The Correlation Coefficient

  1. Who created the Product-Moment Correlation Coefficient?
    Karl Pearson
  2. What is the correlation coefficient?
    • A model dependent measure of the strength of relationship between two variables 
    • It provides an appropriate measure of the strength of a relationship only within the context of linear regression
  3. What happens if the relationship between variables is non linear?
    The use of the correlation as a descriptive statistic is misleading
  4. What does the interpretation of the coefficient assume?
    • An underlying bivariate normal distribution 
    • Normally distributed condition distributions 
    • Homogeneity of variance
  5. What are the relationship denotations for the correlation coefficient?
    • When there is a perfect positive linear
    • relationship, r = 1.0

    • When there is perfect negative linear
    • relationship, r = -1.0

    • When r = 0.0 there is either no relationship,
    • (or possibly a non-linear relationship)
  6. What is the probability formula for the coeffient?
    • The square root of r2
    • If the regression coefficient is negative the r value should also be made negative
    • This means the correlation coefficient is the square root of the proportion of variability accounted for by the straight line regression
  7. What must be remembered when using R2?
    • R2 must be expressed as a proportion when taking the square root (not a percentage)
    • r varies between -1.0+1.0 whereas R2 varies between 0.0+1.0
  8. Give a formula to relate the correlation coefficient to the regression coefficient
    r= slope x the square root of the sum of squares of x over the sum of squares of y
  9. What happens if X and Y are converted into standard scores (M=0.00, SD=1.0)
    • The value of the coefficient will not be affected 
    • The SD will be the same for both
Card Set
The Correlation Coefficient