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Two Variable Systems

Two Variable Systems. Bivariate and Partial Correlations. The Graphical View– A Scatter Diagram. Y (WT). X’. . . . . . . . . . .. . . . . . .. . . . .

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Two Variable Systems

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  1. Two Variable Systems Bivariate and Partial Correlations

  2. The Graphical View– A Scatter Diagram Y (WT) X’ . . . . . . . . . .. . . . . . .. . . . . . .. . . . .. . . .. . . . . Y’ A HIGH AND POSITIVE CORRLEATION X (HT)

  3. The Graphical View– A Scatter Diagram Y (WT) X BAR X’ . .. . . . . . . . . . . .. .. . . . . . . .. . . . . . .. .. . . . . . .. . .. Y’ A HIGH AND NEGATIVE CORRLEATION Y BAR X (HT)

  4. The Graphical View– A Scatter Diagram Y (WT) X’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. .. . .. . .. . . . . . . . . . . . . . . . . . . Y’ NO CORRLEATION X (HT)

  5. The Algebraic View – Shared Variance 1) Take the Variance in X = S2x and the Variance in Y = S2y 2) Then Average the Two Variances: 3) Find the Covariation Sxy : Where Sxy= r = 4) The correlation is simply 3) divided by 2): Hence r =

  6. An Example of Calculating a Correlation 1) Find the raw scores, means, squared deviations and cross-products: X= M Educ Y=D Educ) ) 10 9 -4 -4 16 16 16 12 11 -2 -2 4 4 4 8 12 -6 -1 36 1 6 16 13 +2 0 4 0 0 18 16 +4 +3 16 9 12 20 17 +6 +4 36 16 24 14 13 112 46 62 2) Calculate the correlation: r = = .864 3) Square r to determine variation explained r2 = .746

  7. An Example of Calculating a Correlation from SPSS INPUT

  8. An Example of Calculating a Correlation from SPSS OUTPUT

  9. .55 – (.6) (.4) The Partial Correlation Coefficient Step 1 – Determine the zero order Pearson’s correlations (r). Assume rxy= .55 where x = divorce rate and y = suicide rates. Further, assume unemployment rate (z) is our control variable and that rxz= .60 and ryz= .40 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

  10. Using SPSS for finding Partial Correlation Coefficients INPUT

  11. Using SPSS for finding Partial Correlation Coefficients OUTPUT

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