On Saturday, I posted a poll asking readers to simply pick a number between 1 and 20. I promised I'd explain what this is all about, so here goes.
The poll was inspired by this post on Pharyngula, which in turn was inspired by this article on Cosmic Variance. The idea is that 17 will always be the most common answer when people are asked to choose a number between 1 and 20. But neither Cosmic Variance nor Pharyngula offered a reasonable means of testing this proposition. That's where our poll came in. This morning, I took a look at our data, and with 347 responses, I can confirm that 17 is significantly more popular than any number. Take a look at the chart:
As you can see, the number 17 was picked much more often -- almost 18 percent of the time, compared to the 5 percent you might expect from this sample.
But even random numbers aren't perfectly distributed -- if you roll a die 6 times, you most likely won't get one of each number. Perhaps in a truly random sample, we'd see a similar distribution. So I had my computer generate 347 random numbers in the same range and plotted them in light blue on the chart. Using the computer, the number 19 was most common, but it was chosen just 8 percent of the time. Humans picked the number 17 significantly more often than the computer picked 19.
Are there any other patterns in numbers humans "randomly" choose? Take a look at this chart:
Humans picked odd numbers significantly more often than the computer did. But how much of that effect is due simply to the larger "17 effect"? Consider this chart with the 17 data removed:
Now there is no significant difference between the values picked by humans or by the computer, and both results are no different than the theoretical "random" distribution of numbers.
What about prime numbers? Commenter Fletcher suggested that prime numbers seem more random, so they are more likely to be chosen. Here's a chart of those results:
Yes, we do pick prime numbers more often than computers! A similar analysis, removing "17" from the results, diminished but did not eliminate the effect.
Clearly humans aren't very good random number generators. We predictably select some numbers more than others. If I were to repeat this experiment with a naive audience, I'd very likely find "17" to be the most popular random number, but if I repeated it with the computer, a completely different number would most likely emerge as the preferred number.
Note: There is a wrap-up of all the reaction to this post here.
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You can do a chi-squared test with your data.
It looks like the number 7 is also popular with people. I bet 7 is popular because of our culture. I also bet that people who pick 17 first think of 7 then think that is two obvious so they pick 17.
Don't you psychologists ever put error bars on your "charts"?
"Too obvious" that is.
Yes, psychologists put error bars on their "charts." However, this blog is intended for a general audience, and error bars can be problematic. Are we talking about confidence intervals, standard errors, or what? Lay readers do not understand the difference, and the end result is that they make incorrect assumptions based on an incomplete understanding of the underlying statistics.
Take a look at this post for a good explanation of the difficulties in presenting error bars.
Reed is onto something, I think. It would be interesting to see the results if subject were first primed with a reading sample that involved a heavy use of odd numbers, including 17.
I think humans tend to construe "random" in a non-mathematical way. The interpretation is closer to "uncommon."
Significant how? .05 level? With a binomial test, I presume?
Perhaps this can be seen as a version of the typicality effect. If I ask you to name any bird, you're more likely to say "robin" than "penguin". This effect is explained rather cleverly by connectionist models of memory (e.g., McClelland, gah, lost the reference). In these models, the effect appears because the network favours prototypical nodes - i.e., nodes which are connected to a lot of other related categories, which are presumably also activated by the request to name a number. The most typical member of the category will activate most strongly, and will thus determine the output.
Of course, this only gives an account of the hows, not the whys. I would think that 3, 7, etc would be more typical numbers than 17.
As someone who choseeht number 17 perhaps I can offer my personal insight - I was looking to select the most unlikley number (sorry!). In this sense i wonder if this is actually a measure of percieved least common number rather than random selection - there is a body of research about the ability to actually generate random numbers being very difficult for human subjects (methinks Sallice, T).
In Italy, 17 is considered unlucky, like 13 is in the US, with Friday the 17th being particularly unlucky...
The only problem with this is that it's highly likely many of those who took the survey had read the Pharyngula and/or Cosmic Daily post, compromising the results.
After the Language Log post on 17 back in December (I think that's when it was), I became so curious that I started asking participants for a random number between 1 and 50 at the beginning of every experiment. I'll have data sometime between now and the end of the semester.
My stats knowledge is baby-simple. I first use an unpaired t-test, and if that doesn't give good results, I move on to a paired test (p<.05). That's pretty close to the limit for me.
