CORRELATIONAL RESEARCH 53
Table 2.5 shows the average percentage of times the children behaved pro- socially during these episodes at each of three periods: time 1 (13 to 15 months of age), time 2 (18 to 20 months), and time 3 (23 to 25 months). As the table shows, the percentage of times children behaved prosocially increased dramatically over the course of the year, regardless of whether they witnessed or caused the distress. When the investigators analyzed the changes in rates of prosocial responses over time to both types of distress (witnessed and caused), they found the differences to be statistically significant. A jump from 9 to 49 prosocial behaviors in 12 months was thus probably not a chance occurrence.
Nevertheless, researchers can never be certain that their results are true of the population as a whole; a black swan could always be swimming in the next lake. Nor can they be sure that if they performed the study with 100 different partici- pants they would not obtain different findings. This is why replication—repeating a study to see if the same results occur again—is extremely important in science.
TABLE 2 .5
CHILDREN’S PROSOCIAL RESPONSE TO ANOTHER PERSON’S DISTRESS DURING THE SECOND YEAR OF LIFE
Percentage of Episodes in Which the Child Behaved Prosocially
Type of Incident Time 1 Time 2 Time 3
Witnessed distress 9 21 49
Caused distress 7 10 52
Source: Adapted from Zahn-Waxler et al., 1992a.
C O R R E L A T I O N A L R E S E A R C H
Correlational research attempts to determine the degree to which two or more vari-
ables are related. Although correlational analyses can be applied to data from any kind of study, most often correlational designs rely on survey data such as self-report questionnaires.
For example, for years psychologists have studied the extent to which personality in childhood predicts personality in adulthood (Caspi, 1998). Are we the same person at age 30 as we were at age 4? In one study, researchers followed up children whose personalities were first assessed around age 9, examining their personalities again 10 years later (Shiner, 2000). They then correlated childhood personality variables with personality characteristics in late adolescence. The statistic that allows a researcher to
correlate two variables is called a correlation coefficient. A correlation coefficient
measures the extent to which two variables are related (literally, co-related, or related to each other).
A correlation can be either positive or negative. A positive correlation means that the higher individuals measure on one variable, the higher they are likely to mea- sure on the other. This also means, of course, that the lower they score on one vari- able, the lower they will score on the other. A negative correlation means that the higher participants measure on one variable, the lower they will measure on the other. Correlations can be depicted on scatterplot graphs, which show the scores of every participant along two dimensions (Figure 2.6).
Correlation coefficients vary between +1.0 and -1.0. A strong correlation—one with a value close to either positive or negative 1.0—means that a psychologist who
correlational research research that assesses
the degree to which two variables are related, so that knowing the value of one can lead to prediction of the other
correlate in research, to assess the extent
to which the measure of one variable predicts the measure of a second variable
correlation coefficient an index of the extent
to which two variables are related
positive correlation a relation between two
variables in which the higher one is, the higher the other tends to be
negative correlation a relation between two
variables in which the higher one is, the lower the other tends to be
knows a person’s score on one variable can confidently predict that person’s score on the other. For instance, one might expect a high positive correlation between child- hood aggressiveness at age 9 and social problems at age 19 (i.e., the higher the ag- gressiveness, the higher the person’s score on a measure of social dysfunction). One might equally expect a high negative correlation between childhood aggressiveness and adult academic success. A weak correlation (say, between childhood agreeable- ness and adult height) hovers close to zero, either on the positive or the negative side. Importantly, variables can actually be related to one another, yet the correlation coefficient does not reflect that relationship. Correlation is an index of the linear rela-
tionship between variables. As shown in Figure 2.6, a straight line can be drawn that
captures many of the data points when two variables are related in a linear fashion. Alternatively, however, variables may be related to one another in a curvilinear fash- ion, yet the correlation coefficient does not reflect this relationship. As shown in Fig- ure 2.7, the relationship between arousal and performance is curvilinear, suggesting that there is clearly a relationship between these two variables. However, because the relationship is not linear, the correlation between the two variables approaches zero.
