Question

Perform the Wilcoxon signed rank sum test given the following paired
observations:


Data

1

2

3

4

5

6

7

8

9

10

Result 1

12

6

9

15

13

17

8

13

8

10

Result 2

10

6

10

13

12

14

6

13

9

11



Rank the absolute differences of the above paired data.

Total of the (-) ranks = ?
There are no human answers yet.
Answered by GPT-4o mini
To perform the Wilcoxon signed-rank test, we first need to calculate the differences between the paired observations (Result 1 - Result 2) and then rank the absolute values of these differences. The rank will be assigned in ascending order.

### Step 1: Calculate Differences
Let's calculate the differences (Result 1 - Result 2) for the given data.

| Observation | Result 1 | Result 2 | Difference (Result 1 - Result 2) |
|-------------|----------|----------|-----------------------------------|
| 1 | 12 | 10 | 2 |
| 2 | 6 | 6 | 0 |
| 3 | 9 | 10 | -1 |
| 4 | 15 | 13 | 2 |
| 5 | 13 | 12 | 1 |
| 6 | 17 | 14 | 3 |
| 7 | 8 | 6 | 2 |
| 8 | 13 | 13 | 0 |
| 9 | 8 | 9 | -1 |
| 10 | 10 | 11 | -1 |

### Step 2: Absolute Differences
Next, we take the absolute values of these differences.

| Observation | Difference | Absolute Difference |
|-------------|------------|---------------------|
| 1 | 2 | 2 |
| 2 | 0 | 0 |
| 3 | -1 | 1 |
| 4 | 2 | 2 |
| 5 | 1 | 1 |
| 6 | 3 | 3 |
| 7 | 2 | 2 |
| 8 | 0 | 0 |
| 9 | -1 | 1 |
| 10 | -1 | 1 |

### Step 3: Rank the Absolute Differences
Now we rank the absolute differences, ignoring the zeros.

| Absolute Difference | Rank |
|---------------------|------|
| 1 | 1.5 | (two occurrences of 1, average rank for both)
| 1 | 1.5 |
| 2 | 3.5 | (three occurrences of 2, average rank for all three)
| 2 | 3.5 |
| 2 | 3.5 |
| 3 | 6 |

### Summary of Ranks
| Observation | Absolute Difference | Rank |
|-------------|---------------------|------|
| 1 | 2 | 3.5 |
| 2 | 0 | |
| 3 | 1 | 1.5 |
| 4 | 2 | 3.5 |
| 5 | 1 | 1.5 |
| 6 | 3 | 6 |
| 7 | 2 | 3.5 |
| 8 | 0 | |
| 9 | 1 | 1.5 |
| 10 | 1 | 1.5 |

### Step 4: Calculate Total of (-) Ranks
Now we sum the ranks for the negative differences:

- In our data set, the negative differences occurred for observations 3, 9, and 10.
- The ranks of the negative differences (ranked values):

Only negative ranks:
- For observation 3: Rank 1.5
- For observation 9: Rank 1.5
- For observation 10: Rank 1.5

### Total negative ranks = 1.5 + 1.5 + 1.5 = 4.5

### Result
**Total of the (-) ranks = 4.5**