Bivariate and Partial Correlations

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

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

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

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):

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

An Example of Calculating a Correlation from SPSS INPUT

An Example of Calculating a Correlation from SPSS OUTPUT

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 ( ) or 12% of Y and (.12/.30) or 40% of the relationship between X&Y.55 – (.6) (.4) The Partial Correlation Coefficient

Using SPSS for finding Partial Correlation Coefficients INPUT

Using SPSS for finding Partial Correlation Coefficients OUTPUT