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Simpson’s Paradox

Simpson’s Paradox. Section 4.3.2. Starter 4.3.2. The table at right shows the number of ATM transactions (in millions) in the United States from 1985 to 1996. Sketch the scatterplot and state which of the models we have studied you think will apply, and why you think so.

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Simpson’s Paradox

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  1. Simpson’s Paradox Section 4.3.2

  2. Starter 4.3.2 • The table at right shows the number of ATM transactions (in millions) in the United States from 1985 to 1996. • Sketch the scatterplot and state which of the models we have studied you think will apply, and why you think so. • Find the correct mathematical model that approximates the data. Justify your choice by sketching the residual plot. Clearly state the prediction equation in context. • Predict the number of transactions in 2000 assuming extrapolation is justified.

  3. Objectives • Analyze data in a two-way table in which proportions of sub-groups are inconsistent with proportions of the whole.

  4. Simpson’s Paradox • Consider two hospitals: A and B • Last year, Hospital A did 2100 surgeries, of which 63 patients died. • Hospital B did 800 surgeries, of which 16 patients died • Calculate the proportion of deaths in each hospital and decide which you would choose if you needed surgery.

  5. Simpson’s Paradox • Now consider a lurking variable: how bad was the condition of the patients when they went to the hospital? • For those in good condition • 600 went to A and 6 died • 600 went to B and 8 died • For those in poor condition • 1500 went to A and 57 died • 200 went to B and 8 died • Again calculate the proportion of deaths in each hospital and decide which you would choose if you needed surgery.

  6. Simpson’s Paradox • What you have just seen is an example of Simpson’s Paradox. • Data from an overall group gives proportions that seem to favor one choice over another. • When the groups are broken down into sub-groups, each smaller group can have proportions that gives the opposite outcome.

  7. Homework • Read pages 222 – 226 • Do problems 40, 41

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