Although most researchers understand the importance of careful and rigorous statistical analysis and try to avoid embarrassing errors - there are types of errors that are impossible to avoid at the level of the individual study or the single researcher
Statistics is an important tool in many scientific studies. Almost every academic degree, whether in the natural sciences or in the humanities and social sciences, also includes statistics and probability studies as an integral part of the curriculum. And yet, although most researchers understand the importance of careful and rigorous statistical analysis and try to avoid embarrassing errors - there are types of errors that are impossible to avoid at the level of the individual study or the single researcher: errors that no one is to blame for, yet they constitute a difficult problem in many fields of research. The mistake known as the 'contingency effect' is such a mistake, and to explain it - we will turn to the world of football.
The 2010 World Cup soccer competition was, like all the competitions that preceded it, full of big stars: Casillas, Drogba, Xavi, Ronaldo, Messi... The 2010 World Cup also introduced us to two new, less expected stars. The first was the Weasel, and the other: Paul the Octopus.
Octopuses are extraordinarily intelligent animals: they have an excellent memory and are able to solve simple puzzles with surprising agility. Some compare the level of intelligence of octopuses to that of dogs, for example. Paul, an octopus in the maritime center in the city of Oberhausen in Germany, is also endowed with such wisdom - and perhaps also a completely different kind of mental ability.
In the European football championship held in 2008, Paul managed to guess the results of the games of the German team in four out of six games. This cautious success led Paul's handlers at the Maritime Center to allow him to predict the results of the 2010 World Cup matches as well, perhaps to try and attract media attention and gain some new visitors.
Since octopuses cannot speak or write, Paul's method of guessing was the heuristics based on gastronomy, or in other words - food. The caretaker would lower into the aquarium two glass containers containing identical portions of oyster meat, Paul's favorite food. On each container was a flag of one of the contestants - and the container from which Paul chose to nibble first signified which team would win the match.
Germany's first game was against Australia, and Paul chose the German container. Germany won. The second game was against Serbia, and Paul - in an admirable display of character - went against local patriotism and voted for the Serbs. he was right. In the third game, Germany faced the Ghana team, and Paul chose Germany. Well, even Medusa would take this bet in stride.
But when Paul determined that Germany would beat England - and he was right - it was impossible to deny that there was something different about this octopus...
Football fans from all over the world rallied to curb Paul's menacing powers. An Argentinian chef posted on Facebook a recipe for cooking octopus meat, in an attempt to exert psychological pressure on them - a rather desperate attempt, considering the fact that octopuses don't really have psychology, at least as far as we know today. When Paul predicted that Germany would lose to Spain in the semi-finals, the Spanish prime minister offered to send bodyguards on his behalf to prevent German fans from eating Paul - although he may have been joking. I hope. Paul completed a streak of eight successful predictions out of eight attempts, when he predicted that Spain would beat the Netherlands in the final.
Well, what is the secret of the octopus's power? Paul passed away only a few months later and took his secrets with him to... where octopuses go to die. Apparently he breathed his last just a few weeks before the Israel Football Association was going to offer him the position of national team coach. Lucky for him, if you ask me.
But the statisticians already know the secret. According to the accepted theory, Paul's chance of guessing all the correct results in the World Cup - on the reasonable assumption that all the guesses are completely random - are around one in 250. This is not a particularly high chance, but not impossible either. Why, then, did Paul get so much publicity? The answer lies in the 'contingency effect'.
In any scientific study there is a chance that despite all efforts, we will end up with an improbable result. Suppose, for that matter, that we are testing the effect of a drug on a rare type of cancer and suppose that the drug, unfortunately, has no effect on the disease at all. If a hundred researchers around the world test this drug in controlled trials, 99 of them will get the expected negative result: the drug did not work, and the cancer was not cured. But there is a certain probability that the hundredth trial will receive a positive result for reasons that have nothing to do with the drug itself: the patients participating in the trial recovered for another reason - perhaps a change in diet, or any other earthly reason.
