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Correlation Correlation and Causation

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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
down along your back.
     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
     waking up with a headache.
   – Therefore, sleeping with one's shoes on causes
     headache.
                    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?
    –   Homer: (pause) Lisa, I want to buy your rock.
             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,
  experimental research leads to conclusions
  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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