Galton Board
en.wikipedia.org
Galton Board
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Re: Galton Board
#2Recently 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!
Re: Galton Board
#3If 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.
Re: Galton Board
#4If 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…
> if I am not mistaken then least squares was invented largely due to the central limit theorem by Gauss
I'm not really speaking from expertise here, but I thought least-squares error measurement was based on the fact that the metric is easy to minimize, because taking the derivative of x^2 is easy, whereas taking the derivative of |x| is complicated.
Least cubes doesn't really work conceptually, as it would imply that if an outlier above the fitted curve is bad, then an outlier below the fitted curve is good. That's not what you want.
Re: Galton Board
#5[deleted]
Re: Galton Board
#6If 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…
This might be what you're looking for:
Re: Galton Board
#7I 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.
Re: Galton Board
#8I 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…
If you can post a link to a good one I'd appreciate it. I've generally found expensive ones and bad ones. I've been looking for one that's cheap and good.
Re: Galton Board
#9Is 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?
Re: Galton Board
#10Is 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?
if the distances between circles approaching another circle is more-or-less the width of the ball, the other balls will not affect it much.
+ The additional perturbations make the situation more random, rather than entirely based on the inconsistencies of the board design.