the hypothesis

The hypothesis Perhaps coins with likenesses of U. S. Presidents are more likely to come up “heads” than other coins. It’s important to have some hypothesis in mind, or at least some specific question, so that you can design a survey or experiment that has a reasonable chance to answer the question. Your choice of sample size, for example, will depend on what you expect the data to show. Bring it home State a clear conclusion, and support using statistical methods as appropriate. Can Coin Tosses Identify Future Presidents? Your Names Here Swarthmore College, Department of Mathematics & Statistics References Bender, D.J., E.M Bayne, and R.M. Brigham. 1996. Lunar condition influences coyote (Canis latrans) howling. American Midland Naturalist 136:413-417. Brooks, L.D. 1988. The evolution of recombination rates. Pages 87-105 in The Evolution of Sex, edited by R.E. Michod and B.R. Levin. Sinauer, Sunderland, MA. Scott, E.C. 2005. Evolution vs. Creationism: an Introduction. University of California Press, Berkeley. Society for the Study of Evolution. 2005. Statement on teaching evolution. < http://www.evolutionsociety.org/statemen ts.html >. Accessed 2005 Aug 9. The photograph is from NPR’s website, and the hand might belong to Persi Diaconis. For more information --- wait and see. Our experiment We produced a large supply of coins, identical to U.S. Eisenhower dollars but with likenesses of Senators Clinton, McCain, and Obama, and former Governor Huckabee. We then arranged to flip each category of coin 100,000 times, and counted the number of heads for each type. Acknowledgements We thank our colleagues Marge Inovera and Candace B. Rittenoff, who are also named on the indictment. More Ideas… Colored backgrounds are good if used in moderation. Too much color makes the poster look busy, and also slows printing. Photographs and embedded charts and graphs are good. For example, here is the coin-tossing machine we used: Statistical Significance We say that a result is “statistically significant” if it is not likely to have resulted from chance. Tests for Significance Use appropriate tests from class (or elsewhere). For example, if the results of this experiment were not so obvious, a Chi-Square test would be appropriate. The Results This table shows the numbers of heads and tails observed for each coin. “E” stands for Eisenhower. We see that in this case, the presidential likeness was associated with a surprisingly large number of heads. The other columns are unremarkable, except for column “A”, suggesting that the coin bears a likeness of a future president. Unfortunately we can’t say which image that is, as the coins and the original data are being held as evidence by the Secret Service. Which coin? A B C D E Heads 78,05 0 49,88 9 50,00 2 49,92 5 76,14 0 Tails 21,95 0 50,11 1 49,99 8 50,07 5 23,86 0 Total 100,0 00 100,0 00 100,0 00 100,0 00 100,0 00 percen t heads 78.0% 49.9% 50.0% 49.9% 75.5%

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Can Coin Tosses Identify Future Presidents? Your Names Here Swarthmore College, Department of Mathematics & Statistics. More Ideas… Colored backgrounds are good if used in moderation. Too much color makes the poster look busy, and also slows printing. - PowerPoint PPT Presentation

TRANSCRIPT

The hypothesis

Perhaps coins with likenesses of U. S. Presidents are more likely to come up “heads” than other coins.

It’s important to have some hypothesis in mind, or at least some specific question, so that you can design a survey or experiment that has a reasonable chance to answer the question. Your choice of sample size, for example, will depend on what you expect the data to show.

Bring it home

State a clear conclusion, and support using statistical methods as appropriate.

Can Coin Tosses Identify Future Presidents?Your Names Here

Swarthmore College, Department of Mathematics & Statistics

ReferencesBender, D.J., E.M Bayne, and R.M. Brigham. 1996. Lunar

condition influences coyote (Canis latrans) howling. American Midland Naturalist 136:413-417.

Brooks, L.D. 1988. The evolution of recombination rates. Pages 87-105 in The Evolution of Sex, edited by R.E. Michod and B.R. Levin. Sinauer, Sunderland, MA.

Scott, E.C. 2005. Evolution vs. Creationism: an Introduction. University of California Press, Berkeley.

Society for the Study of Evolution. 2005. Statement on teaching evolution. < http://www.evolutionsociety.org/statements.html >. Accessed 2005 Aug 9.

The photograph is from NPR’s website, and the hand might belong to Persi Diaconis.

For more information --- wait and see.

Our experiment

We produced a large supply of coins, identical to U.S. Eisenhower dollars but with likenesses of Senators Clinton, McCain, and Obama, and former Governor Huckabee. We then arranged to flip each category of coin 100,000 times, and counted the number of heads for each type.

AcknowledgementsWe thank our colleagues Marge Inovera and Candace B.

Rittenoff, who are also named on the indictment.

More Ideas…Colored backgrounds are good if used in moderation. Too much color makes the poster look busy, and also slows printing.

Photographs and embedded charts and graphs are good. For example, here is the coin-tossing machine we used:

Statistical Significance

We say that a result is “statistically significant” if it is not likely to have resulted from chance.

Tests for Significance

Use appropriate tests from class (or elsewhere). For example, if the results of this experiment were not so obvious, a Chi-Square test would be appropriate.

The Results

This table shows the numbers of heads and tails observed for each coin.

“E” stands for Eisenhower. We see that in this case, the presidential likeness was associated with a surprisingly large number of heads.

The other columns are unremarkable, except for column “A”, suggesting that the coin bears a likeness of a future president.

Unfortunately we can’t say which image that is, as the coins and the original data are being held as evidence by the Secret Service.

Which coin? A B C D E

Heads 78,050 49,889 50,002 49,925 76,140

Tails 21,950 50,111 49,998 50,075 23,860

Total100,00

0100,00

percent heads 78.0% 49.9% 50.0% 49.9% 75.5%

The Third Hypothesis