Correlation

Correlation

• Measure and describe the RELATIONSHIP between TWO VARIABLES

• Variables are Observed (as they exist naturally in the environment)

- NOT Manipulated

Correlation Properties

• Coefficients RANGE between -1 and 1

• High Correlation → Strong Relationship between X and Y

• Correlation near ZERO → NO Linear Relationship

Characteristics of a Relationship

1) Direction of Relationship

a. POSSITIVE (+) Correlation

b. NEGATIVE (-) Correlation

2) Form of Relationship

a. Linear

b. Curvilinear

3) Strength of Relationship

a. PERFECT Correlation

b. NO Correlation

Application of Correlation

1) Prediction

a. Two Variables are RELATED → possible to use One Variable to make a PREDICTION about the Other Variable

2) Validity

a. Relationship between NEW Developed Test & ANOTHER Test Measuring the SAME Construct

3) Reliability

a. Relationship between TWO set of Measurements using the SAME Instruments

4) Theory Verification

a. Many THEORIES Make PREDICTIONS about the relationship between TWO Variables

Pearson Correaltion, r

Measure DEGREE of & DIRECTION of LINEAR RELATIONSHIP between Two Variables

r = Degree of Which X and Y Vary TOGETHER / Degree of Which X and Y Vary SEPARATELY

… r = Covariability of X and y / Variability of X and Y Separately

Hypotheses Tests W/ Pearson Correlation

NULL HYPOTHESES

H_0: p = 0, NO Significant effect

ALTERNATIVE HYPOTHESES

H_1: p ≠ 0, YES, and effect

df

df = n -1 → 10 - 2 = 8

CRITICAL VALUE (df = 8) & (α = .05)

CV: r = .632

• Compare CV to absolute value of obtained r = -.782