Tobias Herbst
SigmaCan we approach a normal distribution with µ = 0 and σ = 1?
Please share so we get a pretty graph. ^^"
Please share so we get a pretty graph. ^^"
-3
-2
-1
0
1
2
3
Poll ended at .
Walter Tross@sigmasternchen I think people don't pay enough attention to that σ = 1 part
@waltertross My guess is that most people don't use a random number generator, but just create one in their head. And humans suck at randomness. ^^"
Ianhopkinson@sigmasternchen @waltertross I felt using a generator was not in the spirit of the exercise. You may be in the process of creating a distribution unknown to science!
@ianhopkinson @waltertross ^^ I don't really have a preference how people choose. It’s just a fun experiment anyway.
… Actually that’s not true: I hope they choose without looking at the current state first. ^^
… Actually that’s not true: I hope they choose without looking at the current state first. ^^
Colorblind Cowboy@sigmasternchen @ianhopkinson @waltertross Wait, are we trying to get a bell curve? My knowledge of math skills is lacking — but that’s what I thought. Anyway, I’m glad my vote didn’t mess up the symmetrical distribution.
@colorblindcowboy @ianhopkinson @waltertross Yep, a bell curve with a mean of 0 and a standard deviation of 1.
https://www.wolframalpha.com/input?i=N(0,1)
https://www.wolframalpha.com/input?i=N(0,1)
Le Chep@ianhopkinson @sigmasternchen @waltertross it is not unknown to science, it is "flipping the bird when one has polydactyly"
NeoFox@sigmasternchen @waltertross hmm, I guess humans suck at randomness sequentially, but didn't expect a collective of random humans to have this result. I guess there are some biases at play
@NeoFox @waltertross Probably. Also judging from the other answers I've gotten most people don’t choose randomly anyway. 😂
Nicole Göbel@waltertross @sigmasternchen ... as a psychologist I rather tried to guess the so far most neglected number in relation to the goal.
@waltertross @sigmasternchen Firstly, I suspected that people would prefer + to -, and secondly, I know that people tend towards the middle, which is 2 rather than 1, since 0 is hard to imagine as anything at all. So I thought the best way to balance the likely overuse of +2 was to choose -2. But I underestimated the neglect of -1 and +1.
@waltertross @sigmasternchen maybe the effect to prefer + over - could be reduced bay actually writing +1, +2, +3.
@nicolegoebel @waltertross I actually though about doing that, but I decided to use spaces instead, so everything is aligned nicely. Little did I know that some software (including mastodon) doesn’t display spaces in polls. 🙈
@sigmasternchen @waltertross I wouldn't have thought about it until now 😅
But actually, it could be nice testing those hypotheses more systematically 🤔
But actually, it could be nice testing those hypotheses more systematically 🤔
Alan Langford 🇨🇦🧤🧊摏
Christoph Maier
jonny (good kind)@waltertross
@sigmasternchen
Ya I definitely just was like "ok normal distribution that fits in edit: 7 choices got it"
@sigmasternchen
Ya I definitely just was like "ok normal distribution that fits in edit: 7 choices got it"
Primo@waltertross @sigmasternchen I actually don't know what it means^^'
@Primo @waltertross It's the standard divination - basically how spread out the curve should be.
The 1 means that about two thirds of answers should be between -1 and 1.
The 1 means that about two thirds of answers should be between -1 and 1.
eyajpng@waltertross @sigmasternchen It’s kind of you to assume we even know what it means
@jepyang @waltertross 😅 It's the standard deviation - basically the spread.
