbook or the video series by the same authors. For a gentle introduction, consider watching this BBC documentary on statistics by the late, great Hans Rosling.

I dunno, just on the first page, under "Estimator" the pedagogy goes off the rails. It's not at all clear what is being sampled at each point, and there is no explanation of the "4" and why the ratio is used. This is probably obvious to those who know, the point is teaching those who do not know.

posted by smidgen at 12:14 PM on March 2, 2017 [1 favorite]

posted by smidgen at 12:14 PM on March 2, 2017 [1 favorite]

For those interested in textbooks, Cosma Shalizi's advanced data analysis from an elementary point of view and Richard McElreath's statistical rethinking are pedagogical masterpieces.

posted by MisantropicPainforest at 12:18 PM on March 2, 2017 [10 favorites]

posted by MisantropicPainforest at 12:18 PM on March 2, 2017 [10 favorites]

This is both cool and not cool.

It's cool in the early parts about probability. The interactive sampling widgets can portray the key theoretical behaviour because the theory is compatible with being turned into a generative model.

It's not as cool in the later parts. A good example is the bit on Confidence Intervals. IMHO it doesn't quite work, for the same reason that the title of this post is a mega troll. You really don't want to think about p values and confidence intervals in terms of probabilities, but that is the most obvious interpretation of the visualisation.

posted by ethansr at 12:19 PM on March 2, 2017 [1 favorite]

It's cool in the early parts about probability. The interactive sampling widgets can portray the key theoretical behaviour because the theory is compatible with being turned into a generative model.

It's not as cool in the later parts. A good example is the bit on Confidence Intervals. IMHO it doesn't quite work, for the same reason that the title of this post is a mega troll. You really don't want to think about p values and confidence intervals in terms of probabilities, but that is the most obvious interpretation of the visualisation.

posted by ethansr at 12:19 PM on March 2, 2017 [1 favorite]

*smidgen*- totally agree that Seeing Theory is not great pedagogy, it quickly swings from "coins, got it" to "squared bias estimators plus greek letters"

In the case of the ratio, this is an example of how you calculate pi using Monte Carlo (random) methods. To quote another site using this example:

If a circle of radius R is inscribed inside a square with side length 2R, then the area of the circle will be pi*R^2 and the area of the square will be (2R)^2. So the ratio of the area of the circle to the area of the square will be pi/4.posted by blahblahblah at 12:23 PM on March 2, 2017 [1 favorite]

This means that, if you pick N points at random inside the square, approximately N*pi/4 of those points should fall inside the circle.

BTW, I managed to figure it out, it's the unit circle, which has an area of pi, and 4 is the area of the square, so the ratio of samples inside of the circleto all samples times the area of the square is the area of the circle -- or pi. But, that still seems a long way to travel that could have been fixed with a single sentence in the description. :-)

posted by smidgen at 12:25 PM on March 2, 2017 [1 favorite]

posted by smidgen at 12:25 PM on March 2, 2017 [1 favorite]

Yeah it's a great example of Monte Carlo methods--so great that I've seen it a bunch of times before--but I'm less sure how useful it is to understand what an estimator is. Approximate inference is pretty advanced stuff, but that's what the drop a coin in a circle is for. Estimators are differen beasts.

posted by MisantropicPainforest at 12:26 PM on March 2, 2017 [1 favorite]

posted by MisantropicPainforest at 12:26 PM on March 2, 2017 [1 favorite]

This is always useful: How to Lie with Statistics

posted by chavenet at 12:58 PM on March 2, 2017 [3 favorites]

posted by chavenet at 12:58 PM on March 2, 2017 [3 favorites]

Great post! What's there is tremendously useful - it's not the page to go to to learn probability and statistics by yourself, but as a resource for teaching and a supplement to a class, it looks tremendous.

posted by Wolfdog at 1:28 PM on March 2, 2017 [2 favorites]

posted by Wolfdog at 1:28 PM on March 2, 2017 [2 favorites]

The Central Limit Theorem demonstration is great.

posted by jnnnnn at 6:49 PM on March 2, 2017 [1 favorite]

posted by jnnnnn at 6:49 PM on March 2, 2017 [1 favorite]

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For those who aren't into statistics, it is worth noting that the last has been a long-standing approach to scientific research that is under deep discussion for a number of reasons, including on MetaFilter (and why I actually paused before including a joke p-value in the title of this post).

posted by blahblahblah at 12:13 PM on March 2, 2017 [4 favorites]