Causation Topics I The Definition of Causation II

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Causation Topics I. The Definition of Causation II. The Statistical Elaboration Model III. Non-quantitative

Causation Topics I. The Definition of Causation II. The Statistical Elaboration Model III. Non-quantitative Statistical Example IV. Quantitative Statistical Example

Causation I. The Definition of Causation - Four Characteristics A. Co-variation B. Over a

Causation 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

Causation II. The Statistical Elaboration Model A. Elimination B. Specification 1. Antecedent Spuriousness X

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

Causation III. Non-quantitative Statistical Example Step 1 – Construct the zero order cross-tabulation table.

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

Causation Step 3 – Construct the first order partial tables. The Marginal Table M

Causation Step 3 – Construct the first order partial tables. The Marginal Table M F Tot 25 15 40 Dem 15 25 40 Tot 40 80 Rep 40 Partial Table for Young = M F Tot 15 15 30 Dem 15 15 30 Tot 30 Rep 30 Step 4 – Calculate the partial measures of association. Lambda Partial Table for Old M F Tot Rep 10 0 10 Dem 0 10 10 60 Tot 10 10 20 Total Young Old . 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).

Causation IV. Quantitative Statistical Example Step 1 – Construct the zero order Pearson’s correlations

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