Resource Library

Summary: This article describes the capture-recapture method of estimating the size of a population of fish in a pond and illustrates it with both a “hands-on” classroom activity using Pepperidge Farm Goldfiish^TM crackers and a computer simulation that investigates two different estimators of the population size.  The activity was described in R. W. Johnson, “How many fish are in the pond?,”Teaching Statistics, 18 (1) (1996), 2-5

https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9639.1996.tb00882.x

Specifics: To illustrate the capture-recapture method in the classroom, two different varieties of Pepperidge Farm Goldfish^TM crackers are used. The instructor places all of the Goldfish from a full bag of the original variety in a bowl to correspond to the initial state of the pond (the instructor should have previously counted the true number from the bag, which turned out to be 323 in the paper’s example). Students then captured c = 50 of these fish and replaced them with 50 Goldfish of a flavored variety of different color. After mixing the contents of the bowl, t=6 ‘tagged’ fish - fish of the flavored variety were found in a recaptured sample size of r = 41, giving the estimate cr/t= 341. This used the maximum likelihood (ML method. To examine the behavior of the MLE the capture-recapture ML  method is repeated 1000 times using a computer simulation. The distribution of the results will be heavily skewed since the MLE is quite biased (in fact, since there is positive probability that t = 0, the MLE has an infinite expectation). The simulation is then redone using Seber’s biased-corrected estimate = [(c+1)(r+1)/(t+1)] – 1.  After the true value of the population size is revealed by the instructor, students see that the average of the 1000 new simulations show that the biased-corrected version is indeed closer to the truth (and also that the new estimate has less variability).

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

A cartoon suitable for use in teaching about scatterplots and correlation. The cartoon is number 388 (Feb, 2008) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a creative commons attribution-non-commercial 2.5 license.

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.

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

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

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

The researcher armed with a confidence interval, but deprived of the false respectability of statistical significance, must work harder to convince himself and others of the importance of his findings. This can only be good. is a quote by British statistician Michael W. Oakes. The quote is found in his 1986 book "Statistical Inference: a Commentary for the Social and Behavioural Sciences" published by John Wiley & Sons.

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.

A fun song about the average by American humorist and singer-songwriter Carla Ulbrich. The song was a finalist in the novelty category of the 2018 USA Songwriting Competition.  The song is also available at www.theacousticguitarproject.com/artist/carla-ulbrich/ and more about the singer can be found at her website at www.carlau.com. For classroom use, you might ask which lines in "Totally Average Woman" refer to ways in which the woman in the song is at the mean, and which refer to ways in which she is at the median. Permission from singer is for free use for teaching in classroom and course websites with attribution. Commercial users must contact the copyright holder.

"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.