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 A. Co-variation B. Over a valid time frame C. Of a non-spurious nature D. That is grounded in theory

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

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)2/20 + (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 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 .25 .00 1.00 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).

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 (.30-.18) 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