A psychologist has constructed a paper and pencil test purported to measure depression. To see how the test compares with the ratings of the expert, 12 emotionally disturbed individual are given the paper and pencil test. The individuals are also independently rank-ordered by two psychiatrists according to the degree of depression each psychiatrist finds as a result of detailed interviews. The scores are given here. Higher scores represent greater depression.

QUESTION: WHAT IS THE CORRELATION BETWEEN THE SCORES ON THE PAPER TEST AND THE RANKINGS OF EACH PSYHIATRIST?
I used the spearman rho formula, but I can't get the answer.Thank you.

Individual pa/pe PSYCH
A B
1 48 12 9
2 37 11 12
3 30 4 5
4 45 7 8
5 31 10 11
6 24 8 7
7 28 3 4
8 35 9 6
9 15 2 2
10 42 6 10
11 18 1 1
12 22 5 3

To calculate the correlation between the scores on the paper test and the rankings of each psychiatrist, you can use the Spearman's rank correlation coefficient formula.

1. First, calculate the ranks for each set of rankings. Start by ranking the scores on the paper test. If there are ties, assign each tied value the average of the ranks they would have received.

Individual Paper Test (pa/pe) Rank Psychiatrist A Rank Psychiatrist B Rank
1 48 10 7
2 37 9 12
3 30 5 4
4 45 7 6
5 31 6 11
6 24 4 5
7 28 5 3
8 35 8 8
9 15 1 1
10 42 9 10
11 18 2 2
12 22 3 4

2. Next, calculate the difference in ranks for each individual between the paper test scores and each psychiatrist's rankings.

Individual Rank Difference: A Rank Difference: B
1 3 2
2 -3 0
3 1 1
4 1 2
5 5 6
6 1 1
7 2 1
8 0 2
9 0 0
10 1 0
11 1 1
12 1 1

3. Square the differences in ranks for each individual.

Individual Rank Difference Squared: A Rank Difference Squared: B
1 9 4
2 9 0
3 1 1
4 1 4
5 25 36
6 1 1
7 4 1
8 0 4
9 0 0
10 1 0
11 1 1
12 1 1

4. Calculate the sum of the squared rank differences for each psychiatrist.

Sum of Rank Difference Squares: A = 9 + 9 + 1 + 1 + 25 + 1 + 4 + 0 + 0 + 1 + 1 + 1 = 53
Sum of Rank Difference Squares: B = 4 + 0 + 1 + 4 + 36 + 1 + 1 + 4 + 0 + 0 + 1 + 1 = 53

5. Finally, use the Spearman's rank correlation coefficient formula to calculate the correlation:

ρ = 1 - ( (6 * sum of the rank difference squares) / (N * (N^2 - 1) ) )
= 1 - ( (6 * 53) / (12 * (12^2 - 1) ) )
= 1 - ( (6 * 53) / (12 * 143 ) )
= 1 - (318 / 1716)
= 1 - 0.1856
= 0.8144

So, the correlation (Spearman's rho) between the scores on the paper test and the rankings of each psychiatrist is approximately 0.8144 (positive correlation).