3-3 What does it mean when we say two things are correlated, and what are positive and negative correlations?

Describing behavior is a first step toward predicting it. Naturalistic observations and surveys often show us that one trait or behavior is related to another. In such cases, we say the two correlate. A statistical measure (the correlation coefficient) helps us figure how closely two things vary together, and thus how well either one predicts the other. Knowing how much aptitude test scores correlate with school success tells us how well the scores predict school success.

Throughout this book, we will often ask how strongly two things are related: For example, how closely related are the personality scores of identical twins? How well do intelligence test scores predict career achievement? How closely is stress related to disease? In such cases, scatterplots can be very revealing.

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Each dot in a scatterplot represents the values of two variables. The three scatterplots in FIGURE 3.3 illustrate the range of possible correlations from a perfect positive to a perfect negative. (Perfect correlations rarely occur in the real world.) A correlation is positive if two sets of scores, such as height and weight, tend to rise or fall together.

Saying that a correlation is “negative” says nothing about its strength. A correlation is negative if two sets of scores relate inversely, one set going up as the other goes down. The study of University of Nevada students discussed earlier found their reports of inner speech correlated negatively (−.36) with their reported psychological distress. Those who reported more inner speech tended to report somewhat less psychological distress.

Statistics can help us see what the naked eye sometimes misses. To demonstrate this for yourself, try an imaginary project. You wonder if tall men are more or less easygoing, so you collect two sets of scores: men’s heights and men’s temperaments. You measure the heights of 20 men, and you have someone else independently assess their temperaments from 0 (extremely calm) to 100 (highly reactive).

With all the relevant data right in front of you (TABLE 3.2), can you tell whether the correlation between height and reactive temperament is positive, negative, or close to zero?

Comparing the columns in Table 3.2, most people detect very little relationship between height and temperament. In fact, the correlation in this imaginary example is positive, +.63, as we can see if we display the data as a scatterplot (FIGURE 3.4).

If we fail to see a relationship when data are presented as systematically as in Table 3.2, how much less likely are we to notice them in everyday life? To see what is right in front of us, we sometimes need statistical illumination. We can easily see evidence of gender discrimination when given statistically summarized information about job level, seniority, performance, gender, and salary. But we often see no discrimination when the same information dribbles in, case by case (Twiss et al., 1989).

The point to remember: A correlation coefficient helps us see the world more clearly by revealing the extent to which two things relate.

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3-4 What is regression toward the mean?

Correlations not only make visible the relationships we might otherwise miss, they also restrain our “seeing” nonexistent relationships. When we believe there is a relationship between two things, we are likely to notice and recall instances that confirm our belief. If we believe that dreams are forecasts of actual events, we may notice and recall confirming instances more than disconfirming instances. The result is an illusory correlation.

Illusory correlations feed an illusion of control—that chance events are subject to our personal control. Gamblers, remembering their lucky rolls, may come to believe they can influence the roll of the dice by again throwing gently for low numbers and hard for high numbers. The illusion that uncontrollable events correlate with our actions is also fed by a statistical phenomenon called regression toward the mean. Average results are more typical than extreme results. Thus, after an unusual event, things tend to return toward their average level; extraordinary happenings tend to be followed by more ordinary ones.

The point may seem obvious, yet we regularly miss it: We sometimes attribute what may be a normal regression (the expected return to normal) to something we have done. Consider two examples:

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Failure to recognize regression is the source of many superstitions and of some ineffective practices as well. When day-to-day behavior has a large element of chance fluctuation, we may notice that others’ behavior improves (regresses toward average) after we criticize them for very bad performance, and that it worsens (regresses toward average) after we warmly praise them for an exceptionally fine performance. Ironically, then, regression toward the average can mislead us into feeling rewarded for having criticized others and into feeling punished for having praised them (Tversky & Kahneman, 1974).

The point to remember: When a fluctuating behavior returns to normal, there is no need to invent fancy explanations for why it does so. Regression toward the mean is probably at work.

3-5 Why do correlations enable prediction but not cause-effect explanation?

Consider some recent newsworthy correlations:

What shall we make of these correlations? Do they indicate that students would achieve more if their parents would support them less? That stopping smoking would improve mental health? That abstaining from video games would make reckless teen drivers more responsible?

No, because such correlations do not come with built-in cause-effect arrows. But correlations do help us predict. An example: Parenthood is associated with happiness (Nelson et al., 2013, 2014). So, does having children make people happier? Not so fast, say researchers: Parents also are more likely to be married, and married people tend to be happier than the unmarried (Bhargava et al., 2014). Thus, the correlation between parenthood and happiness needn’t mean that parenting increases happiness.

Another example: Self-esteem correlates negatively with (and therefore predicts) depression. (The lower people’s self-esteem, the more they are at risk for depression.) So, does low self-esteem cause depression? If, based on the correlational evidence, you assume that it does, you have much company. A nearly irresistible thinking error is assuming that an association, sometimes presented as a correlation coefficient, proves causation. But no matter how strong the relationship, it does not. As FIGURE 3.5 indicates, we’d get the same negative correlation between self-esteem and depression if depression caused people to be down on themselves, or if some third factor—such as heredity or brain chemistry—caused both low self-esteem and depression.

This point is so important—so basic to thinking smarter with psychology—that it merits one more example. A survey of over 12,000 adolescents found that the more teens feel loved by their parents, the less likely they are to behave in unhealthy ways—having early sex, smoking, abusing alcohol and drugs, exhibiting violence (Resnick et al., 1997). “Adults have a powerful effect on their children’s behavior right through the high school years,” gushed an Associated Press (AP) story reporting the finding. But again, correlations come with no built-in cause-effect arrow. The AP could as well have reported, “Well-behaved teens feel their parents’ love and approval; out-of-

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The point to remember (turn the volume up here): Correlation does not prove causation.¹ Correlation indicates the possibility of a cause-effect relationship but does not prove such. Remember this principle and you will be wiser as you read and hear news of scientific studies.