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Statistical Inference & Techniques

  • A hands-on activity using the capture-recapture method to estimate the number of M&M’sTM in a population The activity was described in G. D. Bisbee and D. M. Conway, “Studying proportions using the capture-recapture method”, Mathematics Teacher, 92 (3) (1999), 215-218.

    Summary: Scientists use the capture-recapture method as a tool to estimate population size. Animals are captured, tagged, and then released back into the population. Later, a sample is captured and a proportion used to estimate population size.

    Specifics: Let us say that we sample a beetle population of unknown size. We capture and mark ten of those beetles with a spot of India ink, then return them to the population and give them time to mix in with the population. We then recapture another sample consisting of eight beetles, one of which was previously marked. We substitute the numbers into the foregoing proportion to estimate the population size, getting 1/8 = 10/(Pop size). Solving for the Pop size gives us an estimated population of eighty beetles. Students are, predictably, less than enthusiastic about having to handle the creepy-crawly critters so this activity uses a population of M&M’s of unknown size to estimate. Each team of two to four students receives some M&M in a paper cup, which is covered on top with crumpled paper towels. The students “tag” the M&M’s from a random sample and then, after mixing them back in, sample again to estimate the number in the cup (they can later check how far off their estimates  were and compare to other teams).

    (Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)

     

     

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  • A poem written in 2019 by Larry Lesser from The University of Texas at El Paso to discuss statistics examples involving social justice, inspired by his paper in March 2007 Journal of Statistics Education. The poem is part of a collection of 8 poems published with commentary in the January 2020 issue of Journal of Humanistic Mathematics.

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  • A cartoon to illustrate the value of statistics in astronomy, especially in the search for planets.  The cartoon was drawn in 2013 by British cartoonist John Landers based on an idea by Dennis Pearl from Ohio State University.  This item is part of the cartoons and readings from the “World Without Statistics” series that provided cartoons and readings on important applications of statistics created for celebration of 2013 International Year of Statistics.  The series may be found at https://online.stat.psu.edu/stat100/lesson/1/1.4

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  • A cartoon to illustrate the value of statistics in process control.  The cartoon was drawn in 2013 by British cartoonist John Landers based on an idea by Dennis Pearl from Ohio State University.  This item is part of the cartoons and readings from the “World Without Statistics” series that provided cartoons and readings on important applications of statistics created for celebration of 2013 International Year of Statistics.  The series may be found at https://online.stat.psu.edu/stat100/lesson/1/1.4

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  • A cartoon to illustrate the value of statistics in weather forecasting.  The cartoon was drawn in 2013 by British cartoonist John Landers based on an idea by Dennis Pearl from Ohio State University.  This item is part of the cartoons and readings from the “World Without Statistics” series that provided cartoons and readings on important applications of statistics created for celebration of 2013 International Year of Statistics.  The series may be found at https://online.stat.psu.edu/stat100/lesson/1/1.4

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  • A joke for discussing the over-use of hypothesis testing methods.  The joke was written in April 2019 by Larry Lesser from The University of Texas at El Paso.

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  • "Like doctors, data scientists should pledge a Hippocratic Oath, one that focuses on the possible misuses and misinterpretations of their models," is a quote by American mathemetician and data scientist Cathy O'Neil (1972 - ).  The quote is found on page 205 of her 2016 award winning book Weapons of Math Destruction.

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  • A cartoon that can be helpful in introducing scree plots and their interpretation in an exploratory principal components analysis to determine the number of factors to be used.  The cartoon is arendition of Edvard Munch’s famous painting “The Scream”. The cartoon was used in the January 2019 CAUSE cartoon caption contest and the winning caption was submitted by Larry Lesser from The University of Texas at El Paso. An alternative caption: "The feeling you get when the p-value is 0.055," was submitted by Minu Bhunia, a student at University of Minnesota, and can be used in discussing the interpretation of p-values and the arbitrary nature of the 0.05 cutoff.The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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  • A cartoon that provides a nice avenue for facilitating discussions of the importance of modeling in making forecasts. The cartoon was used in the December, 2017 CAUSE cartoon caption contest and the winning caption was submitted by Larry Lesser from The University of Texas at El Paso. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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  • A cartoon to provide a nice avenue for facilitating discussions of power in significance testing.The cartoon was used in the November, 2017 CAUSE cartoon caption contest and the winning caption was written by John Dawson from Texas Tech University. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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