I plotted the result + the target distribution here:
https://comfy.social/notes/9lp6zdrlo0
I plotted the result + the target distribution here:
https://comfy.social/notes/9lp6zdrlo0
Sigma (@sigmasternchen)
Okay, analysis time, here we go! First of all, a short disclaimer: I'm by no means an expert. It has been years since my last statistics class and I hardly remember anything. So take everything with a grain of salt. 😅 My basic method for analysing the result was K-S (Kolmogorow-Smirnow) tests. Very un-scientifically I throw the data against a bunch of different known distributions and fit the parameters to the data (I think the `scipy` library uses MLE as the fitting method) to see which one matches the best. I didn't test any discrete distributions because honestly I couldn't get fitting to work and I didn't want to spend a bunch of time on that. Note: Our data is discrete, so the absolute K-S probability values are going to be tiny. But since we are only comparing them between each other it should be fine (again: This is not scientific, but just for fun. ^^). I tested the following distributions: normal, beta, cosine, semicircular, von Mises, chi, chi2, gamma, Student's t Some of these distributions only work on the range [0, 1], so for the comparison I moved the data accordingly. The distribution that's the closest match is actually the gamma distribution. With a ginormous α value (1110.2) but moved and scaled accordingly. I wanted to plot it but Desmos just bugged out - understandably so. Additionally, since gamma can only deal with variables > 0 we'd additionally have to move it. Let's discard that one since I just don't know how to deal with that. ^^" The next closest is the chi distribution with a k value of 137. Again scaled and moved to accordingly. Same problem, though less sever - let's discard it. This brings us to our 3rd and 4th place: The normal distribution and Student's t distribution. Both have pretty much the same probability value in the test. Looking at the parameters it's obvious why that is: The parameter v is 82104712197. Since the t-distribution converges to N(0,1) with v tending to infinity, we can effectively call them identical. Let's give the win to the normal distribution since the t distribution would need to be scaled and moved (again) and because of this ridiculous v value I can't plot it anyway (Damn you, Γ-function!). ^^ Let's take a closer look at the normal distribution: μ = 0.1829 σ = 1.5710 So the mean value is actually quite good, but the standard deviation is almost 60 % too big. Looking at our graphs we can see that the overall shape of the poll result (blue dots) is way to spread out to fit the target distribution N(0,1) (red), but fits reasonably well to our calculated distribution (green). The obvious exception being the point at x=0 which is noticeably favoured by the participants. That was fun. I should do something similar again some time. 😊 (📎1) RE: Can we approach a normal distribution with µ = 0 and σ = 1? Please share so we get a pretty graph. ^^"
(1) Enno T. Boland@sigmasternchen that's surprisingly accurate
NiceMicro@sigmasternchen okay, so I didn't check the status of the poll, just the number of people voted, and somehow deduced that "well, most people would probably vote zero, but also people who don't will overestimate the need to vote on +/- 2 or 3. Among plus and minus one, more people would chose the positive number probably, so to balance the distribution, I should vote -1".
Does it make sense? probably not.
@nicemicro Seeing how the poll has been progressing the past 2 days this seems about right. ^^
Log 🪵@nicemicro @sigmasternchen You and I did exactly the same thing for exactly the same reason.
xrvs@sigmasternchen i’m glad my selection contributed towards balance
Niclas Hedhman@niclas @[email protected] It wasn't that bad actually. The mean was 0.18 instead of 0 - I'd say close enough. ^^
not a martian, honest@sigmasternchen nobody likes negative ninnies
medium rare bird@sigmasternchen how do I vote no
Ω 🌍 Gus Posey@sigmasternchen I wasn't sure so I just put 'Atlanta.'
Jen@sigmasternchen I voted for the option I thought would be furthest behind where it should be. And I was right! Points to me on predicting fedipoll behaviour.
Arcana 
@sigmasternchen what does this mean? Is it like a maths puzzle?
Anders von Hadern 🐦🔥@sigmasternchen Guck mal, @isisamrita ;-)
Mike P@sigmasternchen This election is clearly rigged.
Metapod@sigmasternchen EVERYONE SKEW OPTION 2 A BUNCH
Josie 
@sigmasternchen well I did my part is messing this up.
@Josie Totally fine. ^^
🏳️⚧️Claire🏳️⚧️@sigmasternchen
Current results are looking more like a Poisson distribution than Gausian. If that's true, I think it's an interesting result 🔬.
@malcircuit
Current results are looking more like a Poisson distribution than Gausian. If that's true, I think it's an interesting result 🔬.
@malcircuit
@elfieclaire @malcircuit I’ll probably do a K-S test at the end. I’m interested to see how far we missed. ^^
@elfieclaire @malcircuit
I wasn't able to fit against for Poisson because of some reason my math lib doesn't support that for discrete distributions.
