Simson’s Paradox

Simpson's paradox

Simpson's paradox is a statistical paradox described by E. H. Simpson in 1951, in which the accomplishments of several groups seem to be reversed with the groups are combined.

It's a well accepted rule of thumb that the larger the data set, the more reliable the conclusions drawn. Simpson' paradox, however, slams a hammer down on the rule and the result is a good deal worse than a sore thumb. Unfortunately Simpson's paradox demonstrates that a great deal of care has to be taken when combining small data sets into a large one. Sometimes conclusions from the large data set are exactly the opposite of conclusion from the smaller sets. Unfortunately, the conclusions from the large set are also usually wrong.

Here is an example. Suppose two people, Ann and Bob, who are let loose on Wikipedia. In the first test, Ann improves 60 percent of the articles she edits while Bob improves 90 percent of the articles he edits. In the second test, Ann improves just 10 percent of the articles she edits while Bob improves 30 percent.

Both times, Bob improved a much higher percentage of articles than Ann - yet when the two tests are combined, Ann has improved a much higher percentage than Bob!

The result comes about this way: In the first test, Ann edits 100 articles, improving 60 of them, while Bob edits just 10 articles,