3.1. Covariation illusions

In order to reason well about social matters, we need to be able to reliably

detect correlations. But in a classic series of studies, Chapman and

Chapman (1967, 1969) found that we can be quite bad at this on tasks that

represent the ordinary challenges facing us. We often don’t recognize

covariations that exist, particularly when they do not conform to our

background beliefs; and we often report covariations where there are none,

particularly when we expect there to be covariation. In the past, many

psychologists used Draw-a-Person (or DAP) tests to make initial diagnoses.

The Amazing Success of Statistical Prediction Rules 37

It was thought that patients’ disorders could be diagnosed from their

drawings of people. For example, it was thought that paranoid patients

would draw large eyes; the drawings of impotent patients would emphasize

male genitalia or would be particularly macho. By the mid-1960s, it was

well known that DAP tests were bunk. There are no such correlations. And

yet clinicians continued to use them. Chapman and Chapman (1967) asked

clinicians who used the DAP test to describe the features of patients’

drawings they thought were associated with six diagnoses. Once they had

these reports, Chapman and Chapman obtained 45 DAP drawings made by

patients in a state hospital and randomly paired those drawings with the six

diagnoses. Each drawing-diagnosis pair was then presented to introductory

psychology students for 30 seconds, and then the students were asked to

report which features of the drawings were most frequently associated with

each diagnosis. Even though there were no systematic relationships in the

data, subjects claimed to detect covariations. Further, they were virtually

the same covariations the clinicians claimed to find in real data! It is

plausible to suppose in this case that widely shared background assumptions

(or perhaps just thoughtless stereotypes) led both expert clinicians

and naıЁve subjects to ‘‘see’’ covariations in data that simply weren’t there.

Interestingly, when Chapman and Chapman built in massive negative covariations

between the features of the drawings and the diagnoses subjects

were likely to make, naıЁve subjects still reported positive covariations—

though somewhat reduced in magnitude.

In another fascinating study, Chapman and Chapman focused on the

famous Rorschach test. While most of the associations clinicians have

believed they detected in Rorschach tests are actually not present, it turns

out that two responses to the Rorschach test are correlated with male

homosexuality. However, these responses are not particularly ‘‘face valid’’

(i.e., they do not strike most people as particularly intuitive). For example,

male homosexuals are not more likely to identify in the Rorschach blots

feminine clothing, anuses or genitalia, or humans with confused or uncertain

sexes. In fact, homosexual men more frequently report seeing monsters

on Card IV and a part-human-part-animal on Card V. (Again, Chapman

and Chapman found that clinicians of the day believed there was a significant

correlation between the ‘‘face valid’’ signs and homosexuality. Only 2

of the 32 clinicians they polled even listed one of the valid signs.) NaıЁve

subjects (1969) were given 30 cards with traits (homosexual or nonhomosexual)

on one side and Rorschach responses on the other (a valid sign,

an invalid but ‘‘face valid’’ sign, or a filler sign) and were given 60 seconds

to review each card. Even though the cards contained no correlations between the traits and the Rorschach responses, subjects reported frequent

correlations between the ‘‘face valid’’ signs and homosexuality. This finding

essentially replicates the DAP test result.

Next, Chapman and Chapman changed the cards so that the valid signs

were associated more often with homosexuality than were the other signs.

Even when the valid signs were associated with homosexuality 100% of the

time, naıЁve observers failed to detect the covariation. So it’s not just that

subjects see correlations when there are none. In fact, we often don’t see

correlations that are actually there, and sometimes we see positive correlations

when in fact the correlations are negative.

It should be noted that Chapman and Chapman did not draw particularly

pessimistic conclusions from their experiments. Nor do we. In

fact, when Chapman and Chapman took out the misleading invalid signs,

subjects were capable of detecting the actual covariations in the data. Nisbett

and Ross (1980) draw the following conclusion from these experiments:

[R]eported covariation was shown to reflect true covariation far less than it

reflected theories or preconceptions of the nature of the associations that

‘‘ought’’ to exist. Unexpected, true covariations can sometimes be detected

but they will be underestimated and are likely to be noticed only when the

covariation is very strong, and the relevant data set excludes ‘‘decoy features’’

that bring into play popular but incorrect theories. (97)

When it comes to social judgment, the evidential situation is likely to be

quite complex—with many signs that are valid but counterintuitive and

other signs that are ‘‘face valid’’ but not predictive. In such an environment,

we are not likely to do a particularly good job of detecting covariations.

And so, unless the theories, background assumptions, and stereotypes

we bring to a particular prediction are accurate, we are not likely to be very

good at identifying what cues are most likely to covary with and so predict

our target property.

