By Karen Auguston Field, Chief Editor --
Design News,
May 20, 2002
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In April I attended the Hannover Fair in Germany. Many of the products on display, ranging from a robotic roller coaster to an extremely dexterous prosthetic hand, employed core technologies like motion control and servo pneumatics in ingenious ways. That's not surprising, given that the fair is a primary venue for companies from around the world to strut their stuff. (See our show coverage in an upcoming issue.)
The opportunity to gather great story leads aside, I was particularly looking forward to going to Europe this year. That's because I recently saw an article on the web (www.newscientist.com) about two Polish statisticians who have concluded that at least one Euro coin is biased. In spinning tests they conducted, the Belgian Euro landed "heads" 56% of the time. The reason for this phenomenon, the statisticians theorized, is because the image on that side is of a plumpish King Albert.
As students of statistics know, the distribution of coin tosses makes a good approximation to a Bernoulli distribution. It says that a random variable X with a parameter p assumes a value of 1 with a probability of p and a value of 0 with a probability of 1-p. In other words, a non-biased coin will land either side face up with equal probability.
I immediately envisioned all kinds of opportunities to get my co-workers to pick up my taxi fare, beer tabs, and anything else I could think of to flip a coin over. As long as I consistently declared heads, I figured I'd come out slightly ahead, so to speak. How did I actually do? Notwithstanding the fact that the head of the German Euro coin features a somewhat stringy looking eagle, heads came up 60% of the time—better than expected.
The catch, of course, is that my results were obtained from just 30 coin tosses over a three-day period, which isn't enough of a sample size to prove anything in this case. In fact, I could have just as easily wound up picking up the tab more often than not. And just in case you're wondering, the Polish statisticians are coming under criticism for their own puny sample size—just 250 spins so far.
As for me, the solution is obvious: More research in German beer halls is definitely in order!
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