Correlation Does Not Equal Causation

Many introductory statistics courses seek to rectify the common misconception that researchers can draw causal conclusions from studies that show correlation.

This module presents students with examples, from outlandish to plausible, and asks students to think critically about variables, their relationships, and their impact on drawing valid conclusions. A PDF of the module can be found here.

Image from https://xkcd.com/552/

Remember that correlation describes the degree to which two (or more) variables vary together. This correlation could be positive (as one variable increases, the other increases), negative (as one variable increases, the other decreases), or zero (there is no relationship between the two variables). In this context, the word “causation” indicates that one variable directly causes the other to occur; in other words, if event A occurs, event B must also occur (though not necessarily vice versa). Causation can only be determined by a well designed experiment that is specifically designed to test for a causal relationship. For example, we know that as the number of drownings increases, the number of ice cream sales increases: number of drownings and ice cream sales are positively correlated. However, it’s unreasonable to conclude that buying ice cream causes drowning. Both are related to temperature: when it’s warmer out, more people spend time in the water, so there are more drownings; we also expect ice cream sales to increase with temperature.

Please read the following two articles and answer the questions for each.

1. Straight A's in High School May Mean Better Health Later in Life

http://www.time.com/time/health/article/0,8599,2036232,00.html?xid=huffpodirect

Thursday, Dec. 09, 2010 , TIME Magazine

Class rank is important for more than just wowing college admissions officers and securing bragging rights. According to new research, the better your grades were in high school, the healthier you are years later. It's not the first time that education has been associated with physical well being — more degrees equal better health — but a study published in the December issue of the Journal of Health and Social Behavior shows that it's not only more schooling but performance that makes a difference. "If you look at two people with high school degrees, the person with better grades is healthier later in life," says Pamela Herd, an associate professor of public affairs and sociology at the University of Wisconsin Madison. Relying on data from the Wisconsin Longitudinal Study, which has tracked more than 10,000 high school graduates from Wisconsin's Class of 1957, Herd found that the higher a person's class rank, the more likely they were to report "excellent" or "very good" health when they were in their early 60s. They were also more likely to report fewer chronic conditions. The participants' self-reporting bodes well for them down the road, says Herd. Asking people to assess their health "is predictive of mortality," she says. "Studies have found individuals are better at predicting their own mortality risk than their doctors would be." Researchers have interviewed the 1957 grads six times since they marched down the aisle to "Pomp and Circumstance." In the 1970s, when they were in their 30s and 40s, the questions emphasized family, work and social lives. By the early 1990s, researchers inquired about psychological well being and health. Now they're embarking on a seventh round of interviews. Why do good grades correlate with better health? Herd answers honestly; she doesn't know. But she's got her hypotheses, which include the possibility that A students are more conscientious — not only about academics but about their health as well. Not only did they buckle down in high school, but that self-discipline may have led them to steer clear of tobacco and get plenty of exercise. Without psychological data dating to their high school selves, though, it's tough to necessarily link the two. There's another possibility too: perhaps the skills required to excel in school — critical thinking, for example — may help good graders make wise decisions about their health care. Herd is continuing to try to suss out a clearer explanation. In the meantime, if you're in high school — or know someone who is — urge them to hit the books. It's the heart smart thing to do.

a. Which are the two correlated variables of interest?

b. Which variable is assumed to cause the other?

c. Do you believe that the data supports the conclusions in the article? Why or why not?

d. Name three to four “other variables” that could impact/predict/cause the relationship.

e. Can we conclude that there is sufficient evidence of causation in this example? Why or why not?

2. Eating Brown Rice to Cut Diabetes Risk

http://well.blogs.nytimes.com/2010/06/15/eatingbrownricetocutdiabetesrisk/

June 15, 2010, New York Times

By Roni Caryn Rabin

Brown rice contains fiber and nutrients that may help ward off diabetes. Next time you order takeout wonton soup and a spicy Number 82, you might want to make sure it comes with brown rice. Brown rice is a whole grain — white rice before it has been refined and polished and stripped of the bran covering, which is high in fiber and nutrients. Brown rice also has a lower glycemic index than white rice, which means it doesn’t cause blood glucose levels to rise as rapidly. Now a new study from researchers at Harvard reports that Americans who eat two or more servings of brown rice a week reduce their risk of developing Type 2 diabetes by about 10 percent compared to people who eat it less than once a month. And those who eat white rice on a regular basis — five or more times a week — are almost 20 percent more likely to develop Type 2 diabetes than those who eat it less than once a month. Just replacing a third of a serving of white rice with brown each day could reduce one’s risk of Type 2 diabetes by 16 percent, a statistical analysis showed. A serving is half a cup of cooked rice. The study, which was published in The Archives of Internal Medicine and used data from two Harvard nurses’ health studies and a separate study of health professionals, isn’t the first to point a finger at foods like white rice as a culprit in Type 2 diabetes. A 2007 study of Chinese women in Shanghai found that middle-aged women who ate large amounts of white rice and other refined carbohydrates were also at increased risk for diabetes compared to their peers who ate less. But the Harvard study is one of the first to distinguish between brown rice and white rice consumption in the United States, where rice is not a staple food and relatively little is eaten overall, said Dr. Qi Sun, an instructor in medicine at Brigham and Women’s Hospital, which is affiliated with Harvard Medical School. Many food studies simply lump brown and white rice together. “The bottom line is we showed evidence that increased consumption of white rice – even at this low level of intake — is still associated with increased risk,” said Dr. Sun, who was at the Harvard School of Public Health when the study was done. “It’s really recommended to replace white rice with the same amount of brown rice or other whole grains.” The researchers who did the study analyzed rice consumption among 39,765 men and 57,463 women who participated in the Health Professionals Followup Study and the Nurses’ Health Study I and II; participants in the three groups ranged in age from 26 to 87. They had filled out food frequency questionnaires when the studies started — in 1986, 1984 and 1991, respectively — and updated their diet information every four years subsequently, through 2005 and 2006. They were also asked about their medical histories. During the course of the studies, more than 10,000 participants developed Type 2 diabetes. Such food studies can be unreliable, since they rely on self-reported surveys. And correlation does not necessarily mean a cause and effect relationship, since factors other than brown rice consumption may have accounted for the decreased diabetes risk that was observed. The researchers tried to control for the fact that Americans who eat brown rice tend to be more healthy overall — they eat more fruits and vegetables and less red meat and trans fats, and they also tend to be thinner, more active and less likely to smoke than those who don’t eat brown rice. But, Dr. Sun said, there were many possible explanations for why brown rice eaters are at lower risk for Type 2 diabetes. In addition to having a lower glycemic index than white rice, brown rice also contains important nutrients like magnesium that are stripped during the refining process; it also contains much more fiber. Earlier studies have found that having these nutrients in the diet protects against diabetes, Dr. Sun said.

a. Which are the two correlated variables of interest?

b. Which variable is assumed to cause the other?

c. Do you believe that the data supports the conclusions in the article? Why or why not?

d. Name three to four “other variables” that could impact/predict/cause the relationship.

e. Can we conclude that there is sufficient evidence of causation in this example? Why or why not?