Introduction
         Introduction
  • Last Week – Recap
  • Correlation
  • How To Draw A Line
  • Simple Linear Regression
  • Summary
        Last Week - Recap
        Last Week - Recap
  • Hypotheses
  • Probability & Significance (p=<0.05)
  • Chi-square test for two categorical variables
  • t-test for one categorical and one interval variables
  • What about a test for two interval variables?...
               Correlation I
               Correlation I
   • Calculates the strength and direction of a linear 
    relationship between two interval variables
   • e.g. is there a relationship between age and income?
   • Measured using the Pearson correlation coefficient (r)
   • Data must be normally distributed (check with a 
    histogram)
           If not normally distributed use Spearman’s Rank Order 
           If not normally distributed use Spearman’s Rank Order 
             Correlation (rho) - consult Pallant (2005:297)
             Correlation (rho) - consult Pallant (2005:297)
                                   Correlation II
                                   Correlation II
       • ‘r’ can take any value from +1 to -1
       • +/- indicates whether the relationship is positive or negative
       • +1 or -1 is a perfect linear relationship, but usually it is not this clear cut
       • Rule of thumb:
          –+/- 0.7 = a strong linear relationship                 Alternatively:
                                                                  Alternatively:
                                                                  -
                                                                  - +/- 0.10 to 0.29 = weak
          –+/- 0.5 = a good linear relationship                     +/- 0.10 to 0.29 = weak
                                                                  -
                                                                  - +/- 0.30 to 0.49 = medium
          –+/- 0.3 = a linear relationship                          +/- 0.30 to 0.49 = medium
                                                                  -
                                                                  - +/- 0.50 to 1.00 - strong
          –Below +/- 0.3 = weak linear relationship                 +/- 0.50 to 1.00 - strong
          –0 = no linear relationship
               Correlation III
               Correlation III
                   No relationship Negative 
       Positive        No          Negative
      Positive         No          Negative
       Positive
                                  relationship
     Relationship   Relationship  Relationship
     relationship   Relationship  Relationship
     Relationship
             Formulate hypotheses and use scatter plots!
             Formulate hypotheses and use scatter plots!