and 6

lol it might even be fun to make sliders for this

Wow yea that's the similar distribution. Very interesting.

OK so basically if you have a small sigma, you will be able to "see" your distribution in the Benford's law graph

I made sliders

I guess I can just make this public for anyone to play with

https://observablehq.com/@realazthat/benfords-law/2

enjoy 😄

just play with the slidy sliders

I took a class in Visual Basics probably 12-14 years ago (poorly) and that's as far as I went. So this is mind blowing to me 😆

ha

I am not an expert in this stuff, observableshq is really making me look better than I am lol

Sorry...I didnt play with the sliders, Its fixed but im not sure if it was only for me or if other people saw it broken

@evildood89 what's the issue?

my takeways from this are:

1. you need a high sigma (a large range of order of magnitudes) to see a Benford-looking graph.

2. you need a large number of samples to reliably reproduce a Benford-looking graph (you can even find the 1s bar lower than the 2s bar at 150 samples if you repeat the simulation over and over , at 150 samples).

3. If you play around with the numbers, you can make or break the law; the law seems to apply only to certain shapes and centerings of the normal distribution

No issue I was just poking around since the site seem to allow me to edit, I changed 1 value then ran it, as expected it broke but I put it back. I just wanted to apologize if it affected other users.

oh no it can't

it is not collaborative, if you change it, then it is local

if you save, it forks to a new copy

Ahh similar to github ?

right

Thats neat I like the interface on mobile :)

I added a regenerate button to make it easy to click fast to see the variations of the bars from simulation to simulation

me playing with the sliders

anyway

I think the conclusion here is: if the variance in magnitude is low, benford's doesn't indicate anything

I think the conclusion here is:


1. if the variance in magnitude is low, Benford's Law doesn't say anything should be expected.
2. Though perhaps one could ask question about why the variance in magnitude is low, and how does this compare to previous elections and so on; I imagine simply looking at the political history of the districts involved etc. would answer such questions.
3. But if the variance in magnitude is high, _and_ there are enough samples, then if the shape of the graph does not follow Benford, then there is something to analyze further.
4. Even in the best case, % deviation from the expected Benford graph is not as useful as it seems, unless you factor in the number of samples (the more samples, the less expected deviation).

All that being said, I bet Mark Nigrini knows more than me

I don't think he'd disagree though

IIRC he did use a lot of samples

https://www.youtube.com/watch?v=QkNkQ2nDQfc&ab_channel=ProjectVeritas

2 hours 👀

YES thank you for this.

https://youtu.be/CMMbZH-H4ks

@realz I think you've put this Benford's law issue to rest ... I work with numbers every day and have for many decades, generally those statistical methods are good for evaluating measurements of physical processes (temperature, wind velocity, etc.) but when you look at numbers associated with human behavior then you'll find many time statistical methods don't readily apply, just take the polling predictions versus the election results both in 2016 and 2020

mhm

that is yet another issue

@realz agreed, that is a separate issue than Bendfords law.

The reason that the first digit appears in ratios is because we have a system of numbers based in 10

So 1 should appear more often than other numbers. It would be different than if it was evaluating the last digit that appears.

I imagine that benford's law actually applies in every base