Table 2.6 shows the correlations among three childhood personality variables— extraversion (sociability), agreeableness, and achievement motivation—and three measures of functioning in late adolescence—academic achievement, conduct (e.g., not breaking rules or committing crimes), and social functioning. These correlations are arrayed as a correlation matrix. As the table shows, childhood extraversion is not a strong predictor of academic functioning and conduct in late adolescence (in fact, if anything, extraverted kids become rowdier adolescents; the correlation coeffi- cient, denoted by the letter r is -0.14). However, extraverted children do tend to be- come socially well-adapted adults (r = 0.35). Childhood agreeableness and achieve- ment motivation both tend to predict positive functioning in all three domains in late adolescence.
In psychological research, theoretically meaningful correlations tend to hover around 0.3, and correlations above 0.5 are considered large (Cohen, 1988). Some- times, however, seemingly tiny correlations can be very meaningful. For example, a study of the impact of aspirin on heart disease in a sample of roughly 20,000 par- ticipants had to be discontinued on ethical grounds when researchers found a -0.03 correlation between use of a single aspirin a day and risk of death by heart attack (Rosenthal, et al., 2000)! This correlation translates to 15 out of 1000 people dying if they do not take an aspirin a day as a preventive measure.
correlation matrix a table presenting the
correlations among several variables
FIGURE 2 .6 (a) Positive, (b) negative, and (c) zero correlations. A correlation expresses the relation between two variables. The panels depict three kinds of correlations on hypothetical scatterplot graphs, which show the way data points fall (are scat- tered) on two dimensions. Panel (a) shows a positive correlation, between height and weight. A comparison of the dots (which represent individual participants) on the right with those on the left shows that those on the left are lower on both variables. The dots scatter around the line that summarizes them, which is the correlation coefficient. Panel (b) shows a negative correla- tion, between socioeconomic status and dropout rate from high school. The higher the socioeconomic status, the lower the dropout rate. Panel (c) shows a zero correlation, between intelligence and the extent to which an individual believes people can be trusted. Being high on one dimension predicts nothing about whether the participant is high or low on the other.
Height (a) Weight Intelligence Socioeconomic status (b) (c)
Dropout rate from high school Interpersonal trust
FIGURE 2 .7 The relationship between arousal and performance is curvilinear. Because correlation assesses only linear relationships, the correlation coefficient reflecting the relationship between arousal and performance is close to zero.
Low Moderate High
Arousal Level
CORRELATIONAL RESEARCH 55
A primary virtue of correlational research is that it allows investigators to study a whole range of phenomena that vary in nature—from personality characteristics to attitudes—but can- not be produced in the laboratory. Like other nonexperimental methods, however, correlational research can only describe re- lationships among variables (which is why it is actually some- times categorized as a descriptive method, rather than placed in its own category). When two variables correlate with each other, the researcher must infer the relation between them: Does one cause the other, or does some third variable explain the correlation?
Media reports on scientific research often disregard or mis- understand the fact that correlation does not imply causation. If a
study shows a correlation between drug use and poor grades, the media often report that “scientists have found that drug use leads to bad grades.” That may be true, but an equally likely hypothesis is that some underlying aspect of personality (such as alienation) or home environment (such as poor parenting, abuse, or neglect) produces both drug use and bad grades (Shedler & Block, 1990).
A second virtue of correlational research is that other researchers often rely on it (as well as experimental methods) to investigate psychological phenomena across cultures. For example, psychologists have used correlational and experimental pro- cedures in other countries to test whether the findings of Western studies replicate cross-culturally, such as studies of perception and obedience to authority (see Berry et al., 1992, 1997; Triandis, 1994).
Psychologists interested in the cross-cultural validity of their theories face many difficulties, however, in transporting research from one culture to another. The same stimulus may mean very different things to people in different cultures.
How might the Efe pygmies in the tropical rain forests of Zaire, who have had minimal exposure to photographs, respond to a study asking them to judge what emotion people are feeling from pictures of faces? Creating an equivalent experimental or correlational design often requires using a differ-
ent design—but then is it really the same study?
