# Simulation

• ### Gallery: Reinterpreting Vincent Willem van Gogh

A sketch by Anastasia Mandel reinterpreting "Field with Flowers" by Vincent Willem van Gogh (1883) with the statistical caption "Experimental Design, decades before Fisher." This is part of a collection of sketches by Anastasia Mandel and their accompanying statistical captions written by Stan Lipovetsky and Igor Mandel that took first place in the cartoon & art category of the 2009 A-Mu-sing contest sponsored by CAUSE. The collection and their accompanying statistical captions discussed in the paper "How art helps to understand statistics" (Model Assisted Statistics and Applications, 2009) by Stan Lipovetsky and Igor Mandel in volume 4 pages 313-324. Free to use in classrooms and on course websites.
• ### Gallery: Reinterpreting Gustave Caillebotte

A sketch by Anastasia Mandel reinterpreting "Fruit Displayed on a Stand" by Gustave Caillebotte (1882) with the statistical caption "Cluster analysis: apples to apples, nuts to nuts - a statistician's dream." This is part of a collection of sketches by Anastasia Mandel and their accompanying statistical captions written by Stan Lipovetsky and Igor Mandel that took first place in the cartoon & art category of the 2009 A-Mu-sing contest sponsored by CAUSE. The collection and their accompanying statistical captions discussed in the paper "How art helps to understand statistics" (Model Assisted Statistics and Applications, 2009) by Stan Lipovetsky and Igor Mandel in volume 4 pages 313-324. Free to use in classrooms and on course websites.
• ### Psychic test

This activity illustrates the convergence of long run relative frequency to the true probability. The psychic ability of a student from the class is studied using an applet. The student is asked to repeatedly guess the outcome of a virtual coin toss. The instructor enters the student's guesses and the applet plots the percentage of correct answers versus the number of attempts. With the applet, many guesses can be entered very quickly. If the student is truly a psychic, the percentage correct will converge to a value above 0.5.
• ### Quote: Coveyou on Random Numbers

The generation of random numbers is too important to be left to chance. The title of a 1969 article by American Mathematician and civil rights activist Robert R. Coveyou (1915 - 1996). ("Appl. Math.," 3 p. 70-111)
• ### Introduction to Experiments Activity

This activity will allow students to learn the difference between observational studies and experiments, with emphasis on the importance of cause-and-effect relationships. The activity will also familiarize students with key terms such as factors, treatments, retrospective and prospective studies, etc.
• ### **Inference for Means Activity

This activity enables students to learn about confidence intervals and hypothesis tests for a population mean. It focuses on the t-distribution, the assumptions for using it, and graphical displays. The activity also focuses on how to interpretations a confidence interval, a p-value, and a hypothesis test.

• ### Cartoon: Raking the Lawn

A cartoon that can be used in teaching about the efficiency of using simulation in statistics. Cartoon 2006 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.

• ### Quote: Darwin on Theory and Observation

On his standard of proof, natural science would never progress, for without the making of theories I am convinced there would be no observation. A quote from a letter English naturalist Charles Darwin (1809 - 1882) wrote to Charles Lyell on June 1, 1860. The letter is found in "The Life and Letters of Charles Darwin" volume II p. 108 published in 1888. The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.
• ### Cartoon: Control Groups

A cartoon to teach the need for a good control group in research studies. Cartoon by John Landers (www.landers.co.uk) in 2003 based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites. The cartoon's caption is similar to one by American cartoonist Peter S Mueller that depicts a control group and an "out of control" group that was produced independently a few years before this one.
• ### Statistical Tables Calculator

This page provides distribution calculators for the binomial, normal, Student's T, Chi-square, and Fisher's F distributions. Users set the parameters and enter either the probability or the test statistic and the calculators return the missing value.