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Logic of Causation

Logic of Causation. Cause and effect Determinism vs. free will Explanation:. Why?. Bi variate relationship (2 variables). Causality. X. Y. (Cause) Independent variable. (Effect) Dependent variable. Multi variate relationship (3+ variables). Causality. X. Y. Z. (Causes)

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Logic of Causation

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  1. Logic of Causation • Cause and effect • Determinism vs. free will • Explanation: Why?

  2. Bivariate relationship (2 variables) Causality X Y (Cause) Independent variable (Effect) Dependent variable

  3. Multivariate relationship (3+ variables) Causality X Y Z (Causes) Independent variables (Effect) Dependent variable

  4. Types of causes (n=2) • Necessary cause: X must happen for Y to happen “Need X to get Y” • Sufficient cause: Y always happens when X happens “Always get Y when you have X”

  5. Criteria for Causality (n=3) • Cause must precede effect: X Y

  6. 2) The two variables must be empirically associated Criteria for Causality X Y

  7. Observed association cannot be explained away by a third variable (test for spuriousness) X = # firefighters Y = amt. of damage Criteria for Causality

  8. Criteria for Causality Y + X Y X= # firefighters Y= amt. of damage X

  9. Spurious relationship? + # babies # storks

  10. Elaboration Paradigm • Purpose: to understand nature of observed relationships • Test: for spuriousness • Move: from bivariate table to trivariate table • Evaluate for possible outcomes: replication, explanation, interpretation, specification

  11. Elaboration Paradigm(Babbie, p. 422)

  12. Explanation: X Z Y

  13. Interpretation: X Z Y

  14. Rules for creating tables • Percentage down (in the direction of causality) • Dependent variable on the side • Independent variable(s) on the top • Compare across • Watch for small Ns in columns • Collapse on theoretical grounds

  15. Elaboration Paradigm

  16. Elaboration Paradigm Succinct table reduces redundancy

  17. Elaboration Paradigm

  18. Elaboration Paradigm Make it succinct!

  19. Elaboration Paradigm What happens to the original relationship within categories of the test variable?

  20. Elaboration Paradigm Source: Eleanor Maccoby 1960 data (reprinted in Travis Hirschi and Hanan Selvin, 1967, Delinquency Research: An Appraisal of Analytic Methods, New York: Free Press, p. 240)

  21. Elaboration Paradigm Source: Eleanor Maccoby 1960 data (reprinted in Travis Hirschi and Hanan Selvin, 1967, Delinquency Research: An Appraisal of Analytic Methods, New York: Free Press, p. 240)

  22. Elaboration Paradigm Source: Eleanor Maccoby 1960 data (reprinted in Travis Hirschi and Hanan Selvin, 1967, Delinquency Research: An Appraisal of Analytic Methods, New York: Free Press, p. 240)

  23. Elaboration Paradigm Source: Eleanor Maccoby 1960 data (reprinted in Travis Hirschi and Hanan Selvin, 1967, Delinquency Research: An Appraisal of Analytic Methods, New York: Free Press, p. 240)

  24. Elaboration Paradigm

  25. Elaboration Paradigm

  26. Testing hypotheses

  27. Testing hypotheses Hypothesis: “Men are more accident prone than women” X = ? Y = ?

  28. Original bivariate relationship

  29. Trivariate relationship

  30. Elaboration Paradigm:using GSS Hypothesis: Women were more likely than men to vote for Bill Clinton in 1996

  31. Elaboration paradigm X = ? Y = ? Z = ?

  32. Elaboration Paradigm Review rules: • Percentage down (in direction of causality) • Compare across • Check N in columns

  33. Original relationship Source: General Social Survey, 1998

  34. Original relationship Rules for interpretation: • General statement about relationship (modeled on the hypothesis) • Compare specific percentages • GEE! (generalization, example, exception)(Miller, 2005)

  35. Trivariate table Source: General Social Survey 1998

  36. Trivariate table Source: General Social Survey 1998

  37. Interpreting trivariate tables Trivariate mantra: What happens to the original relationship within categories of the test variable?

  38. Refinements to elaboration paradigm:suppressor and distorter variables • Suppressor variable (relationship emerges): bivariate = no relationship trivariate = positive or negative relationship • Distorter variable (relationship switches): bivariate = positive relationship trivariate = negative relationship (or negative to positive)

  39. 3 dimensional tables: basic table General Social Survey, 1977-78

  40. 3-D table:statistical interaction General Social Survey, 1977-78 Note: *=Chi square for religion, p=<.05

  41. 3-D table:statistical interaction General Social Survey, 2000-04 Note: Chi square (no p values for religion less than .05)

  42. Additive relationship(hypothetical)

  43. Statistical interaction Question to ask: “Does the effect of one variable (X) on another (Y) remain the same for all groups of the third (Z) variable?”

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