....that should have been "chose the" not "choseeth" - monitoring failure
I think the answer is bisection. Our minds first go to (20+0)/2=10 but then we think, oh that's too obvious. So we next choose (20+10)/2=15. Nope, still too obvious. Then we go (20+15)/2=17.5, round it to 17 and the loop ends, because we are getting too close to 20 to be comfortable.
Nonsense, probably, but that is what comes to mind...
I wonder if the fairly uniform distribution of n*7 modulo 10 (7, 4, 1, 8, 5, 2, 9, 6, 3, 0) has anything to do with the popularity of 7 and 17. I'd bet (x*10)+7 is preferred for most "random" ranges (more so for primes -- and just under 1 in 4 primes less than 100 is 7 modulo 10.)
Here is a nice web site about numbers. Scroll down to see number 17.
If you follow the link on that page you can see that 37 is also claimed to be a "psychologically random number".
Nice swooping pattern to the graph too.
Ascending (sorta) into 7, then descending to 10; ascending back up to 13, then descending to 15/16, etc.
People do not understand the word "random". I suspect that, similarly to Austin's comment, we want to pick an unusual number, perhaps to offset the expected "typical" numbers that others will pick. Notice also that 4, 10, 15, 16, and 20 are under represented in your graph. [Me, I selected either 1 or 20 thinking that they would be under selected. Maybe I don't understand random either.]
Perhaps trying a pair of tests, one asking for a random number and the other for the least likely number to be picked could show that many people have this common confusion of the word "random".
i wonder what would be result of an equivalent experiment carried out on some of our primate cousins? Experiments do suggest that rhesus monkeys, at least, do posses the capacity for "spontaneous number representation."
The famously irritable Phineas Gage said:
". If I ask you to name any bird, you're more likely to say "robin" than "penguin"."
I'd like to see a poll of this. I, for one, would be more likely to say "penguin", probably because of its ubiquity in pop culture. I mean, no one ever heard of an exploding robin on the telly.
This also works with Battleship. Inexperienced players tend to think that certain positions are less "random" than others. They thus tend to shy away from putting their ships on edge or center positions. They also tend to shy away from putting shots onto those positions. When starting to learn to play battleship, this is always one of the first things you have to unlearn.
nice post. just a little note on the statistics: doing only one simulated data set is a little, well, worthless. the goal in a simulation is to estimate the actual distribution of a quantity (in your case, the number of '17's) under the null hypothesis, so you'd need to do a lot of them. Luckily, you already know the distribution you're looking for! It's a binomial with parameters n=367 and p=1/20. So can you reject the null hypothesis at p=0.05 based on your data? I leave this as an exercise for the reader.
Try it in base 16 and see what happens:
I'm not sure how best to present that to a subject, but I would want to try to find ways to separate how much a subject is responding to the numerical concept vs. the numerical symbol. I would think the associations to each are different.
I definitely think people think "unusual" when they see "random". I think that must have happened a bit for me, because I chose 19, which is also a prime. I also like the "7...no, 17" explanation because I do think 7 is many people's favorite number, so I'm not surprised it was chosen a lot, too. I do think people consider 17 to be more "random", though.
I attended a math camp (cult?) where the running joke was the awesomeness of the number 17 (and yellow pigs). The camp director, David Kelly spent a lot of time finding interesting properties of the number 17. An often recounted story is that in a competition between supporters of the number 23 and 17, Kelly and Co were able to name two interesting properties for each interesting property of 23.
Check out the math camp's website: http://www.hcssim.org/
My calculator couldn't handle the concept of 347 trials (too large numbers), but even if you reduce the number of trials to 50 the choice of 17 this many times has a p-value of 0.0005, i.e. statistically significant. And so if there were even more trials, that would only make it less likely, and more significant.
There's a real effect here, both intuitively and statistically.
I think, if "7...no 17" is true, the real winner should be 7. Seventeen is just so artificial. Anyway, you can play 'magician' and find out a random number someone chose from 1 to 10...and be sure to guess "7". You're sooo likely to guess it right, and it works magic with girls ;)
I wonder if the "most random" numbers are just numbers ending in 7. Maybe someone could conduct tests where people are told to choose random numbers from 1 to 30, 40, 50 ... up to 100 (or maybe just do the 1 to 100 test for simplicity). I would like to see the results.
