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 = Covxy = Σ(X-X)(Y-Y)

• Correlation Formula = r = Covxy

(SSx)(SSy)

X X-X (X-X)2 Y Y-Y (Y-Y)2 (X-X)(Y-Y)

200 -200 40,000 0 -2 4 400

300 -100 10,000 1 -1 1 100

400 0 0 2 0 0 0

500 100 10,000 4 2 4 200

600 200 40,000 3 1 1 200

X= 400 100,000 Y= 2.0 10 Sum =900

• r = Σ(X-X)(Y-Y) = CovXY

Σ[(X-X)2][(Y-Y)2] (SSX)(SSY)

• r = 900 = 900 = .90

(100,000)(10) 1000