partial gamma A statistic that indicates the strength of the association between two variables after the effects of a third variable have been removed.

partial tables Tables produced when controlling for a third variable.

elaboration The basic multivariate technique for analyzing variables arrayed in tables.
direct relationship A multivariate relationship in which the control variable has no effect on the bivariate variable.

spurious relationship A multivariate relationship in which a bivariate relationship becomes substantially weaker after a third variable is controlled for.

intervening relationships A multivariate relationship wherein a bivariate relationship becomes substantially weaker after a third variable is controlled for.

interaction A multivariate relationship wherein a bivariate relationship changes across the categories of the control variable.

 Z Symbol for any control variable.

Chapter 16 Elaborating Bivariate Tables
Where Do Control Variables Come From?
The Limitations for Elaborating Bivariate Tables
Interpreting Statistics: Analyzing Political Participation
Reasons for Using Multivariate Techniques
Gathering additional information about a specific bivariate relation by observing how that relationship is affected by a third variable.

Gather evidence in support of causal arguments.
Three Basic Patterns in Partial Tables
Direct relationships - relationships between X and Y  is the same in all partial tables and in the bivariate table.

Spurious relationships and intervening relationships - relationship between X and Y is the same in all partial tables but much weaker than in the bivariate table.

Three Basic Patterns in Partial Tables

Interaction - each partial table and the bivariate table all show different relationships between X and Y.
 

Direct Relationship
Relationship between X & Y same in all partial tables and in bivariate table
 Z has no effect on relationship between X & Y
Also called replication
 

Spurious Relationship
Relationship between X & Y is same in all partial tables, but much weaker than in bivariate table
Z accounts for change in Y, and X is theoretically irrelevant
Also called Explanation
Z is antecedent to X & Y
 

Intervening Relationship
Relationship between X & Y is same in all partial tables, but much weaker than in bivariate table
Z accounts for change in Y, and X is theoretically important
Also called Interpretation
X is related to Y thru Z
 

Interaction Relationship
Each partial table and the bivariate table all show different relationships between X & Y
Also called Specification
Takes various forms

Interaction Relationship
Each partial table and the bivariate table all show different relationships between X & Y
Also called Specification
Takes various forms

Homework
Problems
16.2
16.4
16.6
16.8

Statpak Exercises
16.1 in SAS
16.2 in SPSS