13.4 Consider an experiment where the amount of dry matter is measured on wheat plants grown in different levels of moisture and with different fertilizers (Mil- liken and Johnson, 1984). The experimental material consists of 60 peat pots and 15 plastic trays; four (4) peat pots can be put in one tray. The moisture treat- ment consists of adding 10, 20, 30, 40, or 50 ml of water to the tray, where it will be absorbed by the pots. The experiment is being conducted at 3 different green- houses such that 5 trays are used in each greenhouse and in each greenhouse each moisture level is assigned randomly to one tray. The fertilizer treatments are represented by a 22 factorial of low and high levels of nitrogen and phos- phate. Each fertilizer combination is applied (at random) to individual pots in a tray such that each combination occurs once in each tray. In each pot 5 plants are grown, and observations are made on the individual plants. (i) Give a schematic (that is, graphical) representation of the layout of the experiment. (ii) Give the name of the error-control design for this experiment. (iii) Give an appropriate linear model for the design described in (ii), which reflects the structures of the error-control design, the treatment design, and the sampling design. (iv) Outline the ANOVA table based on the model given in (iii), giving sources of variation, d.f., and E(MS). (v) Explain how you would test whether there exists interaction between nitro- gen and the moisture treatment. (vi) The researcher is interested in finding out whether there exists a linear trend for the effect of moisture on dry matter. Give an expression for the estimate of the linear trend and give its standard error.