In order to reason well about social matters, we need to be able to reliably

detect correlations. But in a classic series of studies, Chapman and

Chapman (1967, 1969) found that we can be quite bad at this on tasks that

represent the ordinary challenges facing us. We often don’t recognize

covariations that exist, particularly when they do not conform to our

background beliefs; and we often report covariations where there are none,

particularly when we expect there to be covariation. In the past, many

psychologists used Draw-a-Person (or DAP) tests to make initial diagnoses.

The Amazing Success of Statistical Prediction Rules 37

It was thought that patients’ disorders could be diagnosed from their

drawings of people. For example, it was thought that paranoid patients

would draw large eyes; the drawings of impotent patients would emphasize

male genitalia or would be particularly macho. By the mid-1960s, it was

well known that DAP tests were bunk. There are no such correlations. And

yet clinicians continued to use them. Chapman and Chapman (1967) asked

clinicians who used the DAP test to describe the features of patients’

drawings they thought were associated with six diagnoses. Once they had

these reports, Chapman and Chapman obtained 45 DAP drawings made by

patients in a state hospital and randomly paired those drawings with the six

diagnoses. Each drawing-diagnosis pair was then presented to introductory

psychology students for 30 seconds, and then the students were asked to

report which features of the drawings were most frequently associated with

each diagnosis. Even though there were no systematic relationships in the

data, subjects claimed to detect covariations. Further, they were virtually

the same covariations the clinicians claimed to find in real data! It is

plausible to suppose in this case that widely shared background assumptions

(or perhaps just thoughtless stereotypes) led both expert clinicians

and naıЁve subjects to ‘‘see’’ covariations in data that simply weren’t there.

Interestingly, when Chapman and Chapman built in massive negative covariations

between the features of the drawings and the diagnoses subjects

were likely to make, naıЁve subjects still reported positive covariations—

though somewhat reduced in magnitude.

In another fascinating study, Chapman and Chapman focused on the

famous Rorschach test. While most of the associations clinicians have

believed they detected in Rorschach tests are actually not present, it turns

out that two responses to the Rorschach test are correlated with male

homosexuality. However, these responses are not particularly ‘‘face valid’’

(i.e., they do not strike most people as particularly intuitive). For example,

male homosexuals are not more likely to identify in the Rorschach blots

feminine clothing, anuses or genitalia, or humans with confused or uncertain

sexes. In fact, homosexual men more frequently report seeing monsters

on Card IV and a part-human-part-animal on Card V. (Again, Chapman

and Chapman found that clinicians of the day believed there was a significant

correlation between the ‘‘face valid’’ signs and homosexuality. Only 2

of the 32 clinicians they polled even listed one of the valid signs.) NaıЁve

subjects (1969) were given 30 cards with traits (homosexual or nonhomosexual)

on one side and Rorschach responses on the other (a valid sign,

an invalid but ‘‘face valid’’ sign, or a filler sign) and were given 60 seconds

to review each card. Even though the cards contained no correlations between the traits and the Rorschach responses, subjects reported frequent

correlations between the ‘‘face valid’’ signs and homosexuality. This finding

essentially replicates the DAP test result.

Next, Chapman and Chapman changed the cards so that the valid signs

were associated more often with homosexuality than were the other signs.

Even when the valid signs were associated with homosexuality 100% of the

time, naıЁve observers failed to detect the covariation. So it’s not just that

subjects see correlations when there are none. In fact, we often don’t see

correlations that are actually there, and sometimes we see positive correlations

when in fact the correlations are negative.

It should be noted that Chapman and Chapman did not draw particularly

pessimistic conclusions from their experiments. Nor do we. In

fact, when Chapman and Chapman took out the misleading invalid signs,

subjects were capable of detecting the actual covariations in the data. Nisbett

and Ross (1980) draw the following conclusion from these experiments:

[R]eported covariation was shown to reflect true covariation far less than it

reflected theories or preconceptions of the nature of the associations that

‘‘ought’’ to exist. Unexpected, true covariations can sometimes be detected

but they will be underestimated and are likely to be noticed only when the

covariation is very strong, and the relevant data set excludes ‘‘decoy features’’

that bring into play popular but incorrect theories. (97)

When it comes to social judgment, the evidential situation is likely to be

quite complex—with many signs that are valid but counterintuitive and

other signs that are ‘‘face valid’’ but not predictive. In such an environment,

we are not likely to do a particularly good job of detecting covariations.

And so, unless the theories, background assumptions, and stereotypes

we bring to a particular prediction are accurate, we are not likely to be very

good at identifying what cues are most likely to covary with and so predict

our target property.