# Estimation Principles

• ### Cartoon: The Aircraft Carrier

A cartoon to teach about confidence intervals. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University) in 2008. Free to use in the classroom and on course web sites.

• ### Simulating Size and Power Using a 10-Sided Die

This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution
• ### 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.
• ### Song: MLE

Song about the properties of Maximum Likelihood Estimation including efficiency, invariance, and asymptotic normality. May sing to the tune of "Let it Be" By Paul McCartney. Recorded June 26, 2009 at the OSU Whisper Room: Larry Lesser, vocals/guitar; Justin Slauson, engineer.

• ### *Using an Applet to Demonstrate Sampling Distributions of Regression Coefficients

This visualization activity combines student data collection with the use of an applet to enhance the understanding of the distributions of slope and intercept in simple linear regression models. The applet simulates a linear regression plot and the corresponding intercept and slope histograms. The program allows the user to change settings such as slope, standard deviation, sample size, and more. Students will then see theoretical distributions of the slope and intercept and how they compare to the histograms generated by the simulated linear regression lines.
• ### Quote: Geary on Normality

Normality is a myth; there never has, and never will be, a normal distribution. A quote by Irish statistician and econometrician Roy C. Geary (1896 - 1983) found in "Biometrika" volume 34, 1947, page 241.

• ### Quote: Brandeis on Averages

I abhor averages. I like the individual case. A man may have six meals one day and none the next, making an average of three meals per day, but that is not a good way to live. A quote by American Supreme Court Justice Louis Dembitz Brandeis (1856 - 1951) as quoted in "Brandeis: A Free Man's Life" by Alpheus Thomas Mason Viking Press, 1946; page 145). The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.

• ### Quote: Eldridge on Discoveries

Those who fear muddy feet will never discover new paths. A quote by American writer and teacher Paul Eldridge (1888- 1982) found in his book "Maxims for a Modern Man" (Thomas Yoseloff Publishing, 1965). The quote also appears in "Statistically Speaking: A dictionary of quotations" compiled by Carl Gaither and Alma Cavazos-Gaither.

• ### Quote: Osler on Variability

Variability is the law of life, and as no two faces are the same, so no two bodies are alike, and no two individuals react alike and behave alike under the abnormal conditions which we know as disease. A quote by Canadian physician and medical educator Sir William Osler (1859 - 1919). The quote appears in William Osler: Aphorisms from his bedside teachings and writings, (Henry Schuman; 1950, page 104).

• ### Cartoon: The Capture-Recapture Method

A cartoon to teach about the capture-recapture method. Cartoon by John Landers (www.landers.co.uk) based on an idea and sketch from Sheila O. Weaver (University of Vermont). This is part of a three cartoon set from Dr. Weaver that took first place in the cartoon category of the 2007 A-Mu-sing competition. Free to use in the classroom and on course web sites.