# Correlation and contingency

• Correlation = Knowing A helps you guess B
• Correlation does not imply causation.
• A is correlated with B implies B is correlated with A. e.g., Height / Weight
• Contingency = Changing A helps you change B
• Contingency implies causation.
• A is contingent on B does not imply B is contingent on A. e.g., alive / heart beating
• Measures of correlation:
r - when A and B are continuous.
φ - when A and B are dichotomous.

# Illusory Correlation (Seeing the Relationship you Expect) Chapman and Chapman (1971):

Draw-a-Person Test
Research has shown it to be useless, but...
``I know that paranoids don't seem to draw big eyes in the research labs, but they sure do in my office.''

Collected a number of draw-a-person test drawings, and labeled them, e.g.:
``suspicious of other people''
``has problems of sexual impotence''

Made sure that the correlations typically believed to exist (e.g. suspiciousness with big eyes) were zero in this set of drawings.

College students who were asked to discover what features of the drawings tended to go with what labels `discovered' the same correlations clinical psychologists tend to believe in.

# Do People Distinguish between Theory and Evidence?

Kuhn studied:
Children (3rd, 6th, & 9th grade)
Experts

e.g., 6th graders shown eight instances, one by one, of evidence about whether eating chocolate cake vs carrot cake was associated with getting or not getting a cold.

After each piece of evidence, child was asked: "Do the findings of the scientists show that the kind of cake makes a difference, doesn't make a difference, or can't you tell what the scientists' findings show?"

# Judging Contingency: Jenkins and Ward (1965):

• "Control means the ability to produce the No Score light as well as to produce the Score light. ... There might be no relation at all between what you press and the light."
• 60 opportunities to press Button A or Button B.
• "Score" or "No Score" light after each press.
• "How much control did you have?" Try it (but here "no score" is just the absense of "score"):

# Jenkins and Ward results

Conditional probabilities:
P(score/L) P(score/R) delta P
.500.5000
B.800.8000
C.133.1330
X.800.500.3
Y.800.200.6

# Alloy and Abramson: Sadder but wiser?

Similar experiment, but question was control over...
"Win 25 cents" vs. "No win"
"Lose 25 cents" vs. "No loss"

Used relatively depressed and nondepressed subjects.
Found illusion of control only among nondepressed subjects judging control over winning.

# McCauley and Stitt (1981)

Criterion and Mean Diagnostic Ratios
(Percentage of Black A mericans/Percentage of All Americans)
```Characteristic
finish         unemp. vict.            female
high   illegit. last   of  welfare 4+  family
Criterion   .65    3.1     1.9    1.5  4.6    1.9  2.8
High sch.   .68    1.8     1.9    .83  2.3    1.6  1.7
College     .73    1.7     1.6    1.8  1.9    1.4  1.9
Union       .67    2.1     1.8    2.0  1.6    1.6  1.7
Choir       .68    1.9     2.6    1.5  1.8    1.3  1.5
MSW stud.   .60    2.3     2.3    2.3  1.4    1.3  1.7
Case wrkrs. .74    2.0     1.9    1.9  2.0    1.4  2.0
```

# Extention to other stereotypes

```                Pct. Pct. Est. Est.
Wh.  CAS  Wh.  CAS
Often wear
preppie clothes 43   25   58   42

Favored Reagan
in `84          65   41   72   46

Willing to move
far from friends
and family for a
job promotion   66   50   71   52

Expect to earn
>\$50,000 in 5
years of degree 70   31   76   41

```
```                Pct. Pct. Est. Est.
Wh.  CAS  Wh.  CAS

Play tennis
and/or golf     61   44   59   51

Think most
Americans get
pretty much what
they deserve
out of life     62   41   63   44

Would never
take a poetry
course          61   32   67   39

```
```                Pct. Pct. Est. Est.
Wh.  CAS  Wh.  CAS
Aware how much
others' clothing
costs           67   39   62   50

Feel that
appearance is
very important in
selecting a spouse
(or long-term
living partner) 74   57   63   54

Feel that who
you know is as
important as
what you know   59   62   69   50
```

Source: Clark Department, McCauley of Psychology, Bryn Mawr College