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Math Help - Help please - statistics

  1. #1
    Member princess_anna57's Avatar
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    Help please - statistics

    URGENT NEED TO SUBMIT TODAY!!!!!!!!!!!!



    Subject A B C D E F G H I
    Anxiety Level 2 5 6 10 10 17 30 10 8
    Self Esteem 5 20 22 30 26 35 40 30 27

    a) Calculate Pearson's linear correlation coefficient to three decimal places.
    b) Rank the scores for each test and calculate Spearman's correlation coefficient for this data.

    Oh dear the numbers won't go under the letters, but basically 2 and 5 under A, 5 and 20 under B, etc etc.
    Last edited by princess_anna57; July 23rd 2007 at 07:29 PM.
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  2. #2
    Senior Member tukeywilliams's Avatar
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    For (b)  \rho = 1- \frac{6 \sum d_{i}^{2}}{n(n^2-1)} (assuming no tied ranks). So sort the first row. Add a rank column. Then rank the second row. Then calculate the difference between the two ranks. Then square this difference. Add up the column of squared differences. This should allow you to calculate  \rho . We know  n = 9 .

    For (a) first calculate the averages of the two rows  \overline{x}, \overline{y} . Then calculate the standard deviations. Then calculate the covariance. So the coefficient is  r = \frac{\sigma_{xy}}{\sigma_{x} \sigma_{y}} .
    Last edited by tukeywilliams; July 23rd 2007 at 07:14 PM.
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  3. #3
    Member princess_anna57's Avatar
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    Nah, I dunno how to do either. This is the first time I've ever attempted questions like this. -is stressed- Your instructions don't mean much to me.
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  4. #4
    Senior Member tukeywilliams's Avatar
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    You have to use the correlation coefficient because there are tied ranks.

    Its like this:
    Code:
            2   5   1   1   0   0   
          5   20   2   2   0   0   
          6   22   3   3   0   0   
          8   27   4   5   1   1   
          10   30   6   6   0   0   
          10   26   6   4   2   4   
          10   30   6   6   0   0   
          17   35   7   7   0   0   
          30   40   8   8   0   0   
          
      
      
      
      
      
      5
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  5. #5
    Member princess_anna57's Avatar
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    I'm so confused.
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  6. #6
    Senior Member tukeywilliams's Avatar
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    Ok so the two rankings are for (b):

    Code:
     1,2,3,4,6,6,6,7,8
    and

    Code:
     1,2,3,5,6,4,6,7,8
    Using the
    kendall tau formula  \tau = \frac{4P}{n(n-1)} -1 we get:

     P = 8 + 7 + 6 + 4 + 2 + 3 + 2 + 1 = 33 .

    So  \tau = \frac{33 \times 4}{72} -1 = 0.8333 .

    For (a) the correlation coefficient is  0.833 . So they are the same. I just used Excel.
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  7. #7
    Member princess_anna57's Avatar
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    For b) it says to use the Spearman's correlation coefficient, and what about for a)?
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  8. #8
    Senior Member tukeywilliams's Avatar
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    For (b) I dont think you can use Spearman's correlation coefficient because some rankings are the same.

    For (a),  r = 0.7473 (from Tao).
    Last edited by tukeywilliams; July 23rd 2007 at 09:48 PM.
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  9. #9
    Senior Member tukeywilliams's Avatar
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    Actually for (b) its  0.946 . Just took regular correlation of two ranks which is equivalent to Spearman's correlation coefficient.
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  10. #10
    Member princess_anna57's Avatar
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    Can you go through the steps as to how you got the answer to a)? I really appreciate all your help. If anyone has a second opinion, please post!

    Okay, so b).... start from the beginning please lol you've lost me again
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  11. #11
    Senior Member tukeywilliams's Avatar
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    For (a) I used the definition  \frac{\sigma_{xy}}{\sigma_{x} \sigma_{y}} .

    So the covariance or  \sigma_{xy} = \frac{2 \cdot 5 + 5 \cdot 20 + 6 \cdot 22 + \ldots - (10.88)(25)}{(8.29)(10.08)} .  10.88 is the average of the first row and  25 is the average of the second row.  8.29 and  10.08 are the standard deviations of the rows respectively.

    I divided this number by  (8.29)(10.08) to get the answer.

    For (b) I did the same thing as above except I used the two rows or ranks as the data. The Tao formula is a totally different result.
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  12. #12
    Member princess_anna57's Avatar
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    Thanks for your help, but it doesn't sound right to me, either of them. Anyone else?
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  13. #13
    Member princess_anna57's Avatar
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    Anyone else know how to do these questions?
    Last edited by princess_anna57; July 23rd 2007 at 10:55 PM.
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  14. #14
    Super Member
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    Quote Originally Posted by princess_anna57 View Post
    URGENT NEED TO SUBMIT TODAY!!!!!!!!!!!!

    Subject A B C D E F G H I
    Anxiety Level 2 5 6 10 10 17 30 10 8
    Self Esteem 5 20 22 30 26 35 40 30 27
    ...
    b) Rank the scores for each test and calculate Spearman's correlation coefficient for this data.

    ...
    Hello,

    tukeywilliams has described precisely what to do if you want to calculate the Spearman's rank correlation coefficient.

    I've made a table. (see attachment)
    Attached Thumbnails Attached Thumbnails Help please - statistics-spearman_tab.gif  
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