It is unfortunately quite easy to report erroneous results when doing data analysis. Simpson's paradox is one of the more common phenomena a that can appear in a data analysis. It occurs when one group shows a higher result than another group, when all the data is aggregated, but it shows the opposite when the data is subdivided into different segments. For instance, let's say we have two students, A and B, who have each been given a test with 100 questions on it. Student A answers 50% of the questions correct, while Student B gets 80% correct. This obviously suggests Student B has greater aptitude:

Let's say that the two tests were very different. Student A's test consisted of 95 problems that were difficult and only five that were easy. Student B was given a test with the exact opposite ratio.

This paints a completely different picture. Student A now has a higher percentage of both the difficult and easy problems but has a much lower percentage as a whole. This is a quintessential example of Simpson's paradox. The aggregated whole shows the opposite of each individual segment.