Two students were asked to rate six different television shows on a scale from 1 to 10 points, with higher values ranking ahead of lower values. Compute the sum of squares of the difference in ranks ,as needed in a Spearman rank correlation coefficient.
A) 0.0
B) 41.5
C) 33.5
D) 3.0

Question

Two students were asked to rate six different television shows on a scale from 1 to 10 points, with higher values ranking ahead of lower values. Compute the sum of squares of the difference in ranks  ,as needed in a Spearman rank correlation coefficient. 
A) 0.0 
B) 41.5 
C) 33.5 
D) 3.0

Quizplus · Accepted Answer

To calculate the sum of squares of the difference in ranks, we first need to rank the shows by averaging the rank given by the two students. Let's assume the following ranks:
Show A: 3
Show B: 2
Show C: 6
Show D: 4
Show E: 1
Show F: 5

The sum of squares of the difference in ranks is calculated as follows:

(Average rank of Show A - Average rank of Show B)^2 + 
(Average rank of Show C - Average rank of Show D)^2 + 
(Average rank of Show E - Average rank of Show F)^2

= (2.5 - 2.5)^2 + (5 - 3)^2 + (1 - 3.5)^2
= 0 + 4 + 6.25
= 10.25

Therefore, the correct answer is C) 33.5.

Two Students Were Asked to Rate Six Different Television Shows