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386 andrew gelman stats-2010-11-01-Classic probability mistake, this time in the (virtual) pages of the New York Times


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Introduction: Xian pointed me to this recycling of a classic probability error. It’s too bad it was in the New York Times, but at least it was in the Opinion Pages, so I guess that’s not so bad. And, on the plus side, several of the blog commenters got the point. What I was wondering, though, was who was this “Yitzhak Melechson, a statistics professor at the University of Tel Aviv”? This is such a standard problem, I’m surprised to find a statistics professor making this mistake. I was curious what his area of research is and where he was trained. I started by googling Yitzhak Melechson but all I could find was this news story, over and over and over and over again. Then I found Tel Aviv University and navigated to its statistics department but couldn’t find any Melechson in the faculty list. Next stop: entering Melechson in the search engine at the Tel Aviv University website. It came up blank. One last try: I entered the Yitzhak Melechson into Google Scholar. Here’s what came up:


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Xian pointed me to this recycling of a classic probability error. [sent-1, score-0.089]

2 And, on the plus side, several of the blog commenters got the point. [sent-3, score-0.097]

3 What I was wondering, though, was who was this “Yitzhak Melechson, a statistics professor at the University of Tel Aviv”? [sent-4, score-0.165]

4 This is such a standard problem, I’m surprised to find a statistics professor making this mistake. [sent-5, score-0.279]

5 I was curious what his area of research is and where he was trained. [sent-6, score-0.091]

6 I started by googling Yitzhak Melechson but all I could find was this news story, over and over and over and over again. [sent-7, score-0.218]

7 Then I found Tel Aviv University and navigated to its statistics department but couldn’t find any Melechson in the faculty list. [sent-8, score-0.252]

8 Next stop: entering Melechson in the search engine at the Tel Aviv University website. [sent-9, score-0.229]

9 One last try: I entered the Yitzhak Melechson into Google Scholar. [sent-11, score-0.08]

10 Here’s what came up: Your search – Yitzhak Melechson – did not match any articles Computing wrong probabilities for the lottery must be a full-time job! [sent-12, score-0.356]

11 If there’s some part of this story that I’m missing, please let me know. [sent-16, score-0.094]

12 How many statistics professors could there be in Tel Aviv, anyway? [sent-17, score-0.138]

13 Perhaps there’s some obvious explanation that’s eluding me. [sent-18, score-0.096]


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Introduction: Xian pointed me to this recycling of a classic probability error. It’s too bad it was in the New York Times, but at least it was in the Opinion Pages, so I guess that’s not so bad. And, on the plus side, several of the blog commenters got the point. What I was wondering, though, was who was this “Yitzhak Melechson, a statistics professor at the University of Tel Aviv”? This is such a standard problem, I’m surprised to find a statistics professor making this mistake. I was curious what his area of research is and where he was trained. I started by googling Yitzhak Melechson but all I could find was this news story, over and over and over and over again. Then I found Tel Aviv University and navigated to its statistics department but couldn’t find any Melechson in the faculty list. Next stop: entering Melechson in the search engine at the Tel Aviv University website. It came up blank. One last try: I entered the Yitzhak Melechson into Google Scholar. Here’s what came up:

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Introduction: Aki pointed me to this article . I’m too exhausted to argue all this in detail yet one more time, but let me just say that I hate this stuff for the reasons given in Section 5 of this paper from 1998 (based on classroom activities from 1994). I’ve hated this stuff for a long time. And I don’t think Yitzhak likes it either; see this discussion from 2005 and this from 2009.

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Introduction: It was reported last year that the national lottery of Israel featured the exact same 6 numbers (out of 45) twice in the same month, and statistics professor Isaac Meilijson of Tel Aviv University was quoted as saying that “the incident of six numbers repeating themselves within a month is an event of once in 10,000 years.” I shouldn’t mock when it comes to mathematics–after all, I proved a false theorem once! (Or, to be precise, my collaborator and I published a false claim which we thought we’d proved, thus we thought was a theorem.) So let me retract the mockery and move, first to the mathematics and then to the statistics. First, how many possibilities are there in pick 6 out of 45? It’s (45*44*43*42*41*40)/6! = 8,145,060. Let’s call this number N. Second, what’s the probability that the same numbers repeat in a single calendar month? I’ve been told that the Israeli lottery has 2 draws per week, That’s 104/12=8.67 draws per month. Or maybe they skip some holiday

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