Probability

  • This Flash based applet simulates data from a case study of treatments for tumor growth in mice. This simulation allows the user to place mice into a control and treatment groups. The simulation then compares the difference in the groups based on this haphazard selection to those of a truly random assignment (the user may also create multiple random assignments and examine the sampling distribution of key statistics). The applet may be used to illustrate three points about random assignment in experiments: 1) how it helps to eliminate bias when compared with a haphazard assignment process, 2) how it leads to a consistent pattern of results when repeated, and 3) how it makes the question of statistical significance interesting since differences between groups are either from treatment or by the luck of the draw. In this webinar, the activity is demonstrated along with a discussion of goals, context, background materials, class handouts, and assessments. Key Note for Instructors: The data are drawn from a real experiment with an effective treatment but where the response is correlated with animal age and size (so tumor size will tend to be smaller in the treatment group when measured at the end of a randomized experiment but animal age and size should not be). Typically people choosing haphazardly will tend to pick larger/older animals for the treatment group and thus create a bias against the treatment.
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  • Essentially, all models are wrong, but some are useful. This quote is generally attributed to George Box. It appears in "Empirical Model-Building and Response Surfaces" (Wiley 1987) p. 424 by George E.P. Box & Norman R. Draper.
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  • Joke from "The Little Black Book of Business Statistics", by Michael C. Thomsett (1990, Amacom) p. 117. also quoted in "Statistically Speaking" compiled by Carl Gaither and Alma Cavazos-Gaither.
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  • This FLASH based applet illustrates the sampling distribution of the mean. This applet allows the user to pick a population from over 2000 pre-defined populations. The user can then choose size of the random sample to select. The applet can produce random samples in one, 10, 100, or 1000 at a time. The resulting means are illustrated on a histogram. The histogram has an outline of the normal distribution and vertical lines at 1, 2, and 3 standard deviations. The applet can be viewed at the original site or downloaded to the instructors machine.
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  • Song addresses the famous probability example of Birthday Problem by contrasting the often confused events of "some people matching" with "someone matches with ME". May be sung to the tune of "Happy Birthday to You" (Mildred J. Hill and Patty Smith Hill). Originally appeared in Winter 2002 "STATS". Recorded June 26, 2009 at the OSU Whisper Room: Larry Lesser, vocals/guitar; Justin Slauson, engineer.
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  • This poem, by North Carolina State University Emeritus Professor of Physics Jasper D. Memory (1935 - ) is designed to teach the difference between the probability of having a disease given a positive screening test and the probability of a positive test result given you have the disease. The poem was published in the October, 2007 issue of "Mathematics Magazine" volume 80 p. 273,
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  • Song of a student forging a commitment to learn major concepts and tools of mathematical probability. May be sung to the tune of "Mr. Tambourine Man" (Bob Dylan).
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  • Song incorporates various terms from areas such as experimental design, graphing, and hypothesis testing. May be sung to the tune of "Desperado" (The Eagles). Musical accompaniment realization are by Joshua Lintz and vocals are by Mariana Sandoval from University of Texas at El Paso.

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  • Statistician's "breakup" song is filled with 2 dozen puns from a variety of (mostly first-year) statistical terms. Song is a 12-bar blues, with the words in parentheses more spoken than sung during the final 2 bars of each 12. Appeared in Winter 2002 "STATS" and Spring 2004 "The Pi".
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  • Song describes conditions for using the t distribution and mentions its inventor William Gosset (and his pseudonym, Student). May be sung to the tune of "Let it Be" (McCartney/Beatles). Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.
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