EXAMPLE 16.12 Perform the Significance Test
weeds
In Example 16.11, there are populations and observations. The sample sizes are equal, . The 16 observations arranged in increasing order, with their ranks, are
| Yield | 142.4 | 153.1 | 156.0 | 157.3 | 158.6 | 161.1 | 162.4 | 162.7 |
| Rank | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Yield | 162.8 | 165.0 | 166.2 | 166.7 | 166.7 | 172.2 | 176.4 | 176.9 |
| Rank | 9 | 10 | 11 | 12.5 | 12.5 | 14 | 15 | 16 |
There is one pair of tied observations. The ranks for each of the four treatments are
| Weeds | Ranks | Rank sums | |||
| 0 | 10 | 12.5 | 14 | 16 | 52.5 |
| 1 | 4 | 6 | 11 | 12.5 | 33.5 |
| 3 | 2 | 3 | 5 | 15 | 25.0 |
| 9 | 1 | 7 | 8 | 9 | 25.0 |
The Kruskal-Wallis statistic is, therefore,
Referring to the table of chi-square critical points (Table F) with , we find that the -value lies in the interval . This small experiment suggests that more weeds decrease yield but does not provide convincing evidence that weeds have an effect.