8' Correlation, Causation, and Controls

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8. Correlation, Causation, and Controls

• Stanovich
• Chapter 5

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Correlation

• Measure X and Y. Then determine if they are
  statistically co-related.
• What does this mean, statistically?
• We havent talked about statistics yet
• So what is a statistic?

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Consider this common expression

• There are 3 kinds of lies in the world lies,
  damned lies, and statistics.
• This is one use of the term, statistics.
• Much of the impetus for this statement comes from
  improper understanding of correlations in
  particular.

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Statistics Definition 1

• a range of techniques and procedures for
  analyzing, interpreting, displaying, and making
  decisions about data.
• This is what courses in "statistics" generally
  cover, like Psyc 218.

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Statistics Definition 2

• a numerical quantity
• Calculated in a sample
• Estimates a parameter
• Your grades are examples of statistics (e.g., the
  class mean, or average, standard deviation)

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Statistics Definition 3

• Any calculated number
• E.g., baseball statistics, government statistics
  car accidents, murder victims, drug users . .
  .Dont become a statistic.

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• Pearson Correlation Coefficient (r) statistic
  that indicates the direction and magnitude of the
  relation between 2 variables
• Positive correlation higher X related to higher
  Y
• Height positively correlated with weight
• Negative correlation higher X related to lower Y
• Education negatively correlated with years in
  jail?
• Correlation coefficients range from 1 to -1

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Variable Y
Positive correlation
Variable X
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Variable Y
Negative correlation
Variable X
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Variable Y
Zero correlation
Variable X
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• Examples
• Warmer parents have better adjusted children
• Couples who live together are more likely to get
  divorced
• Smoking and lung cancer
• Abortion and crime waves?! (lies, damned lies . .
  .)
• Bigger-brained people are smarter (cited in
  Jackson Rushton)

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Correlation Does NOT Equal Causation

• This is the main principle of Stanovich Ch. 5
• Third variable problem
• Could be related to both variables
• E.g., toaster birth control, pellagra
• Directionality problem
• What causes what?

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Third Variable Problem

• Correlation may not indicate a direct causal path
  but may arise because both variables are related
  to a third variable that isnt being studied.
• As the average amount of ice cream consumed
  nationally increases, the number of drownings
  increases

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Multiple Regression

• If you suspect that a third variable is behind a
  correlation you can use a statistical procedure
  known as multiple regression to determine to what
  extent it contributes to the observed variance

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Partial Correlation

• Partial correlation gives you the correlation
  between 2 variables while holding a 3rd (or 4th,
  5th . . .) variable constant.
• Tells you what the relationship would be if not
  for the 3rd variable.

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Directionality

• Correlation between A and B (assume not a
  spurious correlation)
• Does A cause B?
• Does B cause A?
• Low self esteem behaviour problems
• Firefighters fire damage

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When do we use correlation studies?

• For variables we cannot manipulate
• e.g., religion
• e.g., alcohol during pregnancy
• To make predictions
• high school grades performance in university