A cartoon that can be used to discuss the appropriateness of the normal errors assumption in a variety of settings. The cartoon was used in the May 2021 CAUSE cartoon caption contest and the winning caption was written by Dashiell Young-Saver from the Knowledge Is Power Program Public Schools. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.
A song describing how sample means will follow the normal curve regardless of how skewed the population histogram is, provided n is very large. The lyrics were written by Dennis Pearl and Peter Sprangers, both then at The Ohio State University. The audio recording was produced by The University of Texas at El Paso student Nicolas Acedo who also performed the vocals
Funded by the National Science Foundation, workshops were held over a three-year period, each with about twenty participants nearly equally divided between mathematics educators and statisticians. In these exchanges the mathematics educators presented honest assessments of the status of mathematics education research (both its strengths and its weaknesses), and the statisticians provided insights into modern statistical methods that could be more widely used in such research. The discussions led to an outline of guidelines for evaluating and reporting mathematics education research, which were molded into the current report. The purpose of the reporting guidelines is to foster the development of a stronger foundation of research in mathematics education, one that will be scientific, cumulative, interconnected, and intertwined with teaching practice. The guidelines are built around a model involving five key components of a high-quality research program: generating ideas, framing those ideas in a research setting, examining the research questions in small studies, generalizing the results in larger and more refined studies, and extending the results over time and location. Any single research project may have only one or two of these components, but such projects should link to others so that a viable research program that will be interconnected and cumulative can be identified and used to effect improvements in both teaching practice and future research. The guidelines provide details that are essential for these linkages to occur. Three appendices provide background material dealing with (a) a model for research in mathematics education in light of a medical model for clinical trials; (b) technical issues of measurement, unit of randomization, experiments vs. observations, and gain scores as they relate to scientifically based research; and (c) critical areas for cooperation between statistics and mathematics education research, including qualitative vs. quantitative research, educating graduate students and keeping mathematics education faculty current in education research, statistics practices and methodologies, and building partnerships and collaboratives.
This presentation was given by Aneta Siemiginowska at the 4th International X-ray Astronomy School (2005), held at the Harvard-Smithsonian Center for Astrophysics in Cambridge, MA.
Illustrates the central limit theorem by allowing the user to increase the number of samples in increments of 100, 1000, or 10000.
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.
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).
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).
In these activities designed to introduce sampling distributions and the Central Limit Theorem, students generate several small samples and note patterns in the distributions of the means and proportions that they themselves calculate from these samples. Outside of class, students generate samples of dice rolls and coin spins and draw random samples from small populations for which data is given on each individual. Students report their sample means and proportions to the instructor who then compiles the results into a single data file for in-class exploration of sampling distributions and the Central Limit Theorem. Key words: Sampling distribution, sample mean, sample proportion, central limit theorem
The program DistCalc calculates probabilities and critical values for the most important distributions. The purpose of this program is to show the concept of critical values and the replacement of printed distribution tables. The Distribution Calculator offers calculations for the normal distribution, the t distribution, the chi-square distribution, and the F distribution.