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Logic of Causation  Cause and effect  Determinism vs. free will  Explanation:

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Presentation on theme: "Logic of Causation  Cause and effect  Determinism vs. free will  Explanation:"— Presentation transcript:

1 Logic of Causation  Cause and effect  Determinism vs. free will  Explanation:

2 Causality Bivariate relationship (2 variables) XY (Cause) Independent variable (Effect) Dependent variable

3 Causality Multivariate relationship (3+ variables) XY (Causes) Independent variables (Effect) Dependent variable Z

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) 1)Cause must precede effect: X Y

6 Criteria for Causality 2) The two variables must be empirically associated XY

7 Criteria for Causality 3)Observed association cannot be explained away by a third variable (test for spuriousness) X = # firefighters Y = amt. of damage

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

9 Spurious relationship? # storks # babies +

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) Partial relationships compared with original Test variable is: AntecedentIntervening Same relationshipReplication Less or noneExplanationInterpretation Split (one is same or greater, other is less or none) Specification

12 Explanation: Z X Y

13 Interpretation: ZXY

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 Percentage receiving Ph.D. by marriage in grad school (hypothetical) Got married in grad school Got Ph.D.YesNo Yes65.080.0 No35.020.0 Total100.0 N(200)

16 Elaboration Paradigm Percentage receiving Ph.D. by marriage in grad school (hypothetical) Got married in grad school Got Ph.D. YesNo Yes65.080.0 N(200) Succinct table reduces redundancy

17 Elaboration Paradigm Percentage receiving Ph.D. by getting married by sex (hypothetical) Sex MenWomen Got Ph.D.MarriedDidn’t marryMarriedDidn’t marry Yes 80.0 50.080.0 No 20.0 50.020.0 Total 100.0 N (100)

18 Elaboration Paradigm Percentage receiving Ph.D. by getting married by sex (hypothetical) Sex MenWomen Got Ph.D.MarriedDidn’t marryMarriedDidn’t marry Yes 80.0 50.080.0 N (100) Make it succinct!

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

20 Elaboration Paradigm Percent delinquent by suitability of supervision Suitability of supervision SuitableUnsuitable % Delinquent30.383.7 N(628)(375) 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 Percent delinquent by suitability of supervision by mother’s employment Housewife Occasionally Employed Regularly employed Suitable Un- suitable Suitable Un- Suitable Suitable Un- Suitable % Delinquent 31.984.631.588.819.577.3 N (457)(149)(89)(116)(82)(110) 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 Percentage delinquent by mother’s employment Housewife Occasionally employed Regularly employed % Delinquent44.963.952.6 N(606)(205)(192) 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 Percent delinquent by suitability of supervision by mother’s employment Housewife Occasionally Employed Regularly employed Suitable Un- suitable Suitable Un- Suitable Suitable Un- Suitable % Delinquent 31.984.631.588.819.577.3 N (457)(149)(89)(116)(82)(110) 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 Percent delinquent by church attendance (hypothetical) Church attendance Regular/oftenSeldom/never % Delinquent44.056.0 N(150)

25 Elaboration Paradigm Percent delinquent by church attendance by age <=14 years>=15 years Regular/ often Seldom/ never Regular/ often Seldom/ never % Delinquent33.0 67.0 N(100)(50) (100)

26 Testing hypotheses Raw data: predicting traffic accidents SexMiles drivenTraffic accidentsN WomenFewMany20 WomenFew 180 WomenMany 80 WomenManyFew20 MenFewMany5 MenFew 45 MenMany 160 MenManyFew40

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

28 Original bivariate relationship Percentage of traffic accidents by sex (hypothetical) AccidentsMenWomen Few34.066.7 Many66.033.3 Total100.0 N(250)(300)

29 Trivariate relationship Percentage of traffic accidents by miles driven by sex (hypothetical) Sex MenWomen AccidentsFewManyFewMany Few90.020.090.020.0 Many10.080.010.080.0 Total100.0 N(50)(200) (100)

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 Percentage Voting for Clinton in 1996 by Sex Sex 1996 VoteMenWomen Clinton55.465.1 Dole44.634.9 Total100.0 N(634)(877) 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 Percentage Voting for Clinton by Current Work Status by Sex Sex MenWomen 1996 Vote Currently Working Not curr. working Currently Working Not curr. working Clinton 52.763.067.760.8 Dole 47.337.032.339.2 Total 100.0 N (469)(165)(548)(329) Source: General Social Survey 1998

36 Trivariate table Percentage Voting for Clinton by Sex by Current Work Status Current work status Currently working Not currently working 1996 Vote MenWomenMenWomen Clinton 52.767.763.060.8 Dole 47.332.337.039.2 Total 100.0 N (469)(548)(165)(329) 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 Percentage believing abortion should be available by educational degree and religion, 1977-78 Educational degree LT HS HS grad/Jr. coll. BA degreeGrad degree Abortion belief Prot.Cath.Prot.Cath.Prot.Cath.Prot.Cath. Should Be available 22.830.235.428.149.427.555.034.8 N(666)(232)(1008)(409)(160)(69)(80)(23) Chi-squarep=.03p=.01p=.00p=.09 General Social Survey, 1977-78

40 3-D table: statistical interaction Percent believing abortion should be available by educational degree and religion, 1977-78 Educational degree ReligionLT HS HS grad/Jr. coll BA degree Grad degree Protestant 22.8* (666) 35.4* (1008) 49.4* (160) 55.0 (80) Catholic 30.2 (232) 28.1 (409) 27.5 (69) 34.8 (23) General Social Survey, 1977-78 Note: *=Chi square for religion, p=<.05

41 3-D table: statistical interaction Percent believing abortion should be available by educational degree and religion, 2000-04 Educational degree ReligionLT HS HS grad/Jr. coll BA degree Grad degree Protestant 23.4 (291) 34.7 (1140) 40.2 (264) 50.4 (135) Catholic 26.2 (119) 34.2 (535) 37.0 (136) 44.8 (63) General Social Survey, 2000-04 Note: Chi square (no p values for religion less than.05)

42 Additive relationship (hypothetical) Educational degree ReligionLT HS HS grad/Jr. coll. BA degree Grad degree Protestants40.045.055.075.0 Catholic30.035.045.065.0

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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