15.4: Real vs. Illusory Correlations

A pitfall that is especially relevant to this chapter is belief in illusory correlations. We believe in an illusory correlation when we think we perceive a correlation where one doesn’t really exist. More generally, we believe in an illusory correlation when we think that things go together substantially more (or less) often than they do.

A recurrent theme in this course is that human beings are constantly seeking to explain the world around them. We look for order and patterns, and we tend to “see” them even when they don’t exist. For example, most of us will think we detect patterns in the random outcomes of flips of a fair coin. So, it is not surprising that we tend to see strong relationships—correlations— among variables even when the actual correlation between them is minimal or nonexistent. This can be a serious error, because once we think we have found a correlation we typically use it to make predictions, and we frequently develop a causal explanation for it. If the correlation is illusory, the predictions will be unwarranted and our explanation of it will be false.

If Wilbur, for example, believes that women tend to be bad drivers—i.e., if he thinks there is a correlation between gender and driving ability—then it will be natural for him to predict that he will encounter more bad drivers among women than among men. He may even go so far as to predict that Sue, whose driving he has never observed, will be a bad driver. Finally, he may look around for some explanation of why women don’t drive well, one that may suggest they don’t do other things well either. So, beliefs in illusory correlations have consequences, and they are typically bad.

Our tendency to believe in illusory correlations has been verified repeatedly in lab studies. In a series of studies in the 1960s, Loren and Jean Chapman gave subjects information that was supposedly about a group of patients at a mental health facility. The subjects were given a clinical diagnosis of each patient and a drawing of a figure attributed to the patient. The diagnoses and drawings, which were all fictitious, were constructed so that there would be no correlation between salient pairs of features; for example, the figure was just as likely to have unfocused eyes when the diagnosis was paranoia as when it wasn’t.

Subjects were then asked to judge how frequently a given diagnosis, e.g., paranoia, went along with a feature of the drawing, e.g., unfocused eyes. Subjects greatly overestimated the extent to which such things went together, i.e., they overestimated the correlation between them, even when there was data that contradicted their conclusions. And they also had trouble detecting correlations that really were present.

Various things lead us to think we detect correlations when none exist. As we would by now expect, context and expectations often play a major role. We have some tendency to see what we expect, and even hope, to see. And we have a similar tendency to find the patterns we expect, and even hope, to find. For example, in word association experiments, subjects were presented with pairs of words (‘tiger - bacon’, ‘lion - tiger’).

They later judged that words like ‘tiger’ and ‘lion’, or ‘bacon’ and ‘eggs’, which they would expect to go together, had been paired much more frequently than they had been. Similarly, if you expect to encounter women who are bad drivers, you are more likely to notice those who do drive badly, forget about those who don’t, and interpret the behavior of some good women drivers as bad driving.

Many beliefs in illusory correlation amount to superstitions. If you believe that your psychic friend can accurately predict the future, then you believe that there is a positive correlation between what they say and what turns out to be true (i.e., you believe that the probability that a prediction will be true, given that they say it will, is high). Again, we may remember cases where someone wore their lucky sweater and did well on the big exam, which leads them to see an (illusory) correlation between wearing the sweater and success.

Illusory correlations often arise in our reasoning about other people. Many of us tend to think that certain good qualities (like honesty and kindness) are correlated, so, when we learn that a person has one good feature, we think it more likely that they have others. They might in some cases, but it’s not reasonable to draw this conclusion without further evidence. This pattern of thinking occurs so frequently that it has a name—the halo effect— and we return to it in more detail near the end of this chapter.

Illusory correlations also make it easier for people to cling to stereotypes. A stereotype is an oversimplified generalization about the traits or behavior of the members of some group. It attributes the same features to all members of the group, whatever their differences. There are many reasons why people hold stereotypes, but belief in illusory correlations often reinforces them. Thus, people may believe that members of some race or ethnic group tend to have some characteristic— usually some negative characteristic, like being lazy or dishonest—which is just to say that they believe that there is a correlation between race and personality traits.

