European Stars and Stripes (Newspaper) - March 17, 1990, Darmstadt, Hesse                                I Wlyma a the Law of truly Large numbers improbable probably not by Gina Kolata new York times coincidences those surprising and often eerie events that add spice to everyday life May not be so unusual after All. After spending 10 years collecting thousands of stories of coincidences and analysing them two Harvard statisticians report that virtually All coincidences can be explained by some simple rules. Some of the analyses performed by them or other statisticians showed that events that looked extremely unlikely were almost to be expected. When Evelyn Marie Adams of Point pleasant Borough n.j., won the new Jersey lottery twice in four months in 1986, the event was widely reported As an amazing coincidence that beat Odds of one in 17 trillion. But when Analysed it turned out that the Chance that such an event could happen to someone somewhere in the United states was More like one in 30. It was an example of what the authors Persi Diaconis a professor of mathematics at Harvard University and Frederick Mosteller an emeritus mathematics professor at Harvard Call Quot the Law of very Large  that Long understood Law of statistics states in their formulation Quot with a Large enough Sample any outrageous thing is Apt to  some of the findings were published in the december Issue of the journal of the american statistical association others Are now appearing in other professional journals. Diaconis whose work also led to the recent discovery that seven shuffles Are needed to mix a 52-card deck randomly said the findings on coincidence were meeting mixed reactions. Quot some people Are enormously relieved but others Are furious Quot he said. Not everyone who supplied an amazing coincidence to the researchers wanted to hear that a cherished dramatic Story was really nothing special. Quot i think the whole subject is fascinating Quot said Erich Lehmann a statistician at the University of California at Berkeley. Although it can be a difficult statistical problem to decide just How unlikely an event is Lehmann said there is no dispute about the Validity of the findings of Diaconis and Mosteller some of which have been discussed at statistical meetings in recent years. The two Harvard statisticians reviewed a Large body of calculations and analyses of coincidences performed by other researchers and they devised new techniques and approaches for studying the phenomenon in a wide Range of circumstances. The research results Diaconis said Quot Are aimed at very Basic problems of inference that arise in Messy real statistical  Bradley Efron a statistician at Stanford University said coincidences arise Quot All the time Quot in statistical work. When researchers find clusters of Odd cancers or birth defects or other diseases statisticians Are asked Quot to decide which events Are the Luck of the draw and which May reflect some underlying cause run said. Quot that s what Persi and Fred Are trying to unravel Quot he added. Quot i think it s a very interesting  Diaconis said one application of the new analyses is in scrutinizing data from clinical trials of new drugs. A Vuu Are looking around in that mass of data a he said you find that in a certain subgroup there Are Wice As Many deaths in people taking drug a As Ere Are in people taking drug  is it a coincidence r an indication that drug a is so dangerous to some patients that the trial must be stopped Diaconis and Mosteller said they decided to study coincidences because they were fascinated by the role these Odd events play in everyone a lives. Quot All of us feel that our lives Are driven by coincidences Quot Diaconis said. Quot who we live with and where we work Why we do the things we do often rest on slim  these Chance events Quot touch us very deeply Quot he said. The two statisticians defined a coincidence As Quot a surprising concurrence of events perceived As meaningfully related with no apparent casual  Diaconis and Mosteller began with the presumption that there Are no extraordinary forces outside the realm of science that Are acting to produce coincidences. But they also recognized that seeming coincidences Are an important source of insight in science and so should not be dismissed out of hand. What looks like a coincidence May in fact have a hidden cause which can Lead to a new understanding of a phenomenon. A sequence of Odd blips on a Chart a clustering of cases of a rare disease can Tell researchers that a new event is occurring. A decade ago Diaconis and Mosteller started asking their colleagues friends and friends of friends to Send them examples of surprising coincidences. The collection quickly mushroomed. Mosteller said he had 13 notebooks each three and a half inches thick full of coincidences. Quot these notebooks Are eating up the shelves in my Den Quot he said. Diaconis said he had 200 file folders full of coincidences. When they began to study these coincidences they Learned that they fell into several distinct groups. Some coincidences have hidden causes and Are thus not really coincidences at All. Others arise from psychological factors like selective memory or sensitivities that make people think particular events Are unusual whether they Are or not. But Many coincidences Are simply Chance events that turn out to be far More Likely statistically than most people imagine. The analyses often required the researchers to develop new statistical methods but in the end almost All coincidences could be Analysed. The Law of truly Large numbers which explains the double Winner of the new Jersey lottery says that even if there is Only a one in a million Chance that something Wil happen it will happen eventually Given enough time or enough people. Quot its the Blade of grass Paradox Quot Diaconis said. Quot suppose i m standing in a Large Field and i put my Finger on a Blade of grass. The Chance that i would choose that particular Blade May be one in a million. But it is certain that i will choose a  so if something happens to Only one in a million people per Day and the population of the United states is 250 million Quot you expect 250 amazing coincidences every Day. Quot Quot if a one in a million thing happens to you you Start telling people about it Quot Diaconis went on. Quot you might say to me a so what do you think of that Wise Guy and i say its an example of the Law of truly Large numbers Quot when a new Jersey woman won the lottery twice in a four month period it was reported As a one in 17 trillion Long shot. Narrowly speaking that is Correct but As Diaconis and Mosteller reported one in 17 trillion Are the Odds that a Given person who buys a single ticket for exactly two new Jersey lotteries will win both times. The True question they say is Quot what is the Chance that some person out of All the millions and millions of people who buy lottery tickets in the United states hits a lottery twice in a lifetime Quot that event was called Quot practically a sure thing Quot by Stephen Samuels and George Mccabe two statisticians at Purdue University. Over a seven year period they concluded the Odds Are better than even that there will be a double lottery Winner somewhere in the United states. Even Over a four month period the Odds of a double Winner somewhere in the country Are better than one in 30 the stars and stripes a a a Page 13