My calculator couldn't handle the concept of 347 trials (too large numbers)
use the normal approximation to the binomial.
i'd say numbers including either 3, 7, or a combination of the two are more popular as 'random' simply because of the high chance of being prime, and the preconception that the other numbers are more common.
You may want to look into the James Bond roulette theory. I can't get to any of the articles because of a filter at work, but I remember reading that 17 black is the most played number in roulette because James Bond played that in one of the many James Bond films. Perhaps you could do another survey and try to filter out people that have seen those films? Maybe try it with small children?
> Clearly humans aren't very good random number generators.
Roll an ordinary die 100 times and sum the results. Do this repeatedly. You expect to see more results hovering around 350 then elsewhere. We have a bias towards 350. Are we to conclude therefore that dice don't generate numbers randomly. Of course not. The very theory that assumes they are random suggests that we should expect more results around 350. Similarly, the fact that humans prefer 17 to other numbers is in no way an argument that humans aren't very good at generating random numbers. It might be an argument that humans aren't very good at generating uniformly distributed numbers. But as you didn't ask people to select from a uniform distribution, you simply said 'random', you haven't tested that either.
Just to try this out I asked my buddy sitting next to me to think of a number between 1 and 20 and she chose 17 how weird
It's silly to even plot the computer output. If you did more trials, and had a proper random number generator then the distrobution would be even along all the numbers. Always.
Although I think the title and description of this article is misleading, it is interesting. The word "seven" is aesthetically pleasing, in a poetic way. "Seventeen", containing the word "seven", also has the same effect. When you, as a human, are asked to come up with a number, you're thinking of a set of words that represent a number and choosing the one that appeals to you. Just a thought.
For years now 17 has been a "magic" number of mine, showing up everywhere I look. It all started with a joke about a DVD boxed-set being 17 discs large (which seemed crazy in the time before so many tv shows were on disc) and from then on any time I needed to make up a number I used 17. Now I see it everywhere. Including at 2:40 am on a Thursday morning while reading Reddit.
Also, 7 is the only digit besides zero with two syllables in English.
Add a 95% level (binomial distr.) to the first plot!
If you want to "test" whether your set of numbers is really random, it should be much larger ;) . And then you can apply the Diehard test.
You're misunderstanding "random." The reason I plotted the computer's random numbers is to show how much variance there is in a set of random numbers the same size as our poll's sample. The dotted line shows the theoretical limit that a random sample approaches, but with a small sample, there will always be variance in a set of random numbers. As I said in the original post, if you roll a die six times, it's extremely unlikely that you'll get one of each number.
Welcome, Reddit readers!
I don't have a Reddit account, so I'll answer some of the questions in the discussion thread here.
Yes, this is true, but many people misunderstand what random numbers are, so I wanted to give a quick explanation of why random numbers do not, in small samples, evenly distribute themselves along each value. When you say "If they were 'perfectly' distributed in this sense then they would hardly be random," you're saying the same thing I say: "even random numbers aren't perfectly distributed."
Next this commenter is confused about why I say "truly random." The reason is that the poll results may or may not be truly random. I'm trying to compare the poll results to a truly random sample.
Because there were 347 responses to the poll. I wanted to see if computer-generated random numbers showed as much variance from the theoretical distribution as humans do.
Most of our readers are between 20 and 29.
That was addressed in the analysis, except for the "doesn't show up much" part. I'm not sure how we would -- which numbers are you talking about.
As I mention above, that's not the point. The graphs all show the theoretical limit, e.g. if a perfectly distributed set of numbers was produced.
What you mean by "my computer generated"? You always need some specific algorithm, which computes the "random" numbers. Different algorithms may output different numbers, so those "computer" numbers shows nothing relevant.
I think you should also look at what the least popular numbers are: 4, 5, 10, 15, 16, 20. The popular 3 are 7, 13, 17.
It appears to me that people indeed prefer to choose unusual numbers, not random ones, and those common numbers are probably the ones we encounter the most, as in the number of items we see in packages that are sold in shops, for example.
But that theory is contradicted by the popularity of 12 and 8, of medium and just above medium popularity, respectively.
I'm not quite sure why people are so obsessed with the computer-generated numbers. They are a reasonable set of random numbers. For what it's worth, I used the generator at random.org to come up with my list of random numbers.
But that's beside the point. Think of it this way: I could have just compared the percentage of "17" guesses with the theoretical number of times 17 should appear in a random sample, but I wanted assess our poll using a stricter standard. The point is this: it's possible that there were more 17s than any other number just due to random chance. If you roll a die 6 times, and the number "2" comes up twice, you don't have enough evidence to show that the die is biased.
