A different and low-tech coin demo, which can be used to introduce null hypothesis testing, viz p(heads) = .50. Have students balance 10 or 20 pennies on their sides on a sturdy, flat table in front of the room. Then have someone sharply tap the side of the table (or bang on it), with just enough force to make the pennies fall. The p(heads fall up) will be higher than .5 (I used to get 70&, 80% heads). The edge of US pennies have a bevel on them (I believe so they pop out of the mold easier, or something similar). In this situation (note Mike's post below) you are controlling for lots of variables that are usually present in a coin toss. I would guess that with new pennies, with fewer "random" imperfections, the p(heads) approaches 1.0. Talked to a physicist once about spinning pennies on their edge until they drop, and (long explanation about centrifugal force on the topmost part of the coin, if I remember), p (tails) > p (heads). Since the way we spin coins is variable, the effect is not so dramatic but might be quite far from .5 if we had a standard way to spin them.
-------------------------- John W. Kulig Professor of Psychology Plymouth State University Plymouth NH 03264 -------------------------- ----- Original Message ----- From: "Michael Smith" <[email protected]> To: "Teaching in the Psychological Sciences (TIPS)" <[email protected]> Sent: Monday, August 3, 2009 11:30:11 PM GMT -05:00 US/Canada Eastern Subject: Re: [tips] Flipping Out | The Big Money "The machine could make the toss come out heads every time" Maybe it was just an extended pattern that we all know sometimes occurs in random sequences! lol --Mike On Mon, Aug 3, 2009 at 4:13 PM, Mike Palij < [email protected] > wrote: On Mon, 03 Aug 2009 12:54:32 -0700, Christopher D. Green wrote: >The next time you want to use the coin-flip example in stats class... >think about this. > http://www.thebigmoney.com/articles/hey-wait-minute/2009/07/28/flipping-out?g=1 > I think the key passage in the article is the following: |The physics-and math-behind this discovery are very complex. |But some of the basic ideas are simple: If the force of the flip is the |same, the outcome is the same. To understand more about flips, |the academics built a coin-tossing machine and filmed it using a |slow-motion camera. This confirmed that the outcome of flips isn't |random. The machine could make the toss come out heads every time. In some respects, this should not be surprising because if the same amount of force is applied to each toss AND the tossing situation is a closed system (i.e., limited variation in environmental conditions, such as constant temperature, wind speed, air pressure, etc.), then one should have a highly deterministic, mechanistic system -- all third variables that can affect the outcome are effectively controlled. Performing the coin tossing in, say, a hurricaine or near a tornado or on the deck of ship in a storm at sea, are unlikely to provide such uniform results. |When people, rather than a machine, flipped the coin, results were | less predictable, but there was still a slight physical bias favoring the |position the coin started in. If the coin started heads up, then it would |land heads up 51 percent of the time. This, too, should not be surprising because it requires a fair amount of practice in order to do a motor action with little variation (simple RT shows this). There should be moment-to-moment variations in the amount of force used in the coin-toss due to random factors (i.e., changes in attention, motor control, etc) even assuming fixed environmental conditions (not to mention factors such as drinking Long Island Ice Teas during the task or playing tetris while flipping the coin). So, what is the point? If the amount of force used to flip a coin is "optimal", a single outcome can be reliably produced (perhaps with a probability approaching 1.00) under constant environmental conditions. However, if the amount of force used to flip a coin varies, then the predictablity of the outcome is reduced. If the amount of force used is a random variable, then this will reduce the predictably of an outcome. It probably is more complicated than this but I think this is what allows one to continue to use the coin toss example (because force varies from trial to trial in unpredicable ways). -Mike Palij New York University [email protected] --- To make changes to your subscription contact: Bill Southerly ( [email protected] ) --- To make changes to your subscription contact: Bill Southerly ([email protected]) --- To make changes to your subscription contact: Bill Southerly ([email protected])
