Six second-graders tried tossing a ball into a basket ten times each. Their teacher then sug a different way of tossing the ball, and the six students tried again. The number of succes tosses, before and after the teacher's suggestion, are shown below.
$\begin{array}{c|cccccc}
\text { Student } & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} & \mathbf{E} & \mathbf{F} \
\hline \text { Before the suggestion (out of 10) } & 2 & 3 & 7 & 2 & 7 & 3 \
\text { After the suggestion (out of 10) } & 3 & 3 & 5 & 3 & 5 & 3
\end{array}$

Find the sum of the positive and negative rank sums as in a Wilcoxon signed-rank test. gested
A) positive rank sum = 7; negative rank sum = -3
B) positive rank sum = 6; negative rank sum = -2
C) positive rank sum = 4; negative rank sum = -2
D) positive rank sum = 2; negative rank sum = -1

Question

Six second-graders tried tossing a ball into a basket ten times each. Their teacher then sug a different way of tossing the ball, and the six students tried again. The number of succes tosses, before and after the teacher's suggestion, are shown below.
$\begin{array}{c|cccccc}
\text { Student } & \mathbf{A} & \mathbf{B} & \mathbf{C} & \mathbf{D} & \mathbf{E} & \mathbf{F} \
\hline \text { Before the suggestion (out of 10) } & 2 & 3 & 7 & 2 & 7 & 3 \
\text { After the suggestion (out of 10) } & 3 & 3 & 5 & 3 & 5 & 3
\end{array}$

Find the sum of the positive and negative rank sums as in a Wilcoxon signed-rank test. gested
A) positive rank sum = 7; negative rank sum = -3
B) positive rank sum = 6; negative rank sum = -2
C) positive rank sum = 4; negative rank sum = -2
D) positive rank sum = 2; negative rank sum = -1

Quizplus · Accepted Answer

The Wilcoxon signed-rank test involves ranking the differences between paired observations (in this case, the number of successful tosses before and after the suggestion), without considering the sign for the purpose of ranking, then summing the ranks for the positive differences and separately for the negative differences. Here, the differences are: +1 (A), 0 (B), -2 (C), +1 (D), -2 (E), 0 (F). Ignoring the signs and zeros, the ranks are 1.5 (A and D) and 3.5 (C and E). The positive rank sum is 1.5 + 1.5 = 3, and the negative rank sum is -3.5 - 3.5 = -7. However, the correct interpretation of the question's request for "the sum of the positive and negative rank sums" would actually be 3 + (-7) = -4, which does not match any of the provided options, indicating a misunderstanding in the calculation or interpretation of the question's request. Given the options and the typical process for calculating Wilcoxon signed-rank test values, none directly align with the correct calculation process described. The correct calculation should consider all differences, assign ranks, and then sum these ranks for positive and negative differences separately. The misunderstanding seems to be in the interpretation of the question's final request rather than the calculation of the rank sums themselves.

Six Second-Graders Tried Tossing a Ball into a Basket Ten