Pearson Correlation Coefficient

1
Lecture 15

• Pearson Correlation Coefficient

2
rxy (Person Correlation Coefficient)

• Measures the strength of relationships between
  variable x and y
  
• Its sign indicates the direction of the
  relationship
  
• The range of r is from -1 to 1 where
• 1.00 indicates the strongest positive
  relationship
  
• -1.00 indicates the strongest negative
  relationship
  
• .00 indicates no relationship

3
Examples

• height, weight
• SAT, grade-point-average (GPA)
• auto weight, miles-per-gallon
• education, income
• drug dosage level, blood pressure
• amount of homework, achievement
• The Pearson r can be computed between any two
  sets of scores

4
Formula

• r   SPxy / sqrt(SSxSSy)
• where SS sum of squares,
• SP sum of products

5
Computation Example (X Quiz1, Y Quiz 2)
6
Procedure

• From the raw X, Y data, produce deviation scores
  and products
  
• x X X mean
• y Y Y mean

7
x deviation scores for variable Xy deviation
scores for variable Yx y products of the
deviations
8

• 2. Produce sum of squares and sum of products
  (the sum across persons of the product of
  deviations)

9
(No Transcript)
10

• 3. Calculate r
• r SPxy / sqrt(SSxSSy)
• 38/ sqrt (28112) 38 / 56 .679