It is clear that if 99 experiments claim that the drug is not effective, and only one finds it to be effective - the drug is not effective, period. In practice, however, the 99 researchers who failed to cure the cancer will take the trial report, shove it in a drawer and never publish it. What should be published? The experiment did not produce any substantial results... but the single researcher who did manage to produce positive results, will hurry to publish his research. The result: the medical world mistakenly concludes that perhaps the new drug is effective. This is the 'contingency effect'.
The contingency effect, then, is an error caused by the inherent randomness of our world and the way scientific papers are published. To try and fight it, there are a number of professional journals that have announced that they will not accept studies for publication if the researchers do not report their intention to start the experiment ahead of time - so that the magazine's editors can make sure that they will report their results later, even if the results are negative.
This is also what happened to Paul the Octopus. It is likely that all over the world, in all the last ten World Cups (and maybe more), people tried to use animals to try and guess the results of the games. Since animals don't really understand football, all these attempts failed - and that's why the media wasn't interested in them. Who wants to hear in the news about Rex, the dog who failed to guess the results of the World Cup? All those failed attempts do not reach the public consciousness and go, metaphorically, into the drawer.
But if enough animals try to guess the results, one of them will succeed - and only blind fate determined that it would be Paul the Octopus. Indeed, according to Wikipedia, in the same games, Leon the Hedgehog, Patty the Hippopotamus, Jimmy the Pig and Anton the Monkey also tried their luck at guessing the results of the games - all of them missed at one point or another. Anton, by the way, claimed that Ghana would win... and it wasn't the first time that the "monkey" got the interpretation wrong.
[Ran Levy is a writer and hosts the podcast 'Making history!', a radio show about science, technology and history.]
39 תגובות
As a complement according to Ran
Sometimes the experimenter intervenes in the experiment to achieve desired results. This also happens. Especially if it's a restaurant chef who has an octopus who doesn't really understand football. So you can plant in the "right" bowl delicacies that Paul the octopus likes. Although the octopus is not always "disciplined", but often it is.
In addition: no one had heard of Paul the Octopus until it was already known that he had correctly guessed a series of games - according to the testimony of the chef, of course. So maybe he was wrong in these guesses but the concept was pushed... to the hilt.
I want to support Naaman's words, regarding our not being a rational animal.
From the amount of weak knowledge I have about the human brain, I can say that we have a "shell of rationality" (cortex): http://he.wikipedia.org/wiki/%D7%A7%D7%9C%D7%99%D7%A4%D7%AA_%D7%94%D7%9E%D7%95%D7%97
But regarding Octopus, I am not loyal to Naaman:
Guessing who will win 8 games only once is not a sign of any ability, but rather an inability to persist in rational thinking (and that is at best).
Be serious, an octopus or some other owner, will decide to take his food from a certain vessel, because he understands the connection between each flag and the football team of the country to which the flag belongs and thinks that he should eat from the vessel of the winning team?!
Who is the moron who invents these experiments??!
Avi Blizovsky - Your words about the imagination belonging to other realms are nothing short of amazing - the imagination is the one that directs science and not rationality, just as curiosity is the engine for the growth of researchers more than anything else. Humans can claim until tomorrow that they are rational and planned, but they are not (and fail when they make an effort in this direction).
Regarding the story itself, there is a persistent error in the arguments: there is an a priori and a posteriori probability, if the performance of the octopus is analyzed backwards, then guessing eight games in a row is reasonable, even if with a very low probability.
On the other hand, following Paul the Octopus and his ability to predict games ahead of time is amazing, because it is not something that can be faked (in principle)……
"Point"!
Regarding what you said in the second comment presented in this article:
I don't know who taught you statistics but you probably didn't pay them enough.
Because when a person thinks they paid him enough in exchange for the information he has, he doesn't lie to the one who paid!
("You don't spit in a well that you drink from").
Even though you didn't pay me at all and even though I don't know you, I still want to share with you what is really happening statistically in practice.
In practice, a chance of one in 2.5 million and a chance of one in a thousand is the same chance.
Why ?
Because all that is a chance of one to…. It means that at least one succeeded in something (it doesn't matter if the "success" is positive or negative).
Statistical chance is not subject to any absolute time period, which means that the odds above can always equalize if you give them enough time.
And "rare things" are not subject to the number of people who exist, but to the number of events that people experience and the number of times they notice that these events happen.
