Limit Theorems

  • This joke can be used in a discussion of how sample size affects the reliability of the sample mean. The joke may be found amongst the extensive Science Jokes resources at www.newyorkscienceteacher.com
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  • 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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  • The Normal Law is a poem whose words form the shape of the normal density. It was written by Australian-American chemist and statistician William John ("Jack") Youden (1900 - 1971). The poem was published in "The American Statistician" page 11 in v. 4 number 2 (1950).

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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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  • This in-class demonstration combines real world data collection with the use of the applet to enhance the understanding of sampling distribution. Students will work in groups to determine the average date of their 30 coins. In turn, they will report their mean to the instructor, who will record these. The instructor can then create a histogram based on their sample means and explain that they have created a sampling distribution. Afterwards, the applet can be used to demonstrate properties of the sampling distribution. The idea here is that students will remember what they physically did to create the histogram and, therefore, have a better understanding of sampling distributions.
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  • If you can't measure it, I'm not interested. A quote by Canadian educator and management theorist Laurence Johnston Peter (1919 - 1990) from "Peter's People" in "Human Behavior" (August, 1976; page 9). The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.

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  • Those who ignore Statistics are condemned to reinvent it. A quote attributed to Stanford University professor of Statistics Bradley Efron (1938 - ) by his colleague Jerome H. Friedman in a talk to the 29th Symposium on the Interface (May 1997, Houston) and in a paper "The role of Statistics in the Data Revolution" later published in "International Statistical Review" (2001; vol. 69, pages 5 - 10).

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  • This poem was written by Peter E. Sprangers while he was a graduate student in the Department of Statistics at The Ohio State University and published in "CMOOL: Central Moments Of Our Lives" (volume 1; 2006, issue 2). The poem took second place in the poetry category of the 2007 A-Mu-sing competition.

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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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  • This activity represents a very general demonstration of the effects of the Central Limit Theorem (CLT). The activity is based on the SOCR Sampling Distribution CLT Experiment. This experiment builds upon a RVLS CLT applet (http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/) by extending the applet functionality and providing the capability of sampling from any SOCR Distribution. Goals of this activity: provide intuitive notion of sampling from any process with a well-defined distribution; motivate and facilitate learning of the central limit theorem; empirically validate that sample-averages of random observations (most processes) follow approximately normal distribution; empirically demonstrate that the sample-average is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal; illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process); show that the variation of the sample average rapidly decreases as the sample size increases.
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