But even when our expectations and biases don’t color our thinking, we often judge that two factors go together more often than they really do simply because we ignore evidence to the contrary. It is often easier to think of positive cases in which two factors go together than to think of negative cases in which they don’t.

Suppose we learn about several people who have the same illness and some of them got better after they started taking Vitamin E. It can be very tempting to conclude that people who take Vitamin E are more apt to recover than those who do not. But this may be an illusory correlation. Perhaps they would have gotten better anyway—people often do. To know whether there is a genuine correlation here, we need to compare the recovery rate among those who took Vitamin E and those who did not.

Ferreting out Illusory Correlations

In later chapters, we will learn to guard against many of the factors that encourage belief in illusory correlations, but we are already able to note one very important remedy. In this example, we were inclined to see a correlation between taking Vitamin E and recovering from an illness because we focused on just one sort of case, that in which people took Vitamin E and got better. But many people who don’t take Vitamin E may also recover, and perhaps many other people who do take it don’t recover. In fact, it might even turn out that a higher percentage of people who don’t take Vitamin E get better. Correlation is comparative.

One way to begin to see the importance of other cases is to note that the case of people who don’t take Vitamin E but recover anyway provides a baseline against which we can assess the effectiveness of the vitamin. If 87% of those who don’t take the vitamin recover quickly, then the fact that 87% of those who do take it recover quickly doesn’t constitute a positive correlation between taking Vitamin E and recovery. If 87% of those who don’t take it recover quickly, and if 86% (which sounds like a pretty impressive percentage, if we neglect the contrast cases) of those who do recover, taking the vitamin instead lowers the chances of recovery.

A more realistic example illustrates the same point. We may easily remember students who smoked marijuana and got into non-drug-related trouble with the law. They may stand out in our mind for various reasons, perhaps because they are frequently cited as bad examples. This can lead to belief in an illusory correlation between smoking dope and getting into trouble. It may well be that such a correlation exists, but to determine whether it does, we also must consider the contrast groups. In other words, we must consider not just group 1, but also groups 2, 3, and 4:

Group 1: People who smoked marijuana and did get in trouble.

Group 2: People who smoked marijuana but did not get in trouble.

Group 3: People who didn’t smoke marijuana and did get into trouble.

Group 4: People who didn’t smoke marijuana and did not get into trouble.

The relevant question here is whether the probability of getting in trouble is higher if you smoke marijuana than if you don’t. In other words, is it true that Pr(T |M) > Pr(T |~M)?

And it is impossible to answer this question without considering all four groups. To estimate a person’s probability of getting in trouble given that they smoked marijuana (Pr(T |M)), we must first estimate the proportion of marijuana users who did get in trouble, which requires some idea about users who got in trouble (Group 1) and users who did not (Group 2). And then to estimate the probability of a person’s getting in trouble given that they did not smoke marijuana (Pr(T |~M)), we need to estimate proportion of non-users who got in trouble, which requires some idea about non-users who got in trouble (Group 3) and those who did not (Group 4).

But we tend to focus on cases where both variables, here smoking marijuana and getting in trouble with the law, are present. This is an example of our common tendency to look for evidence that confirms our hypotheses and or beliefs, and to overlook evidence that tells against them. This is called confirmation bias, and we will examine it in detail in a later chapter on testing and prediction. But for now, the important point is that we can only make sensible judgments about correlations if we consider all four of the groups in the above list.

In real life, we are unlikely to know exact percentages, and we won’t usually bother to write out tables like the ones above. But if we have reasonable, ballpark estimates of the actual percentages, quickly constructing a comparative table in our heads will vastly improve our thinking about correlations. If we just pause to ask ourselves about the three cells we commonly overlook, we will avoid many illusory correlations. We will get some practice at this in the following exercises.

