MIT Massachusetts Institute of Technology

Is Bigger Better? A Look at a Selection Bias that Is All Around Us

Arnold Barnett
George Eastman Professor of Management Science
Professor of Statistics
The Sloan School of Management and the Operations Research Center
Massachusetts Institute of Technology
Cambridge, MA


Anna Teytelman
The Operations Research Center
Massachusetts Institute of Technology
Cambridge, MA


Lesson vetted and approved by CPALMS

This learning video addresses a particular problem of selection bias, a statistical bias in which there is an error in choosing the individuals or groups to make broader inferences. Rather than delve into this broad topic via formal statistics, we investigate how it may appear in our everyday lives, sometimes distorting our perceptions of people, places and events, unless we are careful. When people are picked at random from two groups of different sizes, most of those selected usually come from the bigger group. That means we will hear more about the experience of the bigger group than that of the smaller one. This isn't always a bad thing, but it isn't always a good thing either. Because big groups "speak louder," we have to be careful when we write mathematical formulas about what happened in the two groups. We think about this issue in this video, with examples that involve theaters, buses, and lemons. The prerequisite for this video lesson is a familiarity with algebra. It will take about one hour to complete, and the only materials needed are a blackboard and chalk. The downloadable Teacher's Guide (see below) provides suggestions for classroom activities during each of the breaks between video segments.

View animated simulation of buses arriving and passengers waiting for them. The simulation depicts one hour of bus operations, with different degrees of arriving randomness for both passengers and buses: deterministic, random or clumped. Key performance statistics for each simulation run are shown in real time as the simulation progresses though the hour. (See "For Teachers" tab)

Arnie Barnett is George Eastman Professor of Management Science at MIT. He uses probability and statistics to work on problems about health and safety. Click here to read more.

Anna Teytelman is a PhD student in the Operations Research Center at MIT. She is working on using probabilistic models to describe pandemic flu transmission.

A Wikipedia entry on various types of sampling bias.
http://en.wikipedia.org/wiki/Sampling_bias

An article from the New York Times entitled "95% of Trains Are on Time? Riders Beg to Differ"
http://www.nytimes.com/2010/07/27/nyregion/27ontime.html?_r=1&emc=eta1

Download PDF of paper: Walk versus Wait: The Lazy Mathematician Wins.
http://arxiv.org/pdf/0801.0297v3

See BLOSSOMS video: “The Flaws of Averages” by Dan Livengood and Rhonda Jordan.
http://blossoms.mit.edu/videos/lessons/flaws_averages

The Flaws of Averages web page by Sam Savage of Stanford University.
http://www.stanford.edu/~savage/flaw/

This article from the New Scientist magazine discusses the clumping phenomenon of busses.
http://www.newscientist.com/article/dn18074-why-three-buses-come-at-once-and-how-to-avoid-it.html

Great

Anonymous
November 12, 2012 at 1:29 pm

Great

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This Lesson is in the following clusters: Probability

Great

Anonymous
November 12, 2012 at 1:29 pm

Great