Similarly, when employing a questionnaire cross-culturally, researchers must be very careful about translation because even minor changes or am- biguities could make cross-cultural comparisons invalid. To minimize dis- tortions in translation, researchers use a procedure called back-translation, in which a bilingual speaker translates the items into the target language, and another bilingual speaker translates it back into the original language (usually English). The speakers then repeat the process until the translation back into English matches the original. Even this procedure is not always adequate; sometimes concepts simply differ too much across cultures to make the items equivalent. Asking a participant to rate the item “I have a good relationship with my brother” would be inappropriate in Japan, for
example, where speakers distinguish between older and younger brothers and lack a general term to denote both (Brislin, 1986).
I N T E R I M S U M M A R Y
Correlational research assesses the degree to which two variables are related; a correla- tion coefficient quantifies the association between two variables and ranges from -1.0
to +1.0. A correlation of zero means that two variables are not related to each other in a linear fashion, whereas a high correlation (either positive or negative) means that partici- pants’ scores on one variable are good predictors of their scores on the other. Correlational research can shed important light on the relations among variables, but correlation does not imply causation.
Life among the Efe people.
TABLE 2 .6
THE RELATION BETWEEN CHILDHOOD PERSONALITY AND LATE ADOLESCENT FUNCTIONING
Late Adolescent Functioning Childhood Personality Trait Academic Conduct Social
Extraversion –0.07 –0.14 0.35
Agreeableness 0.23 0.33 0.19
Achievement motivation 0.37 0.26 0.25
Source: Adapted from Shiner, 2000.
To what extent would you obey an authority figure? Would it depend on what they were asking you to do? Would you take out the trash if your parents asked you? Would you write an answer to a question on the board if your teacher asked you? Would you deliver an electric shock to a total stranger if a researcher asked you? In all likeli-
hood, your (and most other people’s) answer to the third and fourth ques- tions would be “yes” and your answer to the last question, “no.” Of course you wouldn’t shock a stranger if some researcher told you to do so. No re- search is that important, right? Or would you?
Beginning in the 1960s, Stanley Milgram (1963, 1974) conducted a series of classic studies on obedience at Yale University that took many people, in- cluding psychologists, by surprise. The results of his investigations suggested that the philosopher Hannah Arendt may have been right when she said that the horrifying thing about the Nazis was not that they were so deviant but that they were “terrifyingly normal.”
The basic design of the studies was as follows: The experimenter told participants they were participating in an experiment to examine the effect of punishment on learning. Participants were instructed to punish a “learn- er” (actually a confederate of the researcher) in the next room whenever the learner made an error, using an instrument they believed to be a shock gen- erator. Panel switches were labeled from 15 volts (slight shock) to 450 volts (danger: severe shock). The experimenter instructed the participants to begin by administering a slight shock and increase the voltage each time the learner made an error. The learner actually received no shocks, but participants had no reason to disbelieve what they were told—especially since they heard pro- tests and, later, screaming and pounding on the wall from the next room as they increased the punishment.
Milgram was not actually studying the impact of punishment on learn- ing. Rather, he wanted to determine how far people would go in obeying orders. Before conducting the study, Milgram had asked various social scien- tists to estimate how many participants would go all the way to 450 volts. The experts estimated that a very deviant subsample—well below 5 percent— might administer the maximum.
They were wrong. As you can see in Figure 2.8, approximately two-thirds of participants administered the full 450 volts, even though the learner had stopped responding (screaming or otherwise) and was apparently either un- conscious or dead. Many participants were clearly distressed by the expe- rience, but each time they asked if they should continue to administer the shocks, the experimenter told them that the experiment required that they continue. If they inquired about their responsibility for any ill effects the learner might be experiencing, the experimenter told them that he was re- sponsible and that the procedure might be painful but was not dangerous. The experimenter never overtly tried to coerce participants to continue; all he did was remind them of their obligation. To Milgram, the implications were