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					          Correlation

Is there a relationship between……..
Is there a connection between
  gender and religion?

Both variables ordinal or
 nominal.


Use contingency tables
Is there a relationship between
  age and attitude score?

Both variables ordinal or interval

Use correlation.
Correlation
              Correlation
Measures of association for data that is:
     •ordinal
     •interval or
     •ratio
Is there any relationship between
ethnic origins and preferred sport?

 Use Chi-squared since both
 variables are nominal
Is there any relationship between
religion and social class?

 Use Chi-squared since one
 variable is nominal and the
 other ordinal
If both variables are ordinal or
   better then use a suitable
    correlation coefficient
Performance in manual dexterity




                           Pints drunk
Electricity consumption
                                      U.K.




   0            10               20            30
                     Mid-day temperature (C)
Electricity consumption
                                    SINGAPORE




   0           10             20            30   40
                    Mid-day temperature (C)
Attitude to Abortion

10




0

      20                     30   40
                       Age
 Anxiety

High                                           Austria




           England


                   Ireland
Low
             5          10         15     20   25
                 Thunderstorms per year
         We will discuss two
        correlation coefficients

•   Pearson’s Product Moment Correlation
    Coefficient

•   Spearman’s Rank Correlation Coefficient
        Correlation coefficients
Pearson’s correlation coefficient
Use when both variables are measured on an interval or
ratio scale



Spearman’s correlation coefficient
Use when one or more variable is measured on an
ordinal scale
The symbol for the calculated correlation
coefficient is
                    r

 The symbol for the true or population
correlation coefficient is

                 r (rho)
Any correlation coefficient will
    be between -1 and +1

        -1 ≤ r ≤ +1
     Pearson’s correlation coefficient


                  n xy   x y
r
      n x   2
                            
                   ( x ) n y  ( y )
                        2        2       2
                                             
Correlation is positive
Correlation is perfect
Correlation coefficient
  r = +1.0
Correlation is negative
Correlation is perfect
Correlation coefficient

   r = -1.0
Correlation is zero
There is no correlation
Correlation coefficient   r = 0.0
 Attitude to Euthanasia

  For


                                                   r = -0.7


Against


        60                Oldest living relative       100
Resting heart rate

90




                                    r = +0.5

60

      15                     20         25
                     Body fat (%)
 Anxiety

High                                           Austria




           England                        r = +0.53
                   Ireland
Low
             5          10         15     20   25
                 Thunderstorms per year
            26


            24


            22


            20


            18


            16
bodyfat %




            14


            12
             50                 60              70   80   90


                 resting heart rate (per min)
l

t
t
f

.



.
Spearman’s rank correlation coefficient



                   6 d           2

rs  1 
                     (
                  n n 1  2
                                      )
            100



            90



            80



            70



            60
400m time




            50



            40
              50                 60              70   80   90


                  resting heart rate (per min)
l

    t
r   t

 r
.r



.
These correlation coefficients
 measure linear association.

    They do not
  measure all forms
   of dependence
r=-0.5
rs=-0.92
r =0.19
rs=0.14
Data from a previous course
AGE               G                 HEIGHT SHOE                         HEAD              VERT              HORIZ             E
26                1                 72.0   10.0                         57.0              10.5              11.5              2
29                2                 63.0   3.0                          53.0              14.5              16.5              1
33                2                 67.0   6.0                          53.0              6.0               6.0               3
34                1                 68.0   7.0                          55.5              8.6               10.2              5
25                2                 63.0   5.5                          58.0              11.0              12.0              3
31                2                 64.0   4.5                          55.0              7.6               9.0               2
54                1                 72.0   10.0                         60.0              7.0               8.0               2
................................................................................................................................
................................................................................................................................


EYE COLOUR

1               HAZEL
2               BROWN
3               BLUE
4               GREY
5               GREEN/GREY
6               BROWN/GREY
         75
HEIGHT




         70




         65




         60

              3   4   5   6   7   8   9   10   11   12

                              SHOE
         75
HEIGHT




         70




         65




         60

              50   55      60

                    HEAD
         75
HEIGHT




         70




         65




         60

              5   10          15

                       VERT
         75
HEIGHT




         70




         65




         60

              5   10           15

                       HORIZ
                                                         Male
         75
                                                         Female
HEIGHT




         70




         65




         60
              3   4   5   6   7   8   9   10   11   12
                              SHOE
   Association and Causation
A strong correlation between the variables x and
y is NOT enough to draw conclusions about
whether x causes y to change.


It merely supports the idea that there is an
association.
              Better nutrition
      £       Better Health Care
    Wealth TV sets cause
      More    Cleaner water
      higher life expectancy!



More TV                     Higher life
 sets                       expectancy
           High Positive
            Correlation

				
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posted:12/19/2011
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