THE ART (AND SCIENCE?) OF INTERPRETING TABLES
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THE ART (AND SCIENCE?) OF
INTERPRETING TABLES
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BACKGROUND READINGS
• Pollock, Essentials, chs. 3-4
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OUTLINE
1. Components of statistical association
2. Cross-tabulation: format; comparing percentages and means
3. The gamma coefficient
4. Multivariate Relationships
5. Spurious, Enhancement, and Specification Relationships
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The Analytical Challenge: Interpreting and Measuring Relationships
Components of Statistical Association:
1. Form (e.g. positive or negative, varies from -1.0 to + 1.0)
2. Strength (how much X says about Y, varies from zero to 1.0)
3. Significance (i.e., probability of null hypothesis, such as p <.05)
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Arts of Cross-Tabulation
1. Independent variable (X) is the “column” variable
2. Dependent variable (Y) is the “row” variable
3. 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
4. Compute percentages along the independent variable—NOT of the dependent variable
5. For interpretation, compare percentages across columns at the same value of the dependent variable
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On Setting Up Tables
___________X_______________Y_________ Low Medium High
Low (LL)
Medium (MM)
High (HH)
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Cross-Tabulation I: Comparing Percentages
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Cross-Tabulation II: Comparing Percentages
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Comparing Means: Format I
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Comparing Means: Format II
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Cross-Tabulation III: Comparing Percentages
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The Gamma Coefficient
1. Appropriate for ordered nominal variables
2. 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”
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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
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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
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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
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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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