Dan Shamir:
You may pat yourself on the back, even mathematicians (and not only artists) think that the answer is illusory, but this is indeed the probability
Intuition fails in a big way when it comes to probability, no wonder even scientists are wrong about it, maybe they should consult more with craftsmen...
You bugged me and I took it seriously that this is not a joke and after about an hour and a half of thinking I came up with an answer that seems a bit delusional to me (I am after all an artist and not a mathematician) and if I am right I will definitely pat myself on the back.
The chance is 13 to 27
Options:
First son born on Monday - second son on any day of the week or daughter on any day of the week = 14
A first-born son was born on a Monday - the second a son on any day of the week or a daughter on any day of the week = 14
A total of 28 possibilities and of course there is an overlap between the two cases where two sons were born on Monday-
We will offset it and there are 27 options left, of which 13 are boys
??
I now understand your answer - the intention was to ask what the chances are that his second child is a boy
I guess you were joking in your answer but my question was serious.
The chance that the other is also a boy is one-third, because from the data of the question, the possibilities with equal probability are son-daughter, daughter-son, son-son (the assumption is that the chances of a son and a daughter are the same) and the third possibility is the one that interested us.
And now for the more interesting question (I'm not kidding):
David has two children.
One is a boy born on Monday, what are the chances that the other is also a boy?
I agree with you about the perceptual bias and to your credit you phrased it much better than me, I can only say that unfortunately the same perceptual bias spoken about is used cynically by all kinds of charlatans of all kinds.
and on the subject of the "difficulty"
His second son is of course a son
But if we add the data:
David is 84 years old
His wife is 28 years old and is a freed Frenchwoman who is with him for known reasons
And now: what are the chances that his two sons are indeed his sons?
Dan Shamir:
I tend to agree with you that there is seemingly no reason and it is mainly a perceptual bias of our minds.
As for the mixed options, we would feel the same wonder if the order of the shots happened to encode a sentence from your example, or in short the wonder is in the eyes of the beholder.
And more of the wonders of probability:
David has two children.
One of them is a son.
What are the chances that his second son is also a son?
ravine
True, to get a result according to a certain order of shots is a chance of 2 to the power of -1000 and still such a result is obtained
For each series of 1000 shots.
Why wouldn't you hold your head in amazement at every such shot?
Seemingly there is no reason, but I would guess that our mental perception of reality connects all those "mixed" results to one possibility except those blatant results in their departures from the rule.
Dan Shamir, you are talking about the chance of an event where there were x heads and 1000 minus x tails. The probability of such an event can be calculated according to the binomial formula and indeed not all of these events are equal in probability.
I'm not talking about these events, but about a specific result, a certain order of throws (if you want, an event in which the order "yes determines"). These events are all probabilities
ravine
I do not understand
Do you claim that the chance of getting a tree once and a ball once is equal to the chance of getting a tree/ball twice
After all, in the first the chance is 1 to 2 and in the second 1 to 2 to the power of two because it is mandatory to reduce the total number of possibilities
in the number of ways leading to the same result.
A result of 999 wood and 1 pellet is a chance of 2 to the power of 999 - because the screen of all the different shot combinations
1000 of them will lead to the desired result
If you do not agree, then I would ask the mathematician on the site (everyone knows who he is) to intervene in the matter.
Aryeh Seter:
You're definitely wrong.
Given an experiment in which each outcome has a probability of p=0.5 that is repeated a thousand times independently, the outcome (regardless of what it is and whether I predicted it or not) will have a probability of two to the power of minus one thousand.
And what about my question? Why is it for certain results so amazing?
Guy - you are definitely wrong. Your words are only correct in the following case: determine in advance a certain order of results (that is, for example, the first tree, the second, the third, Peli, etc.) and then if the results of the toss are received exactly in the predetermined order, then you can say that the chance of this is 2 to the power of minus one thousand.
Dan Shamir:
I am not wrong. A result according to my definition is a series of tosses (or the result of an experiment). You may define a result as you wish, but I am not bound by your definitions, only mine.
And what about the essence?
A result, i.e. the result of an experiment in which a coin was tossed a thousand times, will have a chance of 2 minus a thousand and it does not matter what the result is because it is a fair coin.
