How Numbers Deceive: Polygraphs, Mammograms, and More Section 3E How Numbers Deceive: Polygraphs, Mammograms, and More Copyright © 2008 Pearson Education, Inc.

3-E Simpson’s Paradox It is possible for a set of data to give different results in each of several groups than it does when the groups are taken together. This is a very straight-forward example of Simpson’s Paradox to use as an introduction. Copyright © 2008 Pearson Education, Inc.

Shaq, Vince and Simpson’s Paradox Since Shaq has the better shooting percentages in both the first half and second half of the game, can he claim that he has the better game compared to Vince? This is a very straight-forward example of Simpson’s Paradox to use as an introduction. No. Vince’s overall shooting percentage is 8/14 = 57.1% while Shaq’s is 7/14 = 50%. Copyright © 2008 Pearson Education, Inc.

Lie Detector/Polygraph Tests http://www.youtube.com/watch?v=N-TZ8Z5S9rI Copyright © 2008 Pearson Education, Inc.

Tree Diagram for Polygraphs Using n = 1000 and 90% accuracy, have students calculate the remaining parts of the tree (true positives, true negatives, and false negatives). Suppose that the polygraph is 90% accurate, how many of those applicants who were accused of lying were actually telling the truth? Copyright © 2008 Pearson Education, Inc.

More Examples for You! Handout for you to work in groups. Copyright © 2008 Pearson Education, Inc.

Political Mathematics Pose the question and encourage classroom discussion or perhaps collaborative group discussion on the clarity of the tax controversy. In light of the intense debates between Bush and Gore during the 2000 campaign, this issue should be one of interest. Republicans: Tax cut would benefit all families and the middle class would receive slightly greater benefits. Democrats: Tax cut would send disproportionate benefits to the rich. Which side was being more fair? Copyright © 2008 Pearson Education, Inc.