Causal Reasoning

1
Causal Reasoning

• Inductive because it is limited by our inability
  to know (1) all of the relevant causes, and (2)
  the ways in which these causes interact
• We can address uncertainty by speaking not of
  CAUSES, but of CAUSAL FACTORS
• Main danger to avoid is the Post Hoc fallacy
  inferring that X caused Y because it happened
  prior to Y. This creates a False Cause.

2
Mills Methods for Analyzing Causes

• Method of Agreement look for common factor in
  all cases where the effect is present
• Method of Difference look for factor that is
  present when the effect occurs, and absent when
  the effect does not occur
• Joint Method combination of Agreement and
  Difference
• Method of Concomitant Variation used when effect
  comes in degrees look for a factor that varies
  along with effect (correlation)

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Correlation

• A correlation is a (statistical) measurement of
  the association of two variables.
• Positive Correlation As one variable increases,
  the other increases. (Examples cigarette
  smoking and lung cancer education and income
  unemployment and homelessness)
• Negative Correlation As one variable increases,
  the other decreases. (Examples caffeine intake
  and sleep age and working memory capacity
  stress and life expectancy)

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Identifying and Assessing Correlations

• Correlations are identified by r.
• Correlations range between -1 and 1 positive
  numbers identify positive correlation, negative
  numbers identify negative correlation. r0 is no
  correlation.
• The further away from 0 the correlation is, the
  more strongly the variables are related.
  Correlations above .5 or below -.5 are strong
  correlations correlations between .2 and .5 (or
  -.2 and -.5) are moderate correlations.
• r2 will give us the percentage of difference in
  one variable that is due to difference in the
  other. (Example if the correlation between
  smoking and lung cancer is .7, 49 of differences
  in lung cancer rates are due to differences in
  smoking levels.)

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2 Basic Forms of Statistical Reasoning

• Statistical Syllogism x of A is B p is an A
  therefore p is a B (to x likelihood). (Example
  86 of college students are broke. Fred is a
  college student, so its pretty likely that hes
  broke.)
• Inductive Generalization x of known As are Bs
  therefore x of As are Bs. (Example Almost all
  of the students in this logic class hated the
  Deductive Reasoning assignment. Thus, I should
  expect that almost all students in any logic
  class would hate that assignment.)

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Components of a Statistical Study

• Target Population This is the group about which
  you want to make an overall judgment. It could
  be all people, voters, college students, etc.
• Sample (or Experimental) Group This is the group
  studied or experimented upon to get information
  used to infer claims about the Target Population.
• Control Group Needed whenever one is looking for
  differences between groups this group serves as
  an anchor against which to evaluate the
  Experimental Group. The Control Group helps to
  weed out spurious results. (Example If you want
  to see if viewing pornography alters perceptions
  about women, you need a Control Group that takes
  the same questionnaire but does not view
  pornography beforehand.)

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Sample Size

• Indicated by N. (Also sometimes ss.)
• Good statistical studies should tell you both (1)
  how many subjects one has overall, and (2) how
  many subjects are in each group.
• Sample size gives us information about how well
  results can be generalized from the Sample Group
  to the Target Group. The larger, the better.
• This is because in large samples, extreme and
  otherwise unrepresentative cases are more likely
  to be balanced off.

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Hasty Generalization

• Small or atypical sample sizes lead to the
  fallacy of Hasty Generalization.
• The Hasty Generalization involves inferring
  claims about the Target Group from the Sample
  Group that lack sufficient support.

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Sample Diversity

• Sample Diversity is important because it (1)
  helps to balance off extreme or unrepresentative
  cases, and (2) reduces the likelihood that the
  study reflects the researchers biases.
• Representative Sample sampling picked to match,
  as closely as possible, the actual distribution
  of traits in the Target Population.
• Random Sample sampling based on some arbitrary
  and irrelevant criterion.

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Other Guidelines for Evaluating Statistical and
Demographic Data

• Date of Study While older studies can still have
  cogent results, in many cases new research (and
  new methodologies) may have invalidated the
  previous results.
• Author and Sponsor of Study Is the study being
  produced by (or funded by) someone with a stake
  in how the results turn out? This can increase
  the likelihood that biased research methods were
  used.
• Publication Conditions Studies published in peer
  reviewed journals have their findings analyzed by
  other experts in the field, some of whom disagree
  with the author. Beware of studies that are
  neither peer reviewed or reviewed only within an
  organization.

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Statistical Significance

• Indicated by p (lt or gt) this is a measurement
  of how likely it is that the results of the
  experiment are due to chance factors.
• This is NOT significant in the sense of
  large, NOR in the sense of important.
• Researchers usually declare a finding
  statistically significant if p lt .05.

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Statistical Significance Continued

• Failing to attain a statistically significant
  result should not necessarily be viewed as a
  failure. The finding that two groups do NOT
  differ in a reliable way (affirming the Null
  Hypothesis) can be a highly important finding.
• Statistical Significance is linked to the
  importance of replication in scientific
  experimentation. A study with p.05 is still 5
  likely to have its results due to chance. Think
  of Significance as a claim on the likelihood that
  repetition will produce the same results, and
  replication as a test of this contention.

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Margin of Error

• Margin of Error this is a measurement of
  variability in the sample. A standard margin of
  error for well-conducted surveys and polls is /-
  2 to 3. This will give us the range of the
  study. (Example if a study shows that 51 of
  IVCC students prefer Coke to Pepsi, with a margin
  of error of 3, this means that between 48-54 of
  IVCC students prefer Coke to Pepsi.)

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Base-Rate Data

• Base-Rate Data is information that tells you how
  prevalent some trait is within the general
  population, or how likely the occurrence of some
  event is independently of what we do.
• This is crucial when you are checking for causal
  factors for ruling out spurious causes.
• Example 1 Freuds It Works! Argument
• Example 2 John Hinckleys brain
• Example 3 Post-9/11 airport security

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Analogies

• Analogies are prevalent in literature,
  philosophy, religion and law
• In literature and religion, they are often
  present as comparisons, metaphors and parables.
• In law, they are typically present as precedents
  and hypothetical cases
• In philosophy, they are typically present as
  thought experiments (intuition pumps)
• Analogies are even present in scienceesp. in
  scientific discovery and in science education

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Steps for Analyzing an Analogy (Simplified)

• Clarify the terms of comparison
• Identify the principle or characteristic that is
  being applied
• Identify relevant similarities (False analogies
  rely on trivial similarities.)
• Identify relevant differences
• Weigh up relative strength of similarities and
  differences to reach a final assessment of
  strength

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Example

• Iraq is the new Vietnam. In both cases, our
  enemy is some nebulous, indefinable entity
  (communism, terrorism). In both cases we lost
  many American lives from insurgency for which we
  were unprepared. Both wars seem like futile
  endeavors with no hope for success. In each
  case, we lacked support for the war, both at home
  and abroad. Presidents Johnson and Nixon both
  escalated the war in Vietnam in response to
  popular dissent President Bush has responded to
  popular dissent by sending more troops. Mission
  creep in Vietnam led us to invade Cambodia the
  Bush administration has been talking about
  expanding the Iraq war into Iran or Jordan.
  Historys verdict on the Vietnam War is clear it
  was an unjustifiable act of aggression.
  Shouldnt we view the Iraq war in the same way?