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THE ART (AND SCIENCE?) OF INTERPRETING TABLES

Learn how to interpret tables and understand statistical associations, cross-tabulation, the gamma coefficient, and multivariate relationships. Explore concepts such as spurious, enhancement, and specification relationships to better analyze data.

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THE ART (AND SCIENCE?) OF INTERPRETING TABLES

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  1. THE ART (AND SCIENCE?) OF INTERPRETING TABLES

  2. BACKGROUND READINGS • Pollock, Essentials, chs. 3-4

  3. OUTLINE • Components of statistical association • Cross-tabulation: format; comparing percentages and means • The gamma coefficient • Multivariate Relationships • Spurious, Enhancement, and Specification Relationships

  4. The Analytical Challenge: • Interpreting and Measuring Relationships • Components of Statistical Association: • Form (e.g. positive or negative, varies from -1.0 to + 1.0) • Strength (how much X says about Y, varies from zero to 1.0) • Significance (i.e., probability of null hypothesis, such as p <.05)

  5. Arts of Cross-Tabulation • 1. Independent variable (X) is the “column” variable • 2. Dependent variable (Y) is the “row” variable • In case of ordered nominal variables, be sure to array • “low-low” values in upper-left hand corner, and “high-high” • values in lower right-hand corner • Compute percentages along the independent variable— • NOT of the dependent variable • For interpretation, compare percentages across columns • at the same value of the dependent variable

  6. On Setting Up Tables ___________X__________ _____Y_________ Low Medium High Low (LL) Medium (MM) High (HH)

  7. Cross-Tabulation I: Comparing Percentages

  8. Cross-Tabulation II: Comparing Percentages

  9. Comparing Means: Format I

  10. Comparing Means: Format II

  11. Cross-Tabulation III: Comparing Percentages

  12. The Gamma Coefficient • 1. Appropriate for ordered nominal variables • Provides measure of form (positive or negative) and • of strength (coefficient varies from –1.0 to +1.0) • 3. Sample computations for 2 x 2 table • 4. Does not provide measure of “significance”

  13. Example and Sample Computation: Gun Control Attitudes and Gender ________Gender______ Gun Ban?___ Male Female Total Oppose 449[a] 358[b] 807 Favor 226[c] 481[d] 707 Total 675 839 1,514

  14. Computing Gamma (AKA Yule’s Q for 2x2 tables): Γ = Yule’s Q = (ad – bc)/(ad + bc) = (449x481 – 226x358)/(449x481 + 226x358) = +.455 Thus a measure of form and strength

  15. MULTIVARIATE RELATIONSHIPS • The “How Else” Question • Spurious, Enhancement, and Specification Relationships (a.k.a. “Interaction”) • Example 1: Race, Education, and Turnout • Example 2: Gender, Race, and Support for the Death Penalty

  16. Examining Relationship between Y and X, Controlling for a Rival Cause Z Potential Outcomes: Spurious relationship—Y a function of Z and not X Enhancement relationship—Y a function of both X and Z Specification relationship—i.e., control variable (Z) specifies or defines conditions under which X affects Y [also known as “interaction”]

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