Had a lot of fun with my stats students today.

[alienghic@timeloop.cafe]

@dlakelan @futurebird

The dictionaries in the Counter() object are the number of times each integer appears.

In [18]: Counter(listA)
Out[18]: Counter(
{2: 17, 3: 17, 5: 16, 1: 17, 4: 17, 6: 16}
)

In [19]: Counter(listB)
Out[19]: Counter(
{4: 12, 2: 17, 5: 14, 6: 17, 3: 24, 1: 16}
)

[danpmoore@mathstodon.xyz]

@dlakelan @futurebird @Bumblefish Based on this description, A looks too uniform. B could be random.

[zalasur@mastodon.surazal.net]

@futurebird @Bumblefish Yes, you can determine probable likelihood. But given any list of items, it is impossible to prove or disprove whether a list is random or not.

[sabrina@fedi01.unicornsparkle.club]

@madjohnroberts @futurebird @Bumblefish

If List A has nearly equal occurrences of each number then that’s the one most likely to have been produced by the equivalent of rolling a die 100 times.

[dlakelan@mastodon.sdf.org]

@alienghic
I'm on my phone at a volleyball game but what's the likelihood for each (probability of seeing that vector of counts given a multinomial distribution with 1/6 as probability for each value)

should be pretty easy in R or Julia or Python though offhand I would need to look at docs for any of them. Julia would be something like
using Distributions
pdf(Multinomial([1/6, 1/6,...], [17,17,17,17,16,16])
@futurebird

[koushiniku@hachyderm.io]

@futurebird @Bumblefish
16 17

[dlakelan@mastodon.sdf.org]

@danpmoore
agreed, the frequencies seem too uniform for the first intuitively.
@futurebird @Bumblefish

[charette@mstdn.ca]

@futurebird Can you settle the question?

(My vote is the many 3x repeated sequences in listA is not random, but I'm not dedicated enough to pull out a die and record 100 rolls to see if that is likely to happen a bunch of times.)

[madjohnroberts@mastodon.social]

@sabrina I think the frequency being within floor/ciel of 100/6 and the first four being ciel(100/6) and last two floor(100/6) shows intentionality. I agree the frequency should be close but not exact! It's harder to say for certain though, 100 samples isn't so much and I think with a larger N the difference would be more apparent with listB showing less volatility
@futurebird @Bumblefish

[futurebird@sauropods.win]

ListA was created by making a list of 16 or 17 of each number. The Stdev **of the frequencies** is much lower than what you will find on random lists of similar size.

ListB was made by rolling dice.

[futurebird@sauropods.win]

@apophis @Bumblefish

I don't think the order should matter. The "problem" isn't related to the order of the list.

[rubinlinux@mastodon.sdf.org]

@futurebird Think of a chat with an LLM similar to a chat with a fellow (but maybe not so great) improv doing a skit. It is trying to play along with anything you give it. Always.

[koushiniku@hachyderm.io]

@futurebird I found out quickly that the entropy tools from NIST and Fourmilab don’t work well with a data set that’s log2(6) bits per element.

[moira@mastodon.murkworks.net]

@futurebird @Bumblefish Heh, this reminds me of something from school where... Evan? Somebody. made a plot of outputs from the system's (pseudo-)random number generator and turns out there some _very visible_ patterns. Like, obvious visible stripes in the number selection density plot.

#maths

[dragonfrog@mastodon.sdf.org]

@futurebird @Bumblefish
I think list B is random.

As others have noted A has 17 @1,2,3,4, and 16@5,6, while B is "lumpier". Also looking at the difference between consecutive numbers, list A has 23 0s (number N = number N+1), 21 +1s (Number N 1 greater than number N+1) - very clustered around repeating numbers or increments by 1. In list B the difference between consecutive numbers is much more evenly distributed, suggesting number N+1 really was independent of number N.

[dhobern@scicomm.xyz]

@futurebird @Bumblefish

Replacing a bad analysis where I forgot we are dealing with dice, not decimal digits.

The first has 23/99 runs of two matching digits and 5/98 runs of three.

The second has 12/99 and 1/98.

The expected mean fractions would be 1/6 and 1/36.

The latter series is a little closer to the expected values, but each of the two series is at some distance (on opposite sides) of the mean.

These are only a couple of the possible information signals that could be checked, but they seem prima facie to suggest the second is a slightly more plausibly random-adjacent series.

[abyssalrook@mstdn.social]

@futurebird Before I look at where the answer shows up, my guess would be that List A is random.

The odds of both dice being the same number when you roll 2 dice is 1/6 (36 possibilities, 6 desired results). For 3, that becomes 1/36. (6*6*6 possibilities, 6 desired).

What we have here is 98 consecutive possible places for a 3-of-a-kind to start. The odds that you would only draw the 1/36 chance ONCE (The 3 2's near the beginning of B) is something like....8%?

[abyssalrook@mstdn.social]

@futurebird The point is, having it appear once is something like a 94% chance. Seeing a 3-of-a-kind appear more than once is very much expected in a random distribution.

But it's NOT what we EXPECT a random distribution to look like, from a human perspective. When people see things like that appear, they get nervous. If they're making a list to LOOK random, having 3 of the same number in a row starts to feel NOT random, like it's some kind of pattern, and so they won't do it much.

[leorjorge@mastodon.social]

@futurebird the first time I had to go nuclear about LLM use in my department was when my boss was showing me her design for a major experiment where they were planting actual trees of different species in long term plots, and when I asked how did they randomise the distribution of species she said the post doc responsible for setting up the experiment had asked chatgpt to randomise it! (1/2)

[leorjorge@mastodon.social]

@futurebird And that was about 2 years ago, when this kind of thing would probably be even worse. It took me half an hour to write code to generate the plots and some nice figures with the positions of every tree... I wonder how long they were fighting the chat box to get any kind of answer. Let alone the fact this experiment will be running for years to come. How can people be so careless? (2/2)