Correlation

Overview Defined: The measure of the strength and direction of the linear relationship between two variables. Variables: IV is continuous, DV is continuous Relationship: Relationship amongst variables Example: Relationship between height and weight. Assumptions: Normality. Linearity.

Strength: ranges from 0 to 1 (or -1) Direction: positive or negative See this link for interactive way to look at scatterplots

Correlation Coefficient A measure of degree of relationship. Based on covariance –Measure of degree to which large scores go with large scores, and small scores with small scores Covariance Formula = Cov xy = Σ(X-X)(Y-Y) Correlation Formula = r = Cov xy (SS x )(SS y )

XX-X(X-X) 2 YY-Y(Y-Y) 2 (X-X)(Y-Y) , , , , X= ,000Y= 2.010Sum =900 r = Σ(X-X)(Y-Y) = Cov XY Σ[(X-X) 2 ][(Y-Y) 2 ] (SS X )(SS Y ) r = 900 = 900 =.90 (100,000)(10) 1000