What is true for the parts is not necessarily true for the whole.
Simpson's paradox (or the Yule–Simpson effect) is a paradox in which a correlation present in different groups is reversed when the groups are combined. This result is often encountered in social-science and medical-science statistics, and it occurs when frequency data are hastily given causal interpretations. Simpson's Paradox disappears when causal relations are brought into consideration (see Implications to decision making).
Though it is mostly unknown to laymen, Simpson's Paradox is well known to statisticians, and it is described in a few introductory statistics books. Many statisticians believe that the mainstream public should be informed of the counter-intuitive results in statistics such as Simpson's paradox.