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Galton Board

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Re: Galton Board

#21

Post by nonfamous »

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.)

Re: Galton Board

#22

Post by mrich »

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 ;)

Re: Galton Board

#23

Post by leni536 »

HeraldEmbar wrote: post #9

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?

Notice how the drawn Gaussian doesn't follow the bottom row of binomial coefficients of the Pascal's triangle[1]. The model that assumes that each ball independently falls left or right exactly one unit is limited and doesn't actually describe many real world Galton boards.

[1] https://upload.wikimedia.org/wikipedia/commons/d/d2/GaltonBo...

Re: Galton Board

#24

Post by kkylin »

apathy wrote: post #7

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 recomme…

As others said, if you can post a link that would be really great. When I've taught probability in years past, I always showed students Galton boards on YouTube, but a real one that doesn't break and doesn't break the budget would be much better.

Re: Galton Board

#25

Post by gwern »

kkylin wrote: post #24
apathy wrote: post #7

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 recomme…

As others said, if you can post a link that would be really great. When I've taught probability in years past, I always showed students Galton boards on YouTube, but a real one that doesn't break and doesn't break the budget would be much better.

You can just search Amazon. There's nothing special about a quincunx, they're simple. Any search query on Amazon, whether 'Galton quincunx' or 'Galton bean machine' or 'Galton board' will pull up a bunch, I just checked.

Re: Galton Board

#26

Post by homonculus1 »

dekhn wrote: post #16

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.

I forget where I first read about hopper theory but I was fascinated to discover that so much analysis has been done on the dimensions of such a simple device. It makes perfect sense in retrospect given all the industrial and agricultural applications but it's one of those little corners of the world where you would never guess the pains engineers go to understand and optimize it.

Re: Galton Board

#29

Post by carapace »

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.)

Re: Galton Board

#30

Post by dxbydt »

apathy wrote: post #7

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 recomme…

How exactly does a Galton board blow through the CLT ?
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