# Correlation Correlation and Causation by cuiliqing

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```									Correlation and Causation in
Research Psychology

Bryce Maritano
Job Talk at Shasta College
July 25, 2007
Correlation
 A correlation is a relationship between two
variables (factors that change). Variables
may include characteristics, attitudes,
behaviors, or events.
 Correlations are either positive (to +1.0),
negative (to–1.0), or nonexistent (0.0).
Positive Correlation

Positive Correlations: Both variables increase or decrease at the same time.

A correlation coefficient close to +1.00 indicates a strong positive correlation.
Examples: Height & Weight, Sit-ups & Abdominal muscles
Negative Correlation

Negative Correlations: Indicates that as the amount of one variable
increases, the other decreases (and vice versa).

A correlation coefficient close to -1.00 indicates a strong negative correlation.
Examples: altitude/Temp, flossing/decay
Nonexistent Correlation

 No Correlation: no relationship between the two variables.
 A correlation coefficient of 0 indicates no correlation.
 Example: intelligence/happiness,
Correlation of
Obesity and Mortality
2.8
Relative
2.6
risk of
death 2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
18.5 18.5- 20.5- 22.0- 23.5- 25.0- 26.5- 28.0- 30.0- 32.0- 35.0-   40
0.8    20.4 21.9 23.4 24.9 26.4 27.9 29.9 31.9 34.9 39.9
0.6                    Body-mass index (BM I)
Men      Women
Sleep Deprivation
Less sleep,                            More sleep,
Accident            more accidents                         fewer accidents
frequency
2,800

2,700                                  4,200

2,600                                  4000

2,500                                  3,800

2,400                                  3,600
Spring time change                 Fall time change
(hour sleep loss)                  (hour sleep gained)
Monday before time change      Monday after time change
Clever Hans
 Clever Hans was a horse that was claimed to have been
able to perform arithmetic and other intellectual tasks.
 After formal investigation in 1907, psychologist Oskar
Pfungst demonstrated that the horse was not actually
performing these mental tasks, but was watching the
reaction of his human observers.
Children’s shoe size correlates with
performance on spelling tests.
Causality
 Causality or causation is defined as the
relationship between one event (called
cause) and another event (called effect)
which is the consequence (result) of the
first.
Flame from lamp (A) catches on curtain (B) and fire department sends
stream of water (C) through window. Dwarf (D) thinks it is raining and
reaches for umbrella (E), pulling string (F) and lifting end of platform (G).
Iron ball (H) falls and pulls string (I), causing hammer (J) to hit plate of
glass (K). Crashof glass wakes up pup (L) and mother dog (M) rocks him
to sleep in cradle (N), causing attached wooden hand (O) to move up and
Correlation does not imply
causation
 Although correlation is commonly confused
with causation, correlational data does not
indicate a cause-and-effect relationship.
When a correlation is present, changes in
the value of one variable reflect changes in
the value of the other. The correlation does
not imply that one variable causes the other
variable, only that both variables are
somehow related.
cum hoc ergo propter hoc
 (Latin for "with this, therefore because of this")

 The cum hoc ergo propter hoc logical fallacy can
be expressed as follows:
 A occurs in correlation with B.
 Therefore, A causes B.
 Example:
– Sleeping with one's shoes on is strongly correlated with
– Therefore, sleeping with one's shoes on causes
Simpson’s Logic
 An episode of The Simpsons (Season 7, "Much Apu About Nothing")
serves as a good example of this principle. Springfield had just
spent millions of dollars creating a highly sophisticated "Bear Patrol"
in response to the sighting of a single bear the week before.
–   Homer: Not a bear in sight. The "Bear Patrol" is working like a charm!
–   Lisa: That's specious reasoning, Dad.
–   Homer: [uncomprehendingly] Thanks, honey.
–   Lisa: By your logic, I could claim that this rock keeps tigers away.
–   Homer: Hmm. How does it work?
–   Lisa: It doesn't work. (pause) It's just a stupid rock!
–   Homer: Uh-huh.
–   Lisa: But I don't see any tigers around, do you?
Possible Explanations
 Generally, if one factor (A) is observed to only be correlated with
another factor (B), it is sometimes taken for granted that A is causing B
even when no evidence supports this. This is a logical fallacy because
there are at least four other possibilities:
 B may be the cause of A, or
 some unknown third factor is actually the cause of the relationship
between A and B, or
 the "relationship" is so complex it can be labeled coincidental (i.e., two
events occurring at the same time that have no simple relationship to
each other besides the fact that they are occurring at the same time).
 B may be the cause of A at the same time as A is the cause of B
(contradicting that the only relationship between A and B is that A
causes B). This describes a self-reinforcing system.
Is There a Connection between
Creativity and Mental Illness?

 The rate of mental illness (in general) is
slightly higher among those in the arts than
those in other professions.
Autism rates are higher in cities with
more rainfall and more cable
television customers.
Experimental research
 To study the effects that variables have on each
other, an investigator must conduct an experiment.

 Experimental research is concerned with how
and why something happens. The goal of
experimental research is to test the effect that an
independent variable, which the scientist
manipulates, has on a dependent variable, which
the scientist observes. In other words,
regarding causation.
Dissociative Identity Disorder
(Multiple Personality) correlates
strongly with childhood abuse.
Dynamic System of 30 billion cells
with trillions of connections
“Correlation is not causation
but it sure is a hint.”

Edward Tufte
– Ice cream sales correlate with the number of
people attacked by sharks.
– Therefore, ice cream causes shark attacks

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