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Research Methods

Research Methods. Measures of Association Chi Square, Correlation, Regression. Relationships Between Two (or More) Variables I. Association: The relationship to which two variables covary Direction: Positive, Negative, or No relationship

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Research Methods

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  1. Research Methods Measures of Association Chi Square, Correlation, Regression

  2. Relationships BetweenTwo (or More) Variables I Association: • The relationship to which two variables covary • Direction: Positive, Negative, or No relationship • Magnitude: Coefficient of Association: (0,1) or (-1,1) • Significance (Statistical Significance)

  3. Relationships BetweenTwo (or More) Variables II Significance (Statistical Significance): • The likelihood that the association is due to chance and is not true of the population • Or (inversely) level of confidence in the results • We don’t expect to find the exact value of a parameter, but something close (better as the random sample is larger)

  4. Measures of Association(very abbreviated) • Nominal data: Lambda(Statistical significance: Chi-square)(Reduction in error: Tau-b) • Ordinal data: Gamma(Statistical significance: Chi-square or Gamma)(Reduction in error: Tau) • Interval or Ratio data: Pearson Correlation Coefficient(Statistical significance: t or Z)(Explained variance or reduction in error: R2)

  5. Multivariate Analysis:Three or More Variables • Control for the effects of other factors:Value of DV is probably not influenced solely by the IV of interest. What else influences DV? • Alternative rival hypotheses:To persuade your audience, show that your theory and evidence is better than, or adds to, other possible explanations • Causality (earlier in semester)

  6. Regression Example:Size of Legislatures • How large should a legislature be? • “…no political problem is less susceptible of a precise solution than that which relates to the number most convenient for a representative legislature” The Federalist, No. 55 • Theory suggests legislature size should be a function of population • Stigler (1972): logged population • Taagepera (1972), Taagepera and Shughart (1989): cube root of population

  7. Simple Regression

  8. How Large Should aState Legislature Be? • H0: Si = ‾Ŝ Representative bodies fulfill functions and, for a certain level or type of government, all legislative chambers should be of the same size (S). Regardless of the polity (i) represented, an optimal size for a legislature exists for given functions. • H1: Si = f( Pi ) Chamber size is positively correlated with population (P) of the polity (through some transformation). • H2: Ci = f( Xi ) Chamber size varies with regard to characteristics of the polity represented. These characteristics include population, political culture, geography, ethnic or other cleavages, social mobilization, the economy, and interest diversity.

  9. Size of Legislatures

  10. Simple Regression

  11. Factors that May Contributeto Legislature Size

  12. Multiple Regression

  13. Crosstabulation Example:Gender and Party • Is there a “Gender Gap” between two parties? • Which is the dependent variable and which is the independent variable? • Compute percentages across the dependent variable, that is, sum to 100% for each independent variable.

  14. Partisanship by Gender

  15. Partisanship by Gender:Significance and Association

  16. Crosstabulation Example:Ideology and Party • Are the two parties ideological distinct? • Which is the dependent variable and which is the independent variable? [Here, party=f(ideology), not all would agree!] • Again, compute percentages across the dependent variable, that is, sum to 100% for each independent variable.

  17. Partisanship by Ideology

  18. An Example:Simpson’s Paradox I

  19. Simpson’s Paradox II

  20. Same Example:Spurious Relationship I

  21. Spurious Relationship II

  22. Causality • “Correlation is not causation” • Null hypothesis can be rejected, not “proven” or “accepted” • Causality can be rejected, not “proven” or “accepted” • Two variables may show a relationship or association. But does one cause the other?

  23. Suggesting Causality • Covariation or Association Demonstrated • Time Order Shown • Causal Linkage Explained • Alternative Explanations Eliminated

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