Perhaps the most pervasive misinterpretation of statistics in everyday life is translating a statistical association (a correlation) into a cause-and-effect relationship.
As noted in the text, there are a number of alternative explanations for a correlation between two variables, X and Y. It could indeed be the case that variable Y changes because of variable X. But there are other possible interpretations. In many cases, the causal arrow may run in the opposite direction--changes in variable X may be due to changes in variable Y. Finally, a third variable, Z, may be causing changes in both X and Y. So, as Z changes, X and Y change simultaneously, leading to their correlation.
A few examples should serve to clarify the various possibilities. Following are some examples of correlations that might be misinterpreted easily and quickly as causal relationships. See if you can come up with possible third variables to explain each of the correlations below before the explanations are discussed.
A TV news show reported that women who have a baby after the age of forty are more likely to live to be one hundred than those who do not. Is having a baby at a relatively late childbearing age responsible for prolonged life? Almost certainly not--there are a number of third variables that could account for the correlation. Women aged forty or older who can bear a child may in general be aging more slowly, hence they will live longer. Also, women who bear children when they are in their forties may tend to be healthier, better off financially, or have other characteristics associated with living longer.
In major cities in the United States, the greater the quantity of ice cream sold, the greater the number of murders. Obviously, ice cream must play a role in today's violent society! Of course, this is a clear case of a third variable that impacts both ice cream sales and murders--heat.
Neale and Liebert (1973) provide another striking example--there is a positive correlation between the number of churches in a city and the amount of crime in that city. Does this mean we should shut down some places of worship to help curb crime? Obviously, a third variable is at work here as well--population size.
A recent finding that a baby's weight at birth is positively correlated with later IQ scores provides an opportunity to consider third variables as well. Explanations include the possibility that the mother's prenatal care and nutrition cause the baby's weight to increase. Large babies tend to be healthier; healthier babies do better physically and cognitively. Other contributing factors to overall infant health include family financial resources and access to quality day care and health care. This is most likely a multi-causal effect.
John Allen Paulos describes in his book Innumeracy how people living in the New Hebrides Islands believed for some time that body lice were a cause of good health. They noticed that people who were ill with influenza and other infectious diseases didn't have body lice. As it turned out, the fever generated by these illnesses drove away the lice.
The more a person weighs, the larger his or her vocabulary is. There is a straightforward third variable in this case--age.
Overweight people who carry their weight in the abdomen ("apple-shaped people") are more prone to die of heart attacks than those who carry their weight in the hips and thighs ("pear-shaped people"). The third variable involved in this well-known misconception is gender--overweight men tend to the apple shape and overweight women tend to the pear shape. Men are more vulnerable to cardiovascular disease due to a variety of causal factors.
A study conducted by researchers at the University of Colorado between 1987 and 1995 showed that regular church attendance possibly resulted in a longer lifespan. Third variables in this case may be linked to lifestyle. Those who attend church are probably less likely to smoke, drink, and engage in other activities that can result in premature death.
Now it's your turn. As you read newspaper, magazines and listen to news broadcasts, find three good examples of correlational results being presented as if they implied causality. For each, include the statement made by the news media and identify as many interpretations of the data (including possible third variables) as you can.
