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Week 10: Chapter 16

Week 10: Chapter 16. Controlling for a Third Variable Multivariate Analyses. Introduction. Social science research projects are multivariate, virtually by definition.

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Week 10: Chapter 16

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  1. Week 10: Chapter 16 Controlling for a Third Variable Multivariate Analyses

  2. 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 12-15 and 17.

  3. 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 (see Healey p. 452) will be used to illustrate these procedures.

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

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

  6. 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).

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

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

  9. 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). • For both sexes, Y increases with X in about the same way. • There seems to be a direct relationship between X and Y.

  10. A. 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

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

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

  13. B. Spurious Relationships • Immigrants with relatives who feel at home in the UK (Z) are more fluent (Y) and more likely to stay (X). Length of Stay Relatives Fluency

  14. With Relatives G = 0.00 B. Spurious Relationships

  15. No relatives G = 0.00 B. Spurious Relationships

  16. B. 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.

  17. C. 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

  18. C. 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.

  19. D. 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 -

  20. D. Interaction • Interaction occurs when the relationship between X and Y changes across the categories of Z. • Perhaps the relationship between fluency and residence is affected by the level of education residents bring with them.

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

  22. Summary: Table 16.5 (see Healey, p. 441)

  23. Summary: Table 16.5 (see Healey, p. 441)

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