Variables such as buffalo and white men can be

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Variables, such as buffalo and White men, can be correlated in two ways—directly and inversely. Which type of correlation is being discussed in this cartoon? Two things that vary in the same direction are said to be directly correlated or to vary directly; the higher one’s age, the more gray hair. Things that are correlated may also vary in opposite directions; these are said to vary inversely. For example, there is an inverse correlation between the size of a car and its fuel economy. In general, the bigger a car is, the lower its fuel economy is. If you want a car that gets high miles per gallon, you should focus on cars that are smaller. There are other factors to consider too, of course. A small sports car may get lower fuel economy than a larger car with less power. Correlation does not mean that the relationship is perfect, only that variables tend to vary in a certain way. You may have heard the phrase “correlation does not imply causation,” or something similar. Just because two things happen together, it does not necessarily follow that one causes the other. For example, there is a well-known correlation between shoe size and reading ability in elementary children. Children with larger feet have a strong tendency to read better than children with smaller feet. Of course, no one supposes that a child’s shoe size has a direct effect on his or her reading ability, or vice versa. Instead, both of these things are related to a child’s age. Older children tend to have bigger feet than younger children; they also tend to read better. Sometimes the connection between correlated things is simple, as in the case of shoe size and reading, and sometimes it is more complicated. Whenever you read that two things have been shown to be linked, you should pay attention to the possibility that the correlation is spurious or possibly has
another explanation. Consider, for example, a study showing a strong correlation between the amount of fat in a country’s diet and the amount of certain types of cancer in that country (such as K. K. Carroll’s 1975 study, as cited in Paulos, 1997). Such a correlation may lead you to think that eating fat causes cancer, but this could potentially be a mistake. Instead, we should consider whether there might be some other connection between the two. It turns out that countries with high fat consumption also have high sugar consumption—perhaps sugar is the culprit. Also, countries with high fat and sugar consumption tend to be wealthier; fat and sugar are expensive compared to grain. Perhaps the correlation is the result of some other aspect of a wealthier lifestyle, such as lower rates of physical exercise. (Note that wealth is a particularly common confounding factor, or a factor that correlates with the dependent and independent variables being studied, as it bestows a wide range of advantages and difficulties on those who have it.) Perhaps it is a combination of factors, and perhaps it is the fat after all; however, we cannot simply

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