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

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

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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)

Instructor Biography

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.

For Teachers

Additional Online Resources

A Wikipedia entry on various types of sampling bias.

An article from the New York Times entitled "95% of Trains Are on Time? Riders Beg to Differ"

Download PDF of paper: Walk versus Wait: The Lazy Mathematician Wins.

See BLOSSOMS video: “The Flaws of Averages” by Dan Livengood and Rhonda Jordan.

The Flaws of Averages web page by Sam Savage of Stanford University.

This article from the New Scientist magazine discusses the clumping phenomenon of busses.