Yes, "17" was chosen significantly more frequently than the 5 percent of the time we would expect, but even in a truly random sampling of a finite number of numbers, we would expect that some numbers would come up more than 5 percent of the time, and some would come up less. By comparing the "17" to the most common number from the computer-generated set of numbers, we can see if the large number of "17" responses the humans came up with reflected a true bias, or if they might have been due simply to chance.
There is certainly a way to do this using a statistical calculation (in fact the 90 percent confidence interval around the theoretical 5 percent value would probably do it), but I wanted to demonstrate it in a way that was clearer to people who do not have a background in statistics.
Interesting idea, but difficult to extract what's real...
Since almost all prime numbers in that range are odd, can you control for the even/odd effect? The ratio of odd primes to total odd numbers (including the number 2) might be interesting (control for 17 effect tricky here).
Do people aim high or low in any sample? (and how to control for the 17 effect again?)
Finally, is it a coincidence that spikes occur at both 17 and 7 (is the 7 in the one's spot compelling)? Does this have anything to do with the fact that we "chunk" items at about 7 (suggesting a number of "registers" in our brains). Or maybe we unconsciously think of 7 as the most powerful hashing number (largest single digit prime)?
I would have guessed that people shy away from the range boundaries.
Some other good comments here:
My first thought was what effect does language have on the results? I'm making an assumption that most people who answered that survey spoke English. I wonder if the results would be different if you polled people who spoke other languages.
Weird..but interesting. Although, I'd say I always choose 15 as my preferred random number.
In the old days, i ran a dungeons and dragons style fantasy role playing game. From time to time, i'd forget my dice. At first, i found it really difficult to come up with randomization, to spice up the game. In the end, i decided to just get on with making up the story without it. So, no, i'm still not very good at generating randomness. But so what?
David Blaine does a magic trick on this. he asks you to pick a number between 1 and 1000, a lot of people choose 333, 666, or 999. give 20 to 1 odds and you will come out a winner.
he also does it with cards, most people choose the ace of spades, queen or hearts, five of clubs or ten or diamonds.
you made it to Digg! well done.
@Stephen - its normal for people to have difficulty coming up with random numbers - it appears to be as much an effect of working memory capacity (after a point you cannot maintain previously generated numbers in memory) and a monitoing failure of some kind.
There are some great points on digg about how come if 17 is so random, how come so many people chose it - it suggests that the number (in the context of other possible selections has some 'activation' during retrieval (perhaps the least activated) which would support the idea that this is a measure of uncommonness of some description - which is, of course, very different to random [within the 1-20 parameter])
apologies ofr all the brackets
How many of the people surveyed were gamers?
In D&D you roll a D20 to hit and most players have figured out that a 17 will hit most anything the DM throws at you. Also, if you give a number higher than 17 the DM is likely to want to look at the die for verification.
Thus, most gamers will report they rolled a "17" when asked to roll a D20.
In comparing our choice of primes vs. non-primes, did you do anything to correct for the fact that primes are relatively rare? For instance, in 1-20, only 8 numbers are prime, but 12 are non-prime (kudos on using the term "not prime" rather than "composite"). I've forgotten most of my stats, but it would seem that this fact would make our preference for primes even more significant.
The number 17 has long been recognized as the most interesting integer, championed at the math program (see www.YP17.org) from which numerous 17 facts are collected.
The article caught my eye when I saw it on Digg. I had to laugh a bit, seeing that the number's appeared everywhere for me for the past couple years...it all started out with D&D where I rolled 17 more times than was liked (most were on the bad side, like failing skill attempts and taking damage, again showing how even though a die is random, it still came up a lot for me) and the most recent instance is my friend (a Colts fan) blaming me for the Bears losing (I'm a Bears fan) in the Super Bowl because they scored 17 points. In all, it kind of reminds me of the new movie The Number 23...which ironically enough in base 16 is seen as 17.
Put down the Transformers and Star Trek trading cards and go outside!
Random is trying to figure out which jock is going to smash your DnD set, which undoubtedly, your are still playing in High school.
how did the people enter their number? did they just type it in a box or was it a "drop down" selection. if the latter, people could be influenced by the order of the numbers they are choosing from i.e "picking towards the "back""
When asked what day it is, people respond quickest at the weekend and slowest on a Wednesday. What does that have to do with the number 17? Well, like Wednesday, it is the midpoint in your list of options.
