Six second-graders tried tossing a ball into a basket ten times each. Their teacher then suggested a different way of tossing the ball, and the six students tried again. The number of successful tosses, before and after the teacher's suggestion, are shown below. Find the sum of the positive and negative rank sums as in a Wilcoxon signed-rank test.

Question

Six second-graders tried tossing a ball into a basket ten times each. Their teacher then suggested a different way of tossing the ball, and the six students tried again. The number of successful tosses, before and after the teacher's suggestion, are shown below.  Find the sum of the positive and negative rank sums as in a Wilcoxon signed-rank test.

Quizplus · Accepted Answer

To find the positive and negative rank sums, we first need to subtract the "before" successes from the "after" successes. That gives us the following differences:

-1, -1, 1, 2, 0, -2

Next, we need to rank these differences in absolute value from smallest to largest, breaking ties by averaging the ranks.

-2: Rank 1
-1: Rank 2.5 (average of ranks 2 and 3)
-1: Rank 2.5 (average of ranks 2 and 3)
0: Rank 4.5 (average of ranks 4 and 5)
1: Rank 6
2: Rank 7

The negative rank sum is the sum of the ranks of the negative differences:

1 + 2.5 + 2.5 = 6

The positive rank sum is the sum of the ranks of the positive differences:

6 + 7 = 13

So the sum of the positive and negative rank sums is:

6 + 13 = 19

Therefore, the correct answer is D, with a positive rank sum of 13 and a negative rank sum of 6.

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