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 $\sum d ^ { 2 }$, as needed in a Spearman rank correlation coefficient.
$\begin{array}{c|cccccc}
\text { Show } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline \text { Student 1 } & 3 & 6 & 8 & 6 & 5 & 7 \
\text { Student 2 } & 7 & 9 & 3 & 5 & 2 & 5
\end{array}$

A) 41.5
B) 3.0
C) 0.0
D) 33.5

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 $\sum d ^ { 2 }$, as needed in a Spearman rank correlation coefficient.
$\begin{array}{c|cccccc}
\text { Show } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline \text { Student 1 } & 3 & 6 & 8 & 6 & 5 & 7 \
\text { Student 2 } & 7 & 9 & 3 & 5 & 2 & 5
\end{array}$

A) 41.5
B) 3.0
C) 0.0
D) 33.5

Quizplus · Accepted Answer

The sum of squares of the difference in ranks is 41.5. This is calculated by taking the difference between the ranks of each show for the two students, squaring the difference, and then summing the squared differences. For example, for show A, the difference in ranks is 4 (7 - 3), and the squared difference is 16. The sum of the squared differences for all six shows is 41.5.

Two Students Were Asked to Rate Six Different Television Shows ∑d2\sum d ^ { 2 }∑d2

Two Students Were Asked to Rate Six Different Television Shows $\sum d ^ { 2 }$