You have to really be careful when you analyze data. In this chapter, we will use careful, logical thinking to resolve the following four famous paradoxes in data analysis and high school math:
- In 1973, a total of 35% of women applying to Berkeley's graduate school were admitted and 44% of men applying to Berkeley's graduate school were admitted (see
homepage.stat.uiowa.edu/~mbognar/1030/Bickel-Berkeley.pdf). Does this discrepancy indicate that Berkeley admissions were biased against women?
- You take the bus to work every morning and the average time between buses is 60 minutes. With a quick calculation, you figure that on average if you arrive in the middle of a 60-minute interval, you should wait on average 30 minutes for a bus. It seems to you, however, that on average you wait much longer. What's going on?
- We drive from Bloomington, Indiana to Evansville, Indiana to visit my mother-in-law. In the morning, we drive the 80 miles at a speed of 80 miles per hour. In the evening, we drive back during rush hour and only average 40 miles per hour. Do we average 60 miles per hour for our trip?
- Your airline reports that the load factor—the average fraction of seats full on a flight—is 77.5%. As we all know, pre COVID-19 most flights were nearly completely full. How is this possible?
Simpson's Paradox and College Admissions
Simpson's paradox takes place when one type of behavior occurs in a total population (in the population of college ...