I did however look at some other distributions, here is my writeup in case you are interested (I have no idea about that stuff so there are probably some mistakes in there.):
https://comfy.social/notes/9lp6zdrlo0
I wasn't able to fit against for Poisson because of some reason my math lib doesn't support that for discrete distributions.
I did however look at some other distributions, here is my writeup in case you are interested (I have no idea about that stuff so there are probably some mistakes in there.):
https://comfy.social/notes/9lp6zdrlo0
Sigma (@sigmasternchen)
Okay, analysis time, here we go! First of all, a short disclaimer: I'm by no means an expert. It has been years since my last statistics class and I hardly remember anything. So take everything with a grain of salt. 😅 My basic method for analysing the result was K-S (Kolmogorow-Smirnow) tests. Very un-scientifically I throw the data against a bunch of different known distributions and fit the parameters to the data (I think the `scipy` library uses MLE as the fitting method) to see which one matches the best. I didn't test any discrete distributions because honestly I couldn't get fitting to work and I didn't want to spend a bunch of time on that. Note: Our data is discrete, so the absolute K-S probability values are going to be tiny. But since we are only comparing them between each other it should be fine (again: This is not scientific, but just for fun. ^^). I tested the following distributions: normal, beta, cosine, semicircular, von Mises, chi, chi2, gamma, Student's t Some of these distributions only work on the range [0, 1], so for the comparison I moved the data accordingly. The distribution that's the closest match is actually the gamma distribution. With a ginormous α value (1110.2) but moved and scaled accordingly. I wanted to plot it but Desmos just bugged out - understandably so. Additionally, since gamma can only deal with variables > 0 we'd additionally have to move it. Let's discard that one since I just don't know how to deal with that. ^^" The next closest is the chi distribution with a k value of 137. Again scaled and moved to accordingly. Same problem, though less sever - let's discard it. This brings us to our 3rd and 4th place: The normal distribution and Student's t distribution. Both have pretty much the same probability value in the test. Looking at the parameters it's obvious why that is: The parameter v is 82104712197. Since the t-distribution converges to N(0,1) with v tending to infinity, we can effectively call them identical. Let's give the win to the normal distribution since the t distribution would need to be scaled and moved (again) and because of this ridiculous v value I can't plot it anyway (Damn you, Γ-function!). ^^ Let's take a closer look at the normal distribution: μ = 0.1829 σ = 1.5710 So the mean value is actually quite good, but the standard deviation is almost 60 % too big. Looking at our graphs we can see that the overall shape of the poll result (blue dots) is way to spread out to fit the target distribution N(0,1) (red), but fits reasonably well to our calculated distribution (green). The obvious exception being the point at x=0 which is noticeably favoured by the participants. That was fun. I should do something similar again some time. 😊 (📎1) RE: Can we approach a normal distribution with µ = 0 and σ = 1? Please share so we get a pretty graph. ^^"
earthtopus@sigmasternchen where are my other -2heads at
Brian Danger Hicks
jden 
Oliver D. Reithmaier@sigmasternchen this serves as a pretty neat demonstration of scale answer patterns/effects.
