but 69 samples is egregiously small

I see what you mean.

I noticed Mark seems to validate the data before the benford's analysis by doing the end digits distribution analysis first before looking at the first digits.

mmm

I can rerun my experiment with 69 samples, it will be quite wild

And I was thinking there must be a lower limit on the sample size.

And maybe the order of magnitude applies within the samples? i.e., some precincts or counties with dozens, hundreds, thousands, ten-thousands, etc. but all those numbers being lumped into the single analysis.

I don't speak math very well not sure if I'm communicating that well.

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

@RobertGrulerEsq The brief teaching I had in my different forensics class Benford's Law can be used on small data sets that have enough number cycles i.e. sufficient use of 1-9

benford's law test, with 69 (number of counties in PA) samples, (random) normally distributed between 0 and 19000000

PA*

That's pretty amazing you can do that so quickly, I'm jealous of your skills.

I had it ready lol

I just changed the number

Have you run any that have a bell-curve distribution that look like Biden's?

to be clear this is not run on real data

oh

normal distribution is a bell curve

it isn't exactly the same as Biden's bell curve though

it is a bell curve centered on zero (I abs() the negative numbers)

I can center it on some number though

I see. Just wondering if adjusting of the sample size adjusted the curve more in alignment with the thumbnail in the math guy's video above of Biden's numbers.

oh I see

no, increasing the sample size for my experiment makes it more like benford's law

@realz Correct me if I am wrong here, but in using Benford distribution as evidence of voter fraud, you would have to have representative sample sizes from an election verified to be true (baseline) and one that has been confirmed as fraud, and calculate probability based on how much the current election approach the latter, yes?

probably because I center around 0

@Doc that is another good point; to test previous elections for the same thing

(but there are those that might say "it's always been going on")

Right, so you need some sort of baseline.

well that is _yet_ another litmus test for these proofs

because all elections will have some systematic and random defects.

my experiment just shows that with few samples, the expected error for each bar is too high

right

very nice.

Sorry for interrupting, I just liked your number-dabbling.

@RobertGrulerEsq I suspect the fact that I center around 0 is why I don't get he same results as the math guy's video

my orders of magnitude are much large as well

a uniform random generator also works, with the weird artifact that it very much depends on what your maximum number is

with a maximum number of say 20000000, almost half your numbers will start with 1

more than half