Why then on the result of a thousand heads I would hold my head in amazement while on most of the other results not so?
The skeptic,
You don't tend to argue with fixed mindsets as you defined only when you know you don't have a case.
Bring evidence or get off the scam story. Accusing without proof just because the case doesn't fit your line of thought is the biggest bias there is.
Even my father surprisingly has no answer to my question.
Guy, you are wrong
Correction of an error, in fact the chance of 2 to the power of minus 1000 is only valid for 2 results: 1000 tree / fruit
Because the chance is about the result and not the way, that is: the chance of 2 to the power of minus one thousand is valid for every result only according to a certain order of throws.
For demonstration let's take 2 shots
The chance of getting a tree-peli (regardless of the order) is half and the chance of a tree-tree or peli-peli is a quarter because there are 4 possibilities for the results:
A tree - a tree
Peli tree
Fli Fli
Peli-wood
2 out of the 4 give the result Etz-Feli (the desire for the result and not for the way), so the chance is half and not a quarter according to your claim.
Dan Shamir:
Tossing a fair coin (that is, the chance of getting one of the sides is equal) 1000 times will give a result whose chance is two to the power of minus one thousand.
Very simple calculation
David:
In financial matters, it is better not to rely fanatically on scientific models. On the opposite side of the scientific (or so-called scientific) models there is the dark side of crooks (on one level or another) who take advantage of the innocence of the "silent majority" to make money from "unreasonable" financial deals.
I mentioned who I think is behind the "successful guesses" of the octopus. (The people behind the story: bookmakers who promote their businesses by using a fraud trick that is very difficult to uncover, and not many are interested in revealing it. There are other potential suspects who profited from the "octopus" story, but this is not the place to go into detail, I don't tend to argue with "fixed minds" (Like two others who responded to the statement that arguing with people seems to be a waste of time.)
By the way, after the Octopus story, the Octopus "retired from the gambling business" a few months later he died (of old age, it is said). It seems to me that there may be another explanation for the octopus's quick retirement from the gambling business, and from life in general. The explanation is "destruction of evidence". If the octopus had continued to bet on sports competitions, the control over his experiment in subsequent bets would have been stronger and then question marks would have emerged.
And more on the same matter from another angle. About a year or two ago, a statistical combination happened with a probability of 1:500000
(Approximately), this screw-up was in the National Lottery Gambling Factory (guessing 6 numbers + an extra number).
Here is Link http://www.ynet.co.il/articles/0,7340,L-3970398,00.html
Following this lottery story, all kinds of scholars were brought to the media to explain the statistics. Just wait to bring to the broadcasts fraud experts who will require the police to conduct a vigorous investigation in an event where the probability of fraud is (it is said) a hundred times greater than the statistical probability.
Why weren't fraud experts brought in for communication regarding the lottery? Why wasn't a serious police investigation conducted following the story? Why will the whole story be forgotten in the media after a week? Because:
* The lottery supports the state (state betting is a type of tax on gamblers),
* The lottery provides means of communication (advertisement broadcasts and advertisements in the newspaper),
A vigorous investigation by the police regarding the lottery scam would have caused damage to the stakeholders I mentioned above.
dependent. If the order is important then it is impossible to reduce.
Avi,
You said and you didn't say anything... I didn't say anything about backtracking but that scientific truths are valid as long as they haven't been disproved, and they are disproved quite often because of new information or a theory that better explains the results. There is no debate about that. And by the way - science and imagination go well in science fiction - to later become reality. You must know Jules Verne.
How exactly does this have anything to do with the fact that it is allowed here to throw wild speculations about Ramya in the mouth thrown by the skeptic without proving anything?
As a matter of fact, reality surpasses all imagination and proves to us time and time again that the tools of probability theory do not work, especially when it comes to humans. The "black swan" phenomenon observed from time to time in the financial markets is in itself conclusive evidence that even 99 studies out of a hundred can be wrong. 4 and 5 sigma events occur more frequently than the statistical models predict. And this is just one example that mathematics, as we know it as a branch of logic, does not agree with the probabilities of Mother Nature.
