March 29, 2012

Very like a whale

The Herald has managed to top Stuff’s suggestion that Powerball is in Wairarapa with a story saying it’s “in the stars”.

Of course, they don’t mean the actual stars, they mean European-style astrological birth signs.  Allegedly (and it’s hardly the sort of claim that it’s worth verifying),  15% of winners over the past two years were born under Taurus.   Now, since there are 104 winners and 12 astrological signs, it’s arithmetically unavoidable that some signs will get more winners than others, but how many more would you expect in a typical two-year period?

The easiest way to approximate this is to ignore the fact that slightly more births occur in some months and just sample 104 winners equally from 12 groups.  Repeating this 10,000 times takes a few seconds, and we get a table showing the percentage chance that the most-sampled star sign will have at least 10, 11, 12, … winners.

10 11 12 13 14 15 16 17 18 19
1 100.00 99.70 94.50 76.30 50.50 28.40 14.40 6.30 2.80 1.20

Getting 15% in one group is not at all  surprising.

This still overestimates the surprise: if there hadn’t been an overall pattern, the story could have said that the chance of winning depends on your star sign and on the time of year, for example.    In fact, they did this as well: the second part of the story says that Taurus is lucky now, but that Capricorn will be lucky in a  few weeks.   Of course, the fact that the second part contradicts the first part isn’t mentioned anywhere, and no data are presented to gesture in the direction of evidence for the claim.

We’re very good at seeing patterns, even when they don’t exist, and statistics is one way of ameliorating this problem.

So what is the best time to buy a lottery ticket?  As Scott Adams shows, the day after the drawing — they are a lot cheaper then.

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Thomas Lumley (@tslumley) is Professor of Biostatistics at the University of Auckland. His research interests include semiparametric models, survey sampling, statistical computing, foundations of statistics, and whatever methodological problems his medical collaborators come up with. He also blogs at Biased and Inefficient See all posts by Thomas Lumley »

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    […] that we can tackle problems that wouldn’t have been worthwhile before.  For example, in a post about the lottery, I wanted to calculate the probability that distributing 104 wins over 12 months would give 15 or […]

    5 years ago