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Galton Board

by bmaeser on 6/18/19, 1:30 PM with 30 comments

• by nonfamous on 6/19/19, 3:37 PM

  One of my Statistics professors made great use of one of these (he called it a Quincunx) our my Six Sigma class. It was about management, and how reacting to processes you can’t control just makes things worse.

  He’d pick someone from the class, tell them he was going to check their performance (like they were a Sales manager), a run a ball through the Quincunx. If the ball landed on the left, that meant they’d underperform, and they got a tongue lashing. If it fell on the right, they got praise. People got angry about the senselessness of it all.

  But that was the point. The lesson: if you mandate targets on something that is essentially random and can’t be controlled, you’re going to have a bad time. (And if you react to those random results by changing the process, results get even worse — but that was another class for another day.)

• by apathy on 6/19/19, 11:09 AM

  I bought one of these to teach a one-shot class on experimental design and statistics.

  To say it served the purpose would be an understatement. We blew through the CLT and derivation of statistical power in 10 minutes, leaving the other 110 minutes for the students to present research papers. One of the best $35 I’ve ever spent (don’t have the Amazon link handy but there are some great versions there). Highly recommended if you teach.

• by bacr on 6/19/19, 3:21 PM

  There was a log-normal version of the Galton board making the rounds last month:

  https://stat.ethz.ch/~stahel/lognormal/bioscience.pdf

  It really clarified where a log-normal distribution comes from: the consequence of switching a sum of random variables for a product.

• by carapace on 6/19/19, 7:16 PM

  One of my favorite photos in the world is of the large (wall-sized) Galton board at the old Princeton Engineering Anomalies Research Lab. There are two guys, visitors, sitting in front of it and they have just used "psychic powers" to affect a run and the balls are ridiculously skewed to one side, just ridiculously, obviously skewed.

  I like the photo because it's a bifurcation point for the viewer: there are two options to resolve what you're seeing:

  1. It's fake.

  2. It's not fake and "there's something there".

  The whole PEAR Lab itself suffers from the same ambiguity: they got consistent positive results, but never so positive that skeptics could be decisively satisfied. (Not including one-off things like the photo of the visiting guys who did produce a dramatic undeniable effect.)

• by eldavojohn on 6/19/19, 1:46 PM

  This was discussed in a really interesting way in the Pearl/MacKenzie book "The Book of Why" which I heavily recommend for people interested in cause & effect. Really opened my eyes to a lot of things I had been doing statistically but never known formally what was going on. http://bayes.cs.ucla.edu/WHY/

• by mrich on 6/19/19, 3:40 PM

  I fondly remember when I wrote a Galton board simulation as a computer science school project. It would show the ball falling down and simulate the coin flip at each stage, summing up the number of balls that fell into each slot. The hard thing was it had to run on a 80286. The final version had some nifty background graphics and advanced drawing routines, written in Pascal and some inline assembly ;)

• by mikorym on 6/19/19, 10:03 AM

  If you vary the size of the opening, am I correct that that just changes the parameters on the curve?

  I've known about the central limit theorem for a long time and was probably taught about it in first year, but I have never managed to sit down and understand how to prove it properly. One side effect of the theorem should be to explain least squares—if I am not mistaken then least squares was invented largely due to the central limit theorem by Gauss.

  We can always do least cubes, but that does not provide us (usually) with better results.

• by samch93 on 6/19/19, 9:30 AM

  Recently a good friend gave me a small Galton board for my birthday and it stands now on my desk. It is so cool to do a little "simulation" and see the magic of the central limit theorem. Highly recommended as a gift for any statistically interested person!

• by HeraldEmbar on 6/19/19, 11:29 AM

  Is it really 50% though since more than one ball is falling through at a time? Wouldn't a steel ball hitting another steel ball affect it's possible path?

• by dekhn on 6/19/19, 1:35 PM

  I built several of these from scratch after realizing that pegboard is already set up in the right pattern and dowel pins fit into peg holes perfectly.

  I demo'd it at a STEM fair and everybody has a great time. It makes a ton of noise and a great visual demo. I even ended up learning a bunch about hopper theory because I had to 3d print a hopper to feed it and it kept jamming.

• by dragontamer on 6/19/19, 7:02 PM

  This was my favorite "game" at Chuck E Cheese as a kid. I'm very sad that they removed these old arcade booths from the modern stores.

• by naringas on 6/19/19, 6:50 PM

  interesting intro by Michael from Vsauce

  https://youtu.be/UCmPmkHqHXk

• by chewxy on 6/19/19, 1:11 PM

  I saw an actual giant Galton board in the Museum of Maths in New York. It was very satisfying