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Correlation and Causation Help

By — McGraw-Hill Professional
Updated on Sep 13, 2011

Correlation and Causation

Correlation between two variables does not imply a direct cause-and-effect relation. Here are some problems involving correlation and causation.

Two Modern Plagues

During the last few decades of the 20th century and into the first years of the 21st century, there was a dramatic increase in the incidence of adult-onset diabetes (let's call it AOD for short) in the United States. This is a syndrome in which the body develops problems regulating the amount of glucose in the blood. (Glucose is a simple form of sugar and an important body fuel.) During the same period of time, there was also an increase in the incidence of obesity (overweight). Scientists and physicians have long suspected that there are cause-and-effect relationships at work here, but the exact mechanisms have been under debate.

Practice 1

It has been found that overweight adults are more likely to have AOD than adults who are not overweight. In fact, if a person is randomly selected from the United States population, the likelihood of that person having AOD increases as the extent of the obesity increases. What sort of correlation is this?

Solution 1

Obesity is positively correlated with AOD. To be more precise, let Mn be the normal mass in kilograms for a person of a certain height, gender, and age, and let Ma be the person's actual mass in kilograms. Then the probability that a randomly selected person has AOD is positively correlated with the value of Ma/Mn.

Practice 2

Does the above correlation, in itself, logically imply that obesity directly causes AOD? Keep in mind that the term logical implication, in this context, means implication in the strongest possible sense. The statement "P logically implies Q" is equivalent to the statement "If P, then Q."

Solution 2

No. The "conventional wisdom" holds that obesity is a contributing factor to the development of AOD, and research has been done to back up this hypothesis. But the mere existence of the correlation, all by itself, does not prove the hypothesis.

Practice 3

Does the above correlation, in itself, logically imply that AOD directly causes obesity?

Solution 3

Again, the answer is "No." Few if any scientists believe that AOD causes obesity, although it can be argued that this idea should get more attention. The correlation is an observable phenomenon, but if we claim that there is a direct cause-and-effect relationship between AOD and obesity, we must conduct research that demonstrates a plausible reason, a modus operandi.

Practice 4

Does the above correlation, in itself, logically imply that both AOD and obesity are caused by some other factor?

Solution 4

The answer is "No" yet again, for the same reasons as those given above. In order to conclude that there is a cause-and-effect relationship of any kind between or among variables, good reasons must be found to support such a theory. But no particular theory logically follows from the mere existence of the correlation.

Most scientists seem to agree that there is a causative factor involved with both AOD and obesity: the consumption of too much food! It has been found that people who overeat are more likely to be obese than people who don't, and the recent increase in AOD has also been linked to overeating. But even this is an oversimplification. Some scientists believe that the overconsumption of certain types of food is more likely to give rise to AOD than the overconsumption of other types of food. There are also sociological, psychological, and even political issues involved. It has been suggested that the stress of modern living, or the presence of industrial pollutants, could give rise to AOD. And who knows that the incidence of AOD might not be influenced by such unsuspected factors as exposure to electromagnetic fields?

Practice 5

We have now seen that the correlation between obesity and AOD, all by itself, does not logically imply any particular cause-and-effect relationship. Does this mean that whenever we see a correlation, be it weak or strong or positive or negative, we must conclude that it is nothing more than a coincidence?

Solution 5

Once again, the answer is "No." When we observe a correlation, we should resist the temptation to come to any specific conclusion about cause-and-effect in the absence of supporting research or a sound theoretical argument. We should be skeptical, but not closed-minded. We should make every possible attempt to determine the truth, without letting personal bias, peer pressure, economic interests, or political pressures cloud our judgment. There is often a cause-and-effect relationship (perhaps more than one!) behind a correlation, but we must also realize that coincidences can and do occur.

More practice problems for these concepts can be found at:

Statistics Practical Problems Practice Test

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