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)

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 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.

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.

A cartoon to provide a nice avenue for facilitating discussions of planning for adequate sample sizes in experiments.The cartoon was used in the October, 2017 CAUSE cartoon caption contest and the winning caption was written by Greg Snow from Grigham Young 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.

A light bulb joke that can be used in discussing how the choice of model might affect the conclusions drawn.  The joke was submitted to AmStat News by Robert Weiss from UCLA and appeared on page 48 of the October, 2018 edition.

This NASA-HANDBOOK is published by the National Aeronautics and Space Administration (NASA) to provide a Bayesian foundation for framing probabilistic problems and performing inference on these problems. It is aimed at scientists and engineers and provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models. The overall approach taken in this document is to give both a broad perspective on data analysis issues and a narrow focus on the methods required to implement a comprehensive database repository.

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.  

This page will calculate the lower and upper limits of the 95% confidence interval for a proportion, according to two methods described by Robert Newcombe, both derived from a procedure outlined by E. B. Wilson in 1927. The first method uses the Wilson procedure without a correction for continuity; the second uses the Wilson procedure with a correction for continuity.

A song for teaching about the Cramer Rao Lower Bound for the variance of an unbiased estimate. The lyrics were written by Kyle White and Bradley Turnbull from North Carolina State University as a parody of the 2003 track "Jerk It Out" by the Swedish band "Caesars". The song won first prize in the song category in the 2013 CAUSE A-Mu-sing competition and is performed by "The Fifth Moment", an NCSU graduate student band (Kristin Linn, Jason Osborne, Siddharth Roy, Bradley Turnbull, Joseph Usset, and Kyle White). Free for use in non-profit education settings.