Because you asked the question "pick a number between 1 and 20", automatically you reduce the chances of someone picking either endpoint.
People will also avoid choosing the midpoint (10) because they anticipate this will be a common response.
Effectively, this divides the list of options into two sub-lists. People are unlikely to pick the endpoints of these sub-lists because of the reasons given above. They are also less likely to give the midpoints of the sub-lists (5 and 15).
People also have a tendency to give a response from the second part of a list. 17 is smack in the middle of the second part of the second sub-list while 7 (another high scoring response) is in the same position in the second part of the first sub-list.
People tend not to make more than two divisions and can be greatly affected by the manner of presentation (whether they are required to type their number in, select it from a list or choose it from a jumbled pile. Also, the results may be more/less pronounced if you use a bigger sample.
True story: A friend teaching a math class years ago had derived some equation and told the class to pick a value for "x" and calculate the result. "What value" someone asked. "Any value." "But which one?" "Seventeen," my friend answered. "Why seventeen?" came the inevitable query. His reply...
"Well, zero times anything gives you zero, so too many things will cancel out. One times anything doesn't change, so that's bad, too. Two and three are too small. Four is a perfect square so that may cause some problem. Five is half of ten, and anything in a decimal world is probably special. Six is a perfect number, so that may affect your results. Seven is too lucky. Eight is a perfect cube. Nine is a perfect square. Ten we already covered, and eleven is too close to ten. Twelve is divisible by practically everything so something is bound to cancel out. Thirteen is unlucky, fourteen is twice seven so it's too lucky. Fifteen we covered, sixteen is a perfect square and even it's square root is a perfect square. Eighteen is twice a perfect square. Anything bigger and by the time you've raised it to some power the results are too big to handle. That leaves seventeen!"
This is kind of funny...I was unaware of the most commonly picked number when told to pick a number between 1 and 20, but I know that if you do the same experiment with 1-4, it will be 3, and if you do 1-10, it will be 7(or 3, unless you've already asked 1-4 prior to asking 1-10). Why do I know this? Because if you do 2 of these in sequence with an idiot in a bar, they think you're a psychic. So, yeah...it's a bar trick. But maybe you want to study the human psyche a little bit more with these other experiments.
Before any more wannabe psychologists start boring me with their "explanation" lmao
The explanation is simple.. Its random! Nothing more than that.
Do the whole thing again from scratch.. Some other number will come out first.
Then again from scratch!.. Another number will come out fist and so on and so on.
How on earth anyone can think otherwise is beyond me! I suggest you all go back to school and learn some common sense!
17 was predicted before we did the experiment. It's not random. And if you take a look at our analysis, we show how the results differ from a true random sample.
I also disagree. If you'd like, try it for yourself. Ask you friends, family, etc. Most of them will pick these "favored" numbers over others more often than not. I haven't tried the 1-20 thing, but I do know that some numbers are just picked more often than not when people are asked to pick a "random" number between 1-4, 1-10, etc. There's probably a number that will be picked more in every set of numbers...1-50, 1-100, etc.
You need to ensure that your random number generator was not using a pseudo random number generator, which would give a predictable order of random numbers every time, given that you know the seed (probably the given time of the sample's creation in milliseconds).
There are systems for acquiring "truly" random numbers, but pseudo random are not one of them.
I don't think that you can say based on these human results that the fact that 17, or any of the other prime numbers (1, 2, 3, 5, 7, 11, 13, and 19) are the reason to be picked because I think it's a lot more generalizable that most people do NOT particularly understand prime numbers.
I am just wondering... do any of you know what logic is? We use logic for a reason.
Brett (Comment #54) pretty much hit it right on the head.
James (#57): There is no such thing as "random."
LOLLLL , i just i ask my friend get a number between 1 and 20 and he response me 17 :p really amasing !
347 responses is not enough and it makes me wonder why the results where revealed after such a "small" amount of responses.
It's like flipping a coin predicting "heads" and stopping on the first flip because you got it right. This could just be a coincedince, stranger things have happened!
Lets see 30,000 even 300,000 responses and perhaps I'll eat my own words... But I doubt I will be doing.