Scientific truths change but they must explain the same findings. That is why there is no going back in science. If something is disqualified because of an experiment, even if the theory changes it will still be disqualified and if something has been tested it will have to be explained by the new theory as well. Science and imagination go well only in one place - in science fiction books and movies.
Science investigates reality.
Avi,
Anyone who claims this is defending one truth belongs to the extremist camp as far as I'm concerned.
The fact is that scientific truths change all the time, and many of them started in the imaginations of geniuses who later found the way to prove the theory.
What the skeptic did in his response is to make a wild hypothesis of the kind you come up against all the time (and rightly so) when we are dealing with creationists for example.
Why is such a wild hypothesis accepted here when it is a strange phenomenon to say the least?
ravine,
A small note
Regarding the coin toss
You really won't throw 1000 times every time, this is a chance of 1 to 2 to the power of 1000, in fact this is a chance that exists in only 4 outcomes: 2 sides one thousand and two times 999 and 1, you will have to reduce all the other outcomes by the number of possibilities to reach the same outcome.
To the other self, the skeptical camp defends one truth while the imagination has infinite realms.
If I toss a fair coin a thousand times and get heads all the times I will hold my head in amazement, is it because the chance of getting heads a thousand times with a fair coin is very small? (2 to the power of minus 1000)
But if I take a fair coin and toss it a thousand times any other result I get will have exactly the same odds!
Why then will I not hold my head in amazement?
skeptic,
Does the duty of proof only apply to the supernatural side? The camp of skeptics is allowed to speculate without substantiating??
What you wrote can also be said about Randy with the award he is waving - not to mention professional prestige and perhaps his entire career...
You've already shot the skeptics in the foot...
For I am another:
The Roman proverb "ki bono" search "who benefits")
http://en.wikipedia.org/wiki/Cui_bono
The bookmakers make a lot of money by using an advertising trick that is difficult to reveal the truth of.
skeptical,
do you have a proof? Or do you just know everything?
The other self:
The octopus guesses are probably a scam exercise by betting agencies. For example: Bribe someone who prepared the food dishes so that he adds a favorite spice of the octopus to the dish: the "correct" one of the two.
What is amazing here is that no one is amazed by this octopus...
All the statements about there being a 1-250 chance of this happening and that it was not reproduced 99 times in other attempts and therefore it is just a "coincidence" - so then there is nothing amazing here that an octopus correctly guessed 8 results out of 8?
If other experiments with animals were to reproduce this - it would no longer be fun to watch football games because we would know the result in advance... Obviously this is not the case (perhaps because it is not amazing enough for anyone to continue testing it), and there is still a completely unbelievable case here Normal - so wave it off because it is impossible to reproduce it or because there is a "reasonable" chance that it will happen?
Where did the curiosity and wonder go? Why don't you say - there is nothing new under the sun - and you will be out of business.
Guy, in any average movie much more amazing things happen.
I don't think Paul the Octopus is a good example of the "drawer effect"...
Paul received worldwide media attention after correctly guessing a small number of games
I think after I heard about him he guessed another 4-5 games correctly
I don't claim that there is anything here other than an interesting coincidence, (and maybe an intentional hand)
It's just that he probably wasn't discovered in retrospect like you describe.
Maybe I'm wrong, but I feel like this article has already been published before...
On the other hand, it might just be a feeling.
The really important thing in research is to understand the model behind the observations.
Collecting statistics and drawing conclusions "blindly" based on statistics alone is worthless.
When a researcher collects data and draws conclusions from them, he unconsciously (with a careful researcher this will be consciously) assumes some kind of model from which the data came, and only the one who gave this model can draw conclusions.
Take for example the following experiment:
A person takes a coin and flips it 10 times. Each time he got a head. What can be concluded from this? If he has to bet on the result of the next toss, how much money should he bet?
The contingency effect is acutely expressed in the fact that most of the time rare things do not happen to most people... and then when something rare happens to someone, they think it is supernatural while it was bound to happen to someone.
There are 2.5 million seconds in a month, and that means that every month there must be one second that something happens to you that the chance of it happening is 2.5 in 7 million...and if there are XNUMX billion people, think how many rare things happen here and there to people.
Interesting but long