Non-symbolic math

  • 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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  • 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 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 relates basic facts (e.g., its parameters and symmetry) about normal curve and standardized z-scores. May be sung to the tune of "Oh Christmas Tree" (traditional). Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.
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  • Song consists of the meaning of a p-value. May be sung to the tune of "Roll out the Barrel" (Lew Brown, Wladimir A. Timm, Vasek Zeman and Jaromir Vejvoda). Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.
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  • Song is an informal overview introducing the conceptual steps of the scientific method. Recorded on the CD "Science Songs and Stories For the Big Questions", available at www.kathleencarroll.com.
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  • A cartoon that can be used in teaching about pie charts. 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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  • Song playfully depicts a college student struggling to master statistics at the hands of authority figures. May be sung to the tune of "Satisfaction" (Mick Jagger, Keith Richards).
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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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  • This article, in a series, describes a game, which tests opposing strategies through aspects of experiemental design.
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