Go out today and ask some random people this question. I gurantee that no matter how many people you ask, the majority of the time, the answers will be the same. I don't know if it's a societal quirk or what, all I know is that it's definately true. Maybe a survey consisting of 347 people isn't very substantial, which is why you should go out and ask some people on your own. Seriously, try it. You won't need to ask that many before you're convinced.
People are avoiding 5, 10, 15 and 20, because they're quarter/half/threequarters: too round, too regular and don't feel random. People feel that they're supposed to pick a "strange" number, a "hard-to-guess" number, an 'out of the ordinary' number so they go for the ones they feel less comfortable with.
Also, 1 or 20 don't feel like they're "between" 1 and 20.
Plus there's an element of "game" to it. I automatically pick a number that would be hard to guess, thinking I'm trying to trick the person asking, making it hard for them to "win."
There's an element of challenge when someone asks you to pick a number.
Plus... There's something slightly hidden about Seventeen. 2,3,4,5,10, 12, 16, those numbers feel like they're out in the bright light, but numbers like 7, 11, 13, 17, 19 feel like they're off to the left, hidden in the dark...
Wow, that's bizarre, I never thought that before...
Hey look at me, I'm a Savant!
As someone who picked 17 myself, I can say that the reason I decided to choose that particular number is because it is the "hardest" of the numbers from 1 through 20 for me to do simple math calculations with. If you were asked to multiply any of the numbers from 1 to 20 by another small number, which would give you the most difficulty? Even numbers are generally easier than odd, so that rules out all evens. The number one is of course simplistic. Three is also fairly easy. Any number that is a power of 5 is easier than the norm, and any that are just one digit off from a power of ten would also be fairly simple. That leaves 7, 13, and 17 as the only remaining numbers, which are amazingly enough the three numbers most chosen in the survey! Maybe not a scientific explanation, but that is my reasoning for why those numbers were most chosen.
Thing is, you asked people to pick a number. You didn't ask them to pick a 'random' number. I would answer differently if asked for a 'random' number, I think. If 17 would have been my answer, the idea that my answer should be 'random' would have thrown me off its scent, so-to-speak.
The movie '23' is coming out soon. I laugh at the 2/3 = .666 used in the trailers. Well, duh! So? Numerology in and of itself is quite a silly exercise, fraught with cultish implications. Monkey's in pants giving street cred to 'special' numbers, thus propagating the beliefs in self-fulfilling ways. 3 is holy. 4 is square (man). 7 is lucky. 13 is unlucky. 17 is random. Yeah, right.
Just to split hairs...
The original request was to pick a number between 1 and 20. Strickly speaking, 1 and 20 are not BETWEEN 1 and 20. Correctly, the instructions should've been somethink like "pick a number in the RANGE of 1 to 20". Yet more correctly,
"pick an integer in the range of 1 to 20". ;-)
I would say that we can do perform random numbers as the computer. Just limit in about 5 seconds to answer the pool.
I chose 5 seconds because we would not be able to associate a number to any memories, those who not respond in time cant be computed.
I wish that people will stop challenging wether or not 17 is the most likely answer when asking someone to choose a number between 1-20. By the way, it is almost irrelevant to ask them to choose a "random" number; first because there is little difference between choosing and choosing randomly -a somewhat rational person does not develop any sort of attachment to one number over the other, therefore choosing and choosing randomly *should* be the same...unless you're getting married to the number-
and second because they do not understand probabilities.
The proof: they are actually trying to find the least likely number when, in fact, each number is equally likely: *randomly*pick any number and no other number will be less likely, more likely, more typical or rare. This whole thread seems to revolve around one topic: people's refusal to believe that heads is just as likely to turn up as tails, following a head landing. Lastly, Jake in post 56 touched up the last point of this post. When picking from 1-4 (and more likely picking 3)then picking from 1-10, picking 3 once again is less likely because "it has allready been used".
People!!! Random Number Generation is equally likely -no least likely numbers-, independent -your last pick or the last outcome is irrelevant and bears 0 influence on the probabilities of the next outcome- and with replacement -Yes!you will randomly pick the same digit twice once in a while. And NO! two reds in a row @ the roulette is less likely than "not-two reds in a row" but this is actually a composite of black then red and red then black, so when adjusting the pool for the fact that black did not happen in the first spin, they are...equally likely-
Even still, the lack of understanding of probabilities should not in any way hamper one from choosing randomly, it is the fixation on a number(s) or "preferential" treatment that is the obstacle.
