Correlation
Many studies look for relationships between one thing -- usually called a variable -- and another. These variables could be almost anything -- physical traits, behaviors, ethnicity, disease, whatever. For example, a study once showed that breastfeeding is related to a child's later high intelligence. Researchers determine whether there is a relationship between two variables by using a mathematical tool called a correlation coefficient. This is a number that indicates how strongly related the two things are; it is expressed using a scale of from -1.0 to +1.0. A score between 0.0 and +1.0 means that there is a positive correlation, with +1.0 being a perfect correlation. An example of a perfect correlation would be the relationship between rainfall in a particular area and the water levels of local reservoirs. In other words, the more it rains, the more likely the higher the reservoirs would be. A score between 0.0 and -1.0 is called a negative correlation. An example of a negative correlation would be the relationship between personal income and receiving welfare benefits. In other words, the higher a person's income, the less likely they would be to qualify for welfare. A correlation coefficient of zero would mean that there is absolutely no relationship between one thing and the other -- for example, a study that compared the longevity of polar bears and the winning percentage of the New York Knicks basketball team would probably find a correlation coefficient of 0.0.

It is very important to remember that correlations tell you whether two variables are related, but they cannot tell you why or how those variables are related. A good example is the above study comparing breastfeeding and children's intelligence. While studies have, in fact, shown that these things are positively correlated, these same studies do not prove in any way that breastfeeding causes a child to become more intelligent. The data are perfectly consistent with other explanations, such as that more educated women tend to choose breastfeeding over bottle feeding. What may really be going on here is that intelligence is passed genetically from mother to child, whether or not the mother breastfeeds.