1. Cause (Part I) - Elaboration
Topics
I. The Definition of Causation
II. The Statistical Elaboration Model
III. Non-quantitative Statistical Example
IV. Quantitative Statistical Example

2. Cause (Part I) - Elaboration
I. The Definition of Causation
- Four Characteristics
A. Co-variation
B. Over a valid time frame
C. Of a non-spurious nature
D. That is grounded in theory

3. Cause (Part I) - Elaboration
II. The Statistical Elaboration Model
A. Elimination
B. Specification
Spuriousness X
e.g. the effect of fire size (Z) on the relationship between # of firemen (X) and damage (Y)
1. Antecedent Z Y
2. Intervening X Y
e.g. the effect of education (Z) on the relationship between age (X) and income (Y) Z

4. Cause (Part I) - Elaboration
III. Non-quantitative Statistical Example
Step 1 – Construct the zero order cross-tabulation table.
The Marginal (Zero-Order) Table M F
Tot
Rep 25 15 40
Dem 80
Step 2 – Calculate the zero order measure of association.
e.g. Lambda = 40/40 – 30/40 = .25
or Phi = (25-20)2/20 + (15-20)2/ (15-20)2/20 + (25-20)2/20 = square root of 5/80 = .25

5. Cause (Part I) - Elaboration
Step 3 – Construct the first order partial tables.
The Marginal Table
Partial Table for Young
Partial Table for Old M F
Tot
Rep 25 15 40
Dem 80 M F
Tot
Rep 15 30
Dem 60 M F
Tot
Rep 10
Dem 20 = +
Step 4 – Calculate the partial measures of association
Total Young Old
Lambda
Step 5 – Form the conclusion
Since the partials have changed from the marginal measure, one getting stronger and the other disappearing, we would say that we have specified the zero order relationship as probably intervening (i.e. we are born into a sex, grow older and as a result, join a political party).

6. Cause (Part I) - Elaboration
IV. Quantitative Statistical Example
Step 1 – Construct the zero order Pearson’s correlations (r).
Assume rxy = .55 where x = divorce rates and y = suicide rates.
Further, assume that unemployment rates (z) is our control variable and that rxz = .60 and ryz = .40
.55 – (.6) (.4)
Step 2 – Calculate the partial correlation (rxy.z) = =
.42
Therefore, Z accounts for ( ) or 12% of Y and (.12/.30) or 40% of the relationship between X&Y
Before z (rxy)2 = .30
Step 3 – Draw conclusions
After z (rxy.z)2 = .18