As much as i would like to know why people pick 17 (and 7 and odds and primes), i would also like to know why we prefer a number over another or what makes a number attractive. Maybe someone can fill me in?
17 is a Full Reptend Prime, as is 7 which is weird that those two got more hits than any other in the first chart. 17 = 0.5882352941176470
If I'm correct, 17 is assumed to have a bad luck in Italy. I think it's a good idea to test the experiments on Italians too, so we can observe if choosing 17 (and 7) are related to cultures or not.
So, was I the only one who noticed that the average number of people who picked each number was`17? (347/20 = 17). I wonder what the cosmic significance of that is.
This topic isn't really about statistics, it's about psychology.
Also, I wonder what the effect would be if people were asked to pick more than one number. I bet even asking for two numbers would make the data look much closer to a uniform distribution. People tend to play games for their first number, but I think subsequent guesses are picked in a more random fashion.
I'm a bit curious why 13 doesn't show up higher in the stats. I'd hypothesis (pardon if this has already been mentioned above, I recall a similar topic on Scienceblogs anyways) that people tend to pick unfamiliar rather than random, as 7 and 17 are primes, there's not so much familiar with them than numbers than have more common primes (2, 3, 5) as factors (i.e. 6 is just 2*3 or 15 is just 3*5). Also a bit weird is that 7 is so significant. I guess that's a number that's slightly too big for human intuition, thus feels unfamiliar. Perhaps the 3 in the 13 confuses people. I wonder if the range was larger, would 27 show up? My hypothesis says that 17 would get more votes, since 27 is 3^3.
A facinating topic anyways, as any topic in cognitive psychology. If peoples' intuitive understanding of randomness is this bad, no wonder people (or politicians) have difficulties with risk assessment, as evidenced by idiotic flight safety regulations.
What I find absolutely incredible, perhaps I should say improbable, is that ALL of the answers are not very "random." Perhaps the first "MOST random number between one and twenty" that I thought of within five seconds is (pi times e), even being non-rational yet it fits the guideline asked for. Out of an infinity of numbers between one and twenty, every one chose a subset, the integers, of the larger class of rational numbers, and ignored an infinity of others. I fear we are, in this instance as well as innumerable others, victims of our unjustified assumptions.
Of course we Illuminati start with 23, then add 2 (yin and yang) making 25, which we use as a base. Then since we've forgotten what the question was, we know the answer must be 42. And 42 modulo 25 is, yes, you guessed it randomly, 17 (sick!) ;-)
A friend of mine had a 3x5 card with "1 2 3 4" printed on one side. He would show it to someone and say "pick a number". When they replied with their choice, he would turn over the card, on the other side of which was printed "why 3?". I don't recall ever seeing it fail. People invariably picked three. Try it.
This effect is obvious to me, and has been since I was a little kid. No testing involved.
If you simply pay attention to how you think, you know exactly why this kind of thing happens.
We generate this number by ELIMINATING numbers that we can not use.
Because when you ask a person to come up with a random number, the human mind reinterprets this to actually mean: Think of a number that does not fit a pattern or rule.
Of course, this is in itself a rule !!! And is why 17, then 7, are most popular.
Here is how the brain does this:
1 - You can't use the numbers at the ends.
2 - You can't use a simple multiple of the range... so 5, 10, 15 are out.
3 - Even numbers suggest a pattern , so they are avoided too.
We are down to 3, 7, 9, 11, 13, 17, and 19.
4 - We are normally asked to choose in a range of 1 - 10, but since we are offered the novelty of choosing in a wider range, we will choose from the new range (fresh numbers).
5 - The 11, and 19 are too close to the ends of the 10-20 range. so they are out.
We are down to 13, or 17
13 has special meaning so we can not choose that.
Now, the order of these rules are approximate... but the brain, in trying to avoid obvious numbers, ends up at the same solution far more often.
I would be interested to see results from people that had no knowledge of the bad luck of #13.
It may also be worth pointing out that 17 is a sacred number to discordians, because, as it was explained to me, "it's the only number between 0 and 20 that's not sacred to someone else already."
Why not get people to pick letters between A and T, if they pick Q - the 17th the most then that would be truly wierd. But then they may pick Q the most since it seems the least likely that anyone else will pick.
Perhaps it is because of a sports figure?
Football, Baseball, Basketball, Hockey, Soccer (Futbol), etc. Players almost always have a number on their jerseys. Also could be something like Apollo 17 as well.
