I have to post about this so that I can get it out of my system. Has anyone else been obsessed with “Paul the psychic octopus”? It’s the only reason I paid any attention to the World Cup hoopla (no offence to the football/soccer fans). I don’t think I watched any actual games during these last few weeks, but I have literally spent hours Googling this octopus.
Paul the Octopus has the uncanny ability to pick winning teams, by selecting a tasty mussel from one of two containers marked with relevant national flags. It all began with the European Championships in 2008 where he picked 4 out of 6 winners correctly. He had a perfect track record during the world cup (8 out of 8 games), correctly predicting Spain to take down the Netherlands in the final.
Apparently he’s been receiving death threats, and his aquarium handlers have announced his retirement from future World Cup predictions. Now he has been immortalized in the form of an iPhone app (which I am downloading as I type).
Statistically speaking, Paul’s impeccable track record causes us to reject the null hypothesis, as noted by Xu Cui:
ll hypothesis (H0): Octopus Paul doesn’t have the ability to predict. Or, the probability that he predicts correctly on each event is 1/2.
Data: In 2010 World Cup, Octopus Paul correctly predicted the outcomes of 8 games out of 8 games.
p-Value: (the probability to obtain the data assuming the null hypothesis is true): 1/2^8 = 0.0039
Statistical significance threshold: alpha = 0.05
Conclusion: as pvalue < alpha, we conclude that the null hypothesis should be rejected. Loosely speaking, octopus Paul does have prediction power.
The problem here is that you’re overlooking the 800 pound elephant seal in the room: Paul the evil mob-boss octopus rigged the World Cup!
He usually picks Germany (his complete record is tabulated on wikipedia.) Because this is a source of bias on his part (although we’d need more tests to tell for sure,) and the most accurate odds estimates we have on football games are not always 50-50, we can’t make the assumptions that test needs. Maybe we could say he is predictive on games involving the German team. Maybe.
It would be great if the aquarium trained him to respond preferentially to the German flag. That would be some marketing genius!
One suggestion I saw somewhere was that he is attracted to yellow, which would mean Germany over most other flags but Spain over Germany. Which is an appealingly ingenious explanation, if nothing else.
I THINK THIS OCTOPUS SHOULD NOT RETIRE UNTIL HE PICKS UP THE WINNING NUMBERS OF THE BIGGEST LOTTERY IN THE WORLD THE AL GORDO HELD IN SPAIN, THE JACK POT IS 500 MILLION DOLLARS ,THEN HIS TRAINER CAN WRITE A BEST SELLER BOOK ABOUT TRAINING THE OCTOPUS,WHICH HE WILL MAKE MORE MONEY, AND BOTH OF THEM (THE OCTOPUS AND THE TRAINER),WILL END UP ON OPRAH SHOW, THEN EVERY KID IN AMERICA WILL END UP WITH AN OCTOPUS, THINGS THEN WILL GET OUT OF HAND AND WE WILL HAVE SOMETHING CALLED OCTOMANIA. IF THIS HAPPENED MY ADVISE PLEASE NOBODY SHOULD BUY AN OCTOPUS AND TORTURE THIS INNOCENT ANIMAL
I typically get irritated by psychic animals in the news, but this flavor of woo is probably mostly harmless.
I don’t know about the theory of paul being attracted to yellow. There is no evidence I am aware of that octopus have color vision. Though they can distinguish polarization, the have only a single visual pigment, making their visual system monochromatic. Behavioral tests in multiple cephalopods seem to confirm this. Paul could still have a preference for design of the german flag, however.
Also, though statistically significant, eight trials can hardly be considered a rigorous behavioral assay.
P = 0.0039 is significant enough to get lots of scientific information published Michael. I’m not sure too many journals would reject an authors assertion of significance at that level, p = 0.05, sure, but not p = 0.0039. If paul wanted to publish his results on how he picks soccer matches , who could reject him ?
Octopuses do have a strong preference for horizontal bars, and it might be that the yellow, red, and black of the German flag are different enough in brightness to make the bars salient. This is probably more important than the colors on the flag.
It isn’t an issue of significance; it’s an issue of attribution of cause. Knowing that Paul usually picks a team that also wins tells us nothing about the mechanism of his success, which is what we need to know if we want generalizable predictive power.
As a test, though, somebody should write this up and submit it to a conference under a fancy title. I can just see it now: “A remotely predictive food rewarded forced choice task in O. Vulgaris: A case study.”
go paul!!!, here is funny joke I saw about Paul getting death threats, http://ponderingstuff.com/2010/08/07/paul-the-psychic-octopus-received-death-threats-after-his-soccer-world-cup-predictions-became-true/