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Bivariate and Partial Correlations

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X (HT) Y (WT)............................. The Graphical View– A Scatter Diagram X’ Y’

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The Graphical View– A Scatter Diagram X (HT) Y (WT)........................ Y BAR X BAR X’ Y’

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The Graphical View– A Scatter Diagram X (HT) Y (WT)............................................................ X’ Y’

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The Algebraic View – Shared Variance Take the Variance in X = S 2 x and the Variance in Y = S 2 y 1) 2) 3) 4) The correlation is simply 3) divided by 2):

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An Example of Calculating a Correlation 1) Find the raw scores, means, squared deviations and cross-products: 3) Square r to determine variation explained r 2 =.746

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An Example of Calculating a Correlation from SPSS INPUT

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An Example of Calculating a Correlation from SPSS OUTPUT

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Step 1 – Determine the zero order Pearson’s correlations (r). Assume r xy =.55 where x = divorce rate and y = suicide rates. Further, assume unemployment rate (z) is our control variable and that r xz =.60 and r yz =.40 Step 2 – Calculate the partial correlation ( r xy.z ) ==.42 Step 3 – Draw conclusions After z ( r xy.z ) 2 =.18 Before z (r xy ) 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) The Partial Correlation Coefficient

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Using SPSS for finding Partial Correlation Coefficients INPUT

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Using SPSS for finding Partial Correlation Coefficients OUTPUT

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