You should use a permutation analysis to test what percentage of the time a computer generates a number with a frequency of 18%. A chi-squared test is not the most appropriate because you're testing multiple samples, e.g. 1, 2, 3, 4, 5, ... 20, and no multiple correction method is perfect for estimating the p-value.
Nevermind, I did it:
I did 250 trials, of 347 excel-generated random number submissions each. The AVERAGE frequency of "17" in the 300 trials was 0.0498, which is within the expected range. The standard deviation is at 0.0114, with the maximum being 0.081, and the minimum being 0.02305.
This puts the p-value at WAY below 0.004 for BOTH 7 AND 17! Exactly estimating the p-value will require many more trials.
Addressing some concerns:
We actually do not need to test for multiple comparisons because it was declared a priori that we were looking only at 17.
Typical random number generators are absolutely fine for these things. I see a lot of users on here that like to try to sound "smart".
The fantasy author Steven Brust is famously (and self-admittedly) septadekaphilic. In his series world of Dragaera, 17 is an explicitly "magical" number.
Dam, I tried this on my dad, but he picked 20.
I noticed that 20 was the "least" random number for humans. lol
I don't know... it maybe there's nothing to do whit it... but seventeen represents the year before you torn overage... lol
Funny- whenever I'm asked to generate random numbers, usually in a classroom setting to prove a point, I try to pick numbers that are what I consider to be balanced. Usually about half odds and half evens, 20%-30% primes (1-100), and not too many repeated digits (ie. many numbers ending in 6 or beginning in 9).
I don't know to what extent I'd choose 17 over others when asked to choose a random number between 1 and 20.
I think there are two issues at work here that boost 17's popularity. First, I am on the side of those who suggested that many American's natural impulse is to select 7 first, then think it is too common and change their response to 17.
Second, I think there may be some testing error in the word random. For instance, if you were describing an event that was very odd, or strange, I many people today might describe it as 'random'. Even though it doesn't really have anything to do with the possibility of the event's occurrence. I propose that there are a significant number of respondents (probably about 17%- pun) that choose 17 not as a random act, but because the number seems more strange or odd than others below 20.
In fact, as I think about it, 17 seems to be the first counting number to which I can't attach any strong significance.
1- the beginning, whole, single, penny
2- pair, even, double, half
3- triple, triad, third
4- quarter, 25%, a perfect square, 4th of July
5- 20%, nickel, fingers on a hand, easy to multiply
6- perfect number, days of creation
7- lucky, days of creation and rest, days of week, many more
8- lucky in China, even, perfect cube, prime-time TV start hour
9- perfect square
10- decimal system counting, easy to multiply
11- considered lucky (esp. with 7)
12- dozen, number of apostles
13- considered unlucky
14- double 7
15- divisible by 5, easier than many numbers to multiply/divide by
16- perfect square
17- ??? (true, it's prime, but I haven't mentioned that for the others)
Considering that most of the other numbers have something that appears to make them less odd (strange) than 17, if I were counting up from 1, and looking for the first strange number I encountered, 17 would probably be my choice. It might also be my choice if I was forced to vote for a number between 1 and 20 to be eliminated from the number line, since compared to the others, it seems to have so little value attached to it.
A possible revealing follow up would be to determine which, if any numbers respondents thought off, then discarded before settling on their final answers- particularly those who suggested 17, since there is clearly something that causes it to be more selected than others.
Fun blog topic!
Better not get anyone from a certain dorm at MIT here...
Only one number squared is between 282 and 290... And about a hundred others.
And Man invented the computer and it doesn't even like seventeen.
When a freshman at Penn State too many years ago to count, the intro psychology prof did an amazing demonstration. I wonder if anyone knows the answer to this which I have long forgotten.
He said he had written the numbers 1 through 5 in random order on a piece of paper. He then asked the very large class to read his mind and write down his number order.
When the class compiled the answers, more than 50% of the class had his order, and so proved that telepathy was possible!!!
The class was ecstatic, until he then told us that humans more often than not arrange those numbers in that particular sequence that he had.
Does anyone know what that sequence order is?
I have puzzled over this for years since.
Bobbysoxer: Maybe we should try that one on the next Casual Friday.
I always play 17 at the roulette table. It is also in a very central position. I wouldn't give this secret away, but what are the odds that someone reading this blog will be at the same table?
I choose 11 between 1 and 20 and 15 between 1 and 33.