# Simulation

• ### Gallery: Reinterpreting Vasily Grigoryevich Perov

A sketch by Anastasia Mandel reinterpreting Hunters at Rest by Vasily Grigoryevich Perov (1871) with the statistical caption "Capture-recapture statistics." This is part of a collection of sketches by Anastasia Mandel 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.
• ### **Histogram Explorer

This applet is designed to allow users to explore the relationship between histograms and the most typical summary statistics. The user can choose from several types of histograms (uniform, normal, symmetric, skewed, etc.), or can create their own by manipulating the bars of the histogram. The statistics available for display are mean, median, mode, range, standard deviation, and interquartile range. Also available is a "Practice Guessing" option, in which the values of the statistics are hidden until the user has entered guesses for each value.

This java applet provides students with opportunities to visualize the Monty Hall paradox (i.e., the famous "three-door" problem often discussed in introductory statistics courses). By going through the simulation and reading the accompanying materials, students can better understand concepts related to probability, and they can also see the need to gather data in order to test theories about what might happen under particular conditions (especially since the outcome of the Monty Hall problem tends to contradict students' initial intuitions).
• ### Song: It Don't Mean A Thing (If You Don't Do Modelling!)

A song to stress the importance of modeling in statistical analyses. Sung by Canadian singer Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre of Pompeu Fabra University, Barcelona, Spain. May be sung to the tune of Duke Ellington and Irving Mills' 1932 big band standard "It Don't Mean a Thing (If It Ain't Got That Swing)"
• ### Song: The model I Love

A song to aid in discussions about various issues in statistical modeling. Sung by Canadian singer Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre of Pompeu Fabra University, Barcelona, Spain. May be sung to the tune of George and Ira Gershwin's 1927 standard "The Man I Love"
• ### Song: It Ain't Necessarily So

A song to aid in discussions about statistical models with non-normal errors. Sung by Canadian singer Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre of Pompeu Fabra University, Barcelona, Spain. May be sung to the tune of George and Ira Gershwin's 1935 standard "It Ain't Necessarily So"
• ### Song: Summertime

A song to aid in discussions about the quality of fit of a statistical model. Sung by Canadian singer Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre of Pompeu Fabra University, Barcelona, Spain. May be sung to the tune of George Gershwin Dubose Hayward's 1935 standard "Summertime"
• ### The Distributions of Sample Statistics

A webpage in which links are provided to histograms of sample statistics (mean, median, standard deviation, maximum etc.) as a function of sample size. Each time the REFRESH button is clicked a new set of 2000 samples is generated.
• ### Quote: Rickey on Luck

Luck is the residue of design is a quote by American baseball executive Branch Rickey. The quote appeared in the February 21, 1946 issue of the "Sporting News". The quote is also often attributed to 17th century English poet John Milton - but that source has not been confirmed.
• ### The Normal Distribution JAVA Applet: An Illustration of Basic Probability

This simulation involves a series of balls passing through bins to eventually yield a normal distribution. Information is also provided about what the normal distribution is.