We continue with the same dataset but use another type of non-parametric test – the Wilcoxon Signed Rank Test. Here, not only the sign of the observation counts but also the distance of departure from the median.
| Case # | Drug A |
| 1 | 12.3 |
| 2 | 13.1 |
| 3 | 11.3 |
| 4 | 10.1 |
| 5 | 14.0 |
| 6 | 13.3 |
| 7 | 10.5 |
| 8 | 12.3 |
| 9 | 10.9 |
| 10 | 11.9 |
The Null Hypothesis, H0: Median = 13.0
The Alternate Hypothesis, H1: Median < 13.0
Steps
- Estimate the difference from the null hypothesis (median = 13.0)
- Calculate the absolute value
- Estimate the rank of the list, with the smallest absolute difference getting the lowest rank
- Add the sign (from the difference of step 1) to the rank
- Add all positives and negatives separately.
- Take the smaller of the two and check against the table of critical values.
| Drug A | Difference | Abs Difference | Rank | Signed Rank |
| 12.3 | -0.7 | 0.7 | 3.5 | -3.5 |
| 13.1 | 0.1 | 0.1 | 1 | 1 |
| 11.3 | -1.7 | 1.7 | 7 | -7 |
| 10.1 | -2.9 | 2.9 | 10 | -10 |
| 14.0 | 1.0 | 1.0 | 5 | 5 |
| 13.3 | 0.3 | 0.3 | 2 | 2 |
| 10.5 | -2.5 | 2.5 | 9 | -9 |
| 12.3 | -0.7 | 0.7 | 3.5 | -3.5 |
| 10.9 | -2.1 | 2.1 | 8 | -8 |
| 11.9 | -1.1 | 1.1 | 6 | -6 |
The sum of positive ranks = 8
The sum of negative ranks = 47
We’ll take the smaller, 8 and check against the table. The number in the table (n = 10, one-sided test, alpha = 0.5) is 10. Since 8 is smaller than 10, we reject the null hypothesis.
Non-parametric tests: zedstatistics
