We wish to study the competition of grass species: in particular, big bluestem (from the tall grass prairie) versus quack grass (a weed). We set up an experimental garden with 24 plots. These plots were randomly allocated to the six treatments: nitrogen level 1 (200 mg N/kg soil) and no irrigation; nitrogen level 1 and 1cm/week irrigation; nitrogen level 2 (400 mg N/kg soil) and no irrigation; nitrogen level 3 (600 mg N/kg soil) no irrigation nitrogen level 4 (800 mg N/kg soil) and no irrigation; and nitrogen level 4 and 1 cm/week irrigation. Big bluestem was seeded in these plots and allowed to establish itself. After one year, we added a measured amount of quack grass seed to each plot. After another year, we harvest the grass and measure the fraction of living material in each plot that is big bluestem. We wish to determine the effects (if any) of nitrogen and/or irrigation on the ability of quack grass to invade big bluestem. (Based on Wedin 1990.) N level 1 1 2 3 4 4
Irrigation N Y N N N Y
97 83 85 64 52 48
96 87 84 72 56 58
92 78 78 63 44 49
95 81 79 74 50 53

Required:
a. Do the data need a transformation? If so, which transformation?
b. Provide an Analysis of Variance for these data. Are all the treatments equivalent?
c. Are there significant quadratic effects of nitrogen under nonirrigated conditions?
d. Is there a significant effect of irrigation?
e. Under which conditions is big bluestem best able to prevent the invasion by quack grass? Is the response at this set of conditions significantly different from the other conditions?