Le Néandertal se sent las, las@sigmasternchen this looks more like a t(1)
@HydrePrever I actually did a K-S test against a fitted t distribution, but the parameter was so huge that it's basically just a normal distribution anyway. ^^"
I actually did a short writeup here in case you are interested (I have no idea but this stuff so there are probably lots of errors ^^):
https://comfy.social/notes/9lp6zdrlo0
I actually did a short writeup here in case you are interested (I have no idea but this stuff so there are probably lots of errors ^^):
https://comfy.social/notes/9lp6zdrlo0
Sigma (@sigmasternchen)
Okay, analysis time, here we go! First of all, a short disclaimer: I'm by no means an expert. It has been years since my last statistics class and I hardly remember anything. So take everything with a grain of salt. 😅 My basic method for analysing the result was K-S (Kolmogorow-Smirnow) tests. Very un-scientifically I throw the data against a bunch of different known distributions and fit the parameters to the data (I think the `scipy` library uses MLE as the fitting method) to see which one matches the best. I didn't test any discrete distributions because honestly I couldn't get fitting to work and I didn't want to spend a bunch of time on that. Note: Our data is discrete, so the absolute K-S probability values are going to be tiny. But since we are only comparing them between each other it should be fine (again: This is not scientific, but just for fun. ^^). I tested the following distributions: normal, beta, cosine, semicircular, von Mises, chi, chi2, gamma, Student's t Some of these distributions only work on the range [0, 1], so for the comparison I moved the data accordingly. The distribution that's the closest match is actually the gamma distribution. With a ginormous α value (1110.2) but moved and scaled accordingly. I wanted to plot it but Desmos just bugged out - understandably so. Additionally, since gamma can only deal with variables > 0 we'd additionally have to move it. Let's discard that one since I just don't know how to deal with that. ^^" The next closest is the chi distribution with a k value of 137. Again scaled and moved to accordingly. Same problem, though less sever - let's discard it. This brings us to our 3rd and 4th place: The normal distribution and Student's t distribution. Both have pretty much the same probability value in the test. Looking at the parameters it's obvious why that is: The parameter v is 82104712197. Since the t-distribution converges to N(0,1) with v tending to infinity, we can effectively call them identical. Let's give the win to the normal distribution since the t distribution would need to be scaled and moved (again) and because of this ridiculous v value I can't plot it anyway (Damn you, Γ-function!). ^^ Let's take a closer look at the normal distribution: μ = 0.1829 σ = 1.5710 So the mean value is actually quite good, but the standard deviation is almost 60 % too big. Looking at our graphs we can see that the overall shape of the poll result (blue dots) is way to spread out to fit the target distribution N(0,1) (red), but fits reasonably well to our calculated distribution (green). The obvious exception being the point at x=0 which is noticeably favoured by the participants. That was fun. I should do something similar again some time. 😊 (📎1) RE: Can we approach a normal distribution with µ = 0 and σ = 1? Please share so we get a pretty graph. ^^"
Sylvain MAILLER@s_mailler @antoinechambertloir I actually did a short analysis of the result in case you are interested:
https://comfy.social/notes/9lp6zdrlo0
https://comfy.social/notes/9lp6zdrlo0
Sigma (@sigmasternchen)
Okay, analysis time, here we go! First of all, a short disclaimer: I'm by no means an expert. It has been years since my last statistics class and I hardly remember anything. So take everything with a grain of salt. 😅 My basic method for analysing the result was K-S (Kolmogorow-Smirnow) tests. Very un-scientifically I throw the data against a bunch of different known distributions and fit the parameters to the data (I think the `scipy` library uses MLE as the fitting method) to see which one matches the best. I didn't test any discrete distributions because honestly I couldn't get fitting to work and I didn't want to spend a bunch of time on that. Note: Our data is discrete, so the absolute K-S probability values are going to be tiny. But since we are only comparing them between each other it should be fine (again: This is not scientific, but just for fun. ^^). I tested the following distributions: normal, beta, cosine, semicircular, von Mises, chi, chi2, gamma, Student's t Some of these distributions only work on the range [0, 1], so for the comparison I moved the data accordingly. The distribution that's the closest match is actually the gamma distribution. With a ginormous α value (1110.2) but moved and scaled accordingly. I wanted to plot it but Desmos just bugged out - understandably so. Additionally, since gamma can only deal with variables > 0 we'd additionally have to move it. Let's discard that one since I just don't know how to deal with that. ^^" The next closest is the chi distribution with a k value of 137. Again scaled and moved to accordingly. Same problem, though less sever - let's discard it. This brings us to our 3rd and 4th place: The normal distribution and Student's t distribution. Both have pretty much the same probability value in the test. Looking at the parameters it's obvious why that is: The parameter v is 82104712197. Since the t-distribution converges to N(0,1) with v tending to infinity, we can effectively call them identical. Let's give the win to the normal distribution since the t distribution would need to be scaled and moved (again) and because of this ridiculous v value I can't plot it anyway (Damn you, Γ-function!). ^^ Let's take a closer look at the normal distribution: μ = 0.1829 σ = 1.5710 So the mean value is actually quite good, but the standard deviation is almost 60 % too big. Looking at our graphs we can see that the overall shape of the poll result (blue dots) is way to spread out to fit the target distribution N(0,1) (red), but fits reasonably well to our calculated distribution (green). The obvious exception being the point at x=0 which is noticeably favoured by the participants. That was fun. I should do something similar again some time. 😊 (📎1) RE: Can we approach a normal distribution with µ = 0 and σ = 1? Please share so we get a pretty graph. ^^"
Nice ! Any idea why the average is so close to 0, and the symmetry is so well balanced ?
