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Laws of Large Numbers

  • A song about two-tailed tests for hypotheses about the mean that may be sung to the tune of the 1966 song "Break on Through (to the other side)" by the Doors. Lyrics by Dennis Pearl of The Ohio State University. Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.

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  • A cartoon to teach ideas of probability ad the Law of Large Numbers. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.

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  • A cartoon that might accompany a discussion about the use and misuse of significance tests like the T-Test. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
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  • A cartoon to teach about the law of large numbers and the expected value under the assumption that future events are unknown to the betting strategy. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
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  • While nothing is more uncertain than the duration of a single life, nothing is more certain than the average duration of a thousand lives. A quote of American actuary and abolitionist Elizur Wright (1804 - 1885).
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  • I feel like a fugitive from the law of averages. A quote of soldier and U.S. cartoonist William H. Mauldin (1921 - 2003) from a cartoon caption in the first published collection of his work, "Up Front" (H. Holt and Co., 1945)
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  • The individual source of the statistics may easily be the weakest link. Harold Cox tells a story of his life as a young man in India. He quoted some statistics to a Judge, an Englishman, and a very good fellow. His friend said, Cox, when you are a bit older, you will not quote Indian statistics with that assurance. The Government are very keen on amassing statistics ... they collect them, add them, raise them to the nth power, take the cube root and prepare wonderful diagrams. But what you must never forget is that every one of these figures comes in the first place from the `chowty dar` [village watchman], who just puts down what he damn pleases." Quoted from "Some Economic Factors in Modern Life" (King and Son, 1929; p. 258) by Sir Josiah Charles Stamp (1880 - 1941), British economist, statistician, director of the Bank of England and president of the Royal Statistical Society.
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  • This applet was designed to illustrate the impact on simple linear regression output caused by adding a new data point. The applet simulates data and provides a graphical display of the data points and fitted regression line as well as the updated regression line after the addition of a data point.
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  • This activity uses a computer program to explore probability concepts such as sample space, independent events, law of large numbers, and reliability. An outline of the activity and the computer program are provided.
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  • This program allows the student to explore the nature of sampling distributions of sample means and sample proportions. The software provides separate windows for building population distributions, drawing and viewing random samples from the population, exploring the behavior of sampling distributions of sample means, and exploring the behavior of confidence intervals.
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