Suppose the batting averages of two Major League baseball players are compared over a 3-year period. Each year, Player “X” outhits Player “Y.” However, when the data from the 3 years are lumped together, it turns out that Player “Y” now has the higher batting average. This strange and unexpected situation not only is possible, it actually has occurred! It’s an example of something called “Simpson’s Paradox.”
This paradox can show up in places other than sports. Take the medical field, for example. Suppose a researcher wants to compare 2 drugs—Drug “A” and Drug “B”—to see which one is more effective at curing people from a bad disease. In an effort to be careful, the researcher conducts 2 trials. The results of the 1st trial show that Drug “B” is better than Drug “A.” So do the results of the 2nd trial. However, when the data from the 2 trials are combined, Drug “A” shows up as more effective!
To see a write-up of the baseball data and other examples of this statistical oddity, click: Simpson’s Paradox
Here’s a short and entertaining video that gives a clear example of Simpson’s Paradox (and how best to make sense out of data that have conflicting interpretations when looked at in different “parts” versus in their “totality”).