After all there is no reason that as many users chose positive and negative values, and that more users chose 0 than any other value ! Unless many people "cheated" and decided their answer by actually using the output of a normal law, which I guess 99% of users are too lazy/unable to do.
So, is it sheer miracle that a bell shape is actually found ? ?
@s_mailler @antoinechambertloir From what I saw in the replies a lot of people actually tried to predict what other users would do. ^^
Maybe they were like "I'd probably choose the positive number, so I'll choose a negative one instead."
Maybe they were like "I'd probably choose the positive number, so I'll choose a negative one instead."
@sigmasternchen @antoinechambertloir @s_mailler Does thi make it a normal student's distribution? Asking for my invisible friend.
Moose Jolly Holcomb@sigmasternchen I find it interesting that the skew in the graph is the same at ~4K as it was when I voted at ~1K.
@ReverendMoose True. I wonder why. 🤔
C for CharlieYou are lucky 🍀 now it’s closed it’s a pretty pretty graph 😍
@grisish I think so too. ^^ I actually did a short analysis of the result in case you are interested:
https://comfy.social/notes/9lp6zdrlo0
https://comfy.social/notes/9lp6zdrlo0
Sigma (@sigmasternchen)
Okay, analysis time, here we go! First of all, a short disclaimer: I'm by no means an expert. It has been years since my last statistics class and I hardly remember anything. So take everything with a grain of salt. 😅 My basic method for analysing the result was K-S (Kolmogorow-Smirnow) tests. Very un-scientifically I throw the data against a bunch of different known distributions and fit the parameters to the data (I think the `scipy` library uses MLE as the fitting method) to see which one matches the best. I didn't test any discrete distributions because honestly I couldn't get fitting to work and I didn't want to spend a bunch of time on that. Note: Our data is discrete, so the absolute K-S probability values are going to be tiny. But since we are only comparing them between each other it should be fine (again: This is not scientific, but just for fun. ^^). I tested the following distributions: normal, beta, cosine, semicircular, von Mises, chi, chi2, gamma, Student's t Some of these distributions only work on the range [0, 1], so for the comparison I moved the data accordingly. The distribution that's the closest match is actually the gamma distribution. With a ginormous α value (1110.2) but moved and scaled accordingly. I wanted to plot it but Desmos just bugged out - understandably so. Additionally, since gamma can only deal with variables > 0 we'd additionally have to move it. Let's discard that one since I just don't know how to deal with that. ^^" The next closest is the chi distribution with a k value of 137. Again scaled and moved to accordingly. Same problem, though less sever - let's discard it. This brings us to our 3rd and 4th place: The normal distribution and Student's t distribution. Both have pretty much the same probability value in the test. Looking at the parameters it's obvious why that is: The parameter v is 82104712197. Since the t-distribution converges to N(0,1) with v tending to infinity, we can effectively call them identical. Let's give the win to the normal distribution since the t distribution would need to be scaled and moved (again) and because of this ridiculous v value I can't plot it anyway (Damn you, Γ-function!). ^^ Let's take a closer look at the normal distribution: μ = 0.1829 σ = 1.5710 So the mean value is actually quite good, but the standard deviation is almost 60 % too big. Looking at our graphs we can see that the overall shape of the poll result (blue dots) is way to spread out to fit the target distribution N(0,1) (red), but fits reasonably well to our calculated distribution (green). The obvious exception being the point at x=0 which is noticeably favoured by the participants. That was fun. I should do something similar again some time. 😊 (📎1) RE: Can we approach a normal distribution with µ = 0 and σ = 1? Please share so we get a pretty graph. ^^"