The Halo Effect: A Case Study in Illusory Correlation

Seeing More Connections Than Are There

When we give a person a strong positive evaluation on one important trait (like intelligence), we often assume that they should also receive positive evaluations on other traits (like leadership potential). This is called the halo effect. The one positive trait sets up a positive aura, or halo, around the person that leads us to expect other positive traits.

The reverse also holds; when a person seems to have one important negative trait, we tend to think that they will have other negative traits as well. The halo effect is a common example of our vulnerability to illusory correlations. We tend to think that one trait (e.g., honesty) is highly correlated with another (e.g., courage), when it fact it may not be. We don’t do this consciously, but it shows up in our actions.

In one real-world study, flight commanders tended to see a strong relationship between the intelligence of a flight cadet and his physique, between his intelligence and his leadership potential, and between his intelligence and his character. These traits are not completely unrelated, but the commanders greatly overestimated the strength of their connections. In another study, students who were told that their instructor would be warm were more likely to see them as considerate, good-natured, sociable, humorous, and humane. Being warm set up a halo that they thought extended to these other traits.

If two traits really do tend to go together, then we can draw a reasonable (but fallible) inference from one to the other. But such inferences are only legitimate if there truly is a strong objective connection—a high correlation— between the two traits. In many cases there is not, so the halo effect leads us to “see” more correlations or connections than there really are. We tend to see sets of traits as package deals, when in fact they are quite separate.

What is Beautiful is Good

Physical attractiveness provides one of the most striking examples of the halo effect. Different cultures perceive different attributes as attractive, but within most cultures (or subcultures), there is a good deal of agreement on what is viewed as attractive and what is not. Many people act as though they believe that there is a strong positive correlation between physical attractiveness (as rated by members of their culture) and other positive characteristics. For example, physically attractive people are viewed as happier, stronger, kinder, and more sensitive than less attractive people.

Of course, there may be some connection between being attractive and being happy, or between being attractive and having good social skills (why might this be so?). But attractiveness creates a halo that extends to completely unrelated characteristics. For example, experimenters had subjects read a set of essays. Each essay had a picture attached to it that the experimenter said was a picture of the author (although this was just a ruse). The quality of an essay was judged to be better when it was attributed to an attractive author.

Illusory correlations based on attractiveness occur in many settings in the real world. Attractive job candidates are more likely to be hired than less attractive ones. In one real-world study, physically attractive men earned a higher starting salary, and they continued to earn more over a ten-year period, than less attractive men. And although physically attractive women did not have higher starting salaries, they soon earned more than their less attractive counterparts.

The phenomenon even affects basic issues involving justice and fairness. The transgressions of attractive children are judged less severely by adults than similar actions by less attractive children. A mock jury sentenced an unattractive defendant to more years in prison than an attractive defendant, even though the crime was described in the same words in each case. And killing an attractive victim gained a stiffer sentence than killing an unattractive one.

Perhaps these findings should not be surprising. Beauty is held up as an ideal in commercials, movies, and TV, and on-screen heroes and heroines are almost always attractive. In fact, there is a physical attractiveness stereotype, and this is probably what sets up the halo. Once we classify someone as attractive, the attractiveness stereotype or schema is activated, and we find it natural to suppose that a person has other components of the stereotype.

There are a few exceptions to the attractiveness halo. Physically attractive women are more likely to be judged vain and egotistical, although people tend to think better of beautiful women, unless they are viewed as misusing their beauty. Physically attractive men are more likely to be judged less intelligent. But in general, physical attractiveness establishes a strong, positive halo.

As in most cases of the halo effect, the physical attractiveness stereotype is based on bad reasoning (although it does have some features of a self-fulfilling prophecy: if attractive people are treated better, they may do better in various ways). It is also unfair. But if we know about the phenomenon, we can more easily guard against it in our own judgments and try to protect ourselves against other people’s tendencies to fall victim to it in their own reasoning.