EXAMPLE 16.11 Weeds and Corn Yield
weeds
Lamb’s-quarter is a common weed that interferes with the growth of corn. A researcher planted corn at the same rate in 16 small plots of ground and then randomly assigned the plots to four groups. He weeded the plots by hand to allow a fixed number of lamb’s-quarter plants to grow in each meter of corn row. These numbers were zero, one, three, and nine in the four groups of plots. No other weeds were allowed to grow, and all plots received identical treatment except for the weeds. Here are the yields of corn (bushels per acre) in each of the plots:14
| Weeds per meter |
Corn yield |
Weeds per meter |
Corn yield |
Weeds per meter |
Corn yield |
Weeds per meter |
Corn yield |
| 0 | 166.7 | 1 | 166.2 | 3 | 158.6 | 9 | 162.8 |
| 0 | 172.2 | 1 | 157.3 | 3 | 176.4 | 9 | 142.4 |
| 0 | 165.0 | 1 | 166.7 | 3 | 153.1 | 9 | 162.7 |
| 0 | 176.9 | 1 | 161.1 | 3 | 156.0 | 9 | 162.4 |
The summary statistics are
| Weeds | Mean | Standard deviation | |
| 0 | 4 | 170.200 | 5.422 |
| 1 | 4 | 162.825 | 4.469 |
| 3 | 4 | 161.025 | 10.493 |
| 9 | 4 | 157.575 | 10.118 |
Reminder
rule for standard deviations in ANOVA, p. 720
The sample standard deviations do not satisfy our rule of thumb that for safe use of ANOVA the largest should not exceed twice the smallest. A careful look at the data suggests that there may be some outliers. These are the correct yields for their plots, so we have no justification for removing them. Let’s use a rank test that is not sensitive to outliers.