Simpson’s paradox, or the Yule–Simpson effect, is a phenomenon in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined. It is sometimes given the descriptive title reversal paradox or amalgamation paradox. (Wikipedia)
At the 2017 Q2 meeting the Northeast Regional Corporate ILG was dazzled by David Cohen of DCI Consulting with, among other insightful information, Simpson’s paradox.
Here are some more information sites for this phenomenon