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

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

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Causation II. The Statistical Elaboration Model A. Elimination B. Specification 1. Antecedent 2. Intervening Spuriousness X Y Z XY 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)

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Causation III. Non-quantitative Statistical Example Step 1 – Construct the zero order cross-tabulation table. The Marginal (Zero-Order) Table MFTot Rep Dem Tot40 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

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Causation Step 3 – Construct the first order partial tables. The Marginal Table M FTot Rep Dem Tot40 80 Step 4 – Calculate the partial measures of association. = M FTot Rep15 30 Dem15 30 Tot M FTot Rep10 0 Dem 010 Tot10 20 Partial Table for YoungPartial Table for Old TotalYoungOld Lambda 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

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

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