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Chapter 16

Chapter 16. Elaborating Bivariate Tables. Chapter Outline. Introduction Controlling for a Third Variable Interpreting Partial Tables Partial Gamma (Gp ). Chapter Outline. Where Do Control Variables Come From? The Limitations of Elaborating Bivariate Tables

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Chapter 16

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  1. Chapter 16 Elaborating Bivariate Tables

  2. Chapter Outline • Introduction • Controlling for a Third Variable • Interpreting Partial Tables • Partial Gamma (Gp )

  3. Chapter Outline • Where Do Control Variables Come From? • The Limitations of Elaborating Bivariate Tables • Interpreting Statistics: Analyzing Civic Engagement

  4. In This Presentation • The logic of the elaboration technique. • The construction and interpretation of partial tables. • The interpretation of partial measures of association. • Direct, spurious, intervening, and interactive relationships.

  5. Introduction • Social science research projects are multivariate, virtually by definition. • One way to conduct multivariate analysis is to observe the effect of 3rd variables, one at a time, on a bivariate relationship. • The elaboration technique extends the analysis of bivariate tables presented in Chapters 12-14.

  6. Elaboration • To “elaborate”, we observe how a control variable (Z) affects the relationship between X and Y. • To control for a third variable, the bivariate relationship is reconstructed for each value of the control variable. • Problem 16.1 will be used to illustrate these procedures.

  7. Proble m 16.1:Bivariate Table • Sample - 50 immigrants • X = length of residence • Y = Fluency in English • G = .71

  8. The column %s and G show a strong, positive relationship: fluency increases with length of residence. Problem 16.1: Bivariate Table

  9. Problem 16.1 • Will the relationship between fluency (Y) and length of residence (X) be affected by gender (Z)? • To investigate, the bivariate relationship is reconstructed for each value of Z. • One partial table shows the relationship between X and Y for men (Z1)and the other shows the relationship for women (Z2).

  10. Problem 16.1: Partial Tables • Partial table for males. • G = .78

  11. Problem 16.1: Partial Tables • Partial table for females. • G = .65

  12. Problem 16.1: A Direct Relationship • The percentage patterns and G’s for all three tables are essentially the same. • Sex (Z) has little effect on the relationship between fluency (Y) and length of residence (X).

  13. Problem 16.1:A Direct Relationship • For both sexes, Y increases with X in about the same way. • There seems to be a direct relationship between X and Y.

  14. Direct Relationships • In a direct relationship, the control variable has little effect on the relationship between X and Y. • The column %s and gammas in the partial tables are about the same as the bivariate table. • This outcome supports the argument that X causes Y. X Y

  15. Other Possible Relationships Between X, Y, and Z: • Spurious relationships: • X and Y are not related, both are caused by Z. • Intervening relationships: • X and Y are not directly related but are linked by Z.

  16. Other Possible Relationships Between X, Y, and Z: • Interaction • The relationship between X and Y changes for each value of Z. • We will extend problem 16.1 beyond the text to illustrate these outcomes.

  17. Spurious Relationships • X and Y are not related, both are caused by Z. X Z Y

  18. Spurious Relationships • Immigrants with relatives who are Americanized (Z) are more fluent (Y) and more likely to stay (X). Length of Res. Relatives Fluency

  19. With Relatives G = 0.00 Spurious Relationships

  20. No relatives G = 0.00 Spurious Relationships

  21. Spurious Relationships • In a spurious relationship, the gammas in the partial tables are dramatically lower than the gamma in the bivariate table, perhaps even falling to zero.

  22. Intervening Relationships • X and Y and not directly related but are linked by Z. • Longer term residents may be more likely to find jobs that require English and be motivated to become fluent. Z X Y Jobs Length Fluency

  23. Intervening Relationships • Intervening and spurious relationships look the same in the partial tables. • Intervening and spurious relationships must be distinguished on logical or theoretical grounds.

  24. Interaction • Interaction occurs when the relationship between X and Y changes across the categories of Z.

  25. Interaction • X and Y could only be related for some categories of Z. • X and Y could have a positive relationship for one category of Z and a negative one for others. Z1 X Y Z2 0 Z1 + X Y Z2 -

  26. Interaction • Perhaps the relationship between fluency and residence is affected by the level of education residents bring with them.

  27. Interaction • Well educated immigrants are more fluent regardless of residence. • Less educated immigrants are less fluent regardless of residence.

  28. Summary: Table 16.5

  29. Summary: Table 16.5

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