1. ## 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.

2. 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 $r = \frac{\sigma_{xy}}{\sigma_{x} \sigma_{y}}$.

3. 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.

4. 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

5. I'm so confused.

6. 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.

7. For b) it says to use the Spearman's correlation coefficient, and what about for a)?

8. 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).

9. Actually for (b) its $0.946$. Just took regular correlation of two ranks which is equivalent to Spearman's correlation coefficient.

10. 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

11. 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.

12. Thanks for your help, but it doesn't sound right to me, either of them. Anyone else?

13. Anyone else know how to do these questions?

14. Originally Posted by princess_anna57
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)