i. the definition of causation
DESCRIPTION
Cause (Part I) - Elaboration. Topics. I. The Definition of Causation. II. The Statistical Elaboration Model. III. Non-quantitative Statistical Example. IV. Quantitative Statistical Example. Cause (Part I) - Elaboration. I. The Definition of Causation. - Four Characteristics. - PowerPoint PPT PresentationTRANSCRIPT
I. The Definition of Causation
Cause (Part I) - Elaboration
II. The Statistical Elaboration Model
III. Non-quantitative Statistical Example
IV. Quantitative Statistical Example
Topics
I. The Definition of Causation
A. Co-variation
B. Over a valid time frame
C. Of a non-spurious nature
D. That is grounded in theory
- Four Characteristics
Cause (Part I) - Elaboration
II. The Statistical Elaboration Model
A. Elimination
B. Specification
1. Antecedent
2. Intervening
Spuriousness
X
YZ
X Y
Z
e.g. the effect of fire size (Z) on the relationship between # of firemen (X) and damage (Y)
e.g. the effect of education (Z) on the relationship between age (X) and income (Y)
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 15 25 40
Tot 40 40 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)2/20 + (15-20)2/20 + (25-20)2/20 =
square root of 5/80 = .25
Cause (Part I) - Elaboration
Step 3 – Construct the first order partial tables.
The Marginal Table
M F Tot
Rep 25 15 40
Dem 15 25 40
Tot 40 40 80
Step 4 – Calculate the partial
measures of association
=
M F Tot
Rep 15 15 30
Dem 15 15 30
Tot 30 30 60
+
M F Tot
Rep 10 0 10
Dem 0 10 10
Tot 10 10 20
Partial Table for Young Partial Table for Old
Total Young Old
Lambda .25 .00 1.00
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).
Step 5 – Form the conclusion
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
Step 2 – Calculate the partial correlation (rxy.z)
= = .42
Step 3 – Draw conclusions
After z (rxy.z)2 = .18
Before z (rxy)2 = .30 Therefore, Z accounts for (.30-.18) or 12% of Y and (.12/.30) or 40% of the relationship between X&Y
.55 – (.6) (.4)
16.136.1
Cause (Part I) - Elaboration