Magnesium Ammonium Phosphate and Chrysanthemums. Walpole et al. (2007) provide data from a study on the effect of magnesium ammonium phosphate on the height of chrysanthemums, which was conducted at George Mason University in order to determine a possible optimum level of fertilization, based on the enhanced vertical growth response of the chrysanthemums. Forty chrysanthemum seedlings were assigned to 4 groups, each containing 10 plants. Each was planted in a similar pot containing a uniform growth medium. An increasing concentration of MgNH4PO4, measured in grams per bushel, was added to each plant. The 4 groups of plants were grown under uniform conditions in a greenhouse for a period of 4 weeks. The treatments and the respective changes in heights, measured in centimeters, are given in the following table:

Treatment

50 g/bu 13.2 12.4 12.8 17.2 13.0 14.0 14.2 21.6 15.0 20.0

100 g/bu 16.0 12.6 14.8 13.0 14.0 23.6 14.0 17.0 22.2 24.4

200 g/bu 7.8 14.4 20.0 15.8 17.0 27.0 19.6 18.0 20.2 23.2

400 g/bu 21.0 14.8 19.1 15.8 18.0 26.0 21.1 22.0 25.0 18.2

Solve the problem as a Bayesian one-way ANOVA. Use STZ constraints on treatment effects.

(a) Do different concentrations of MgNH4PO4 affect the average attained height of chrysanthemums? Look at the 95% credible sets for the differences between treatment effects.

(b) Find the 95% credible set for the contrast ?1 ? ?2 ? ?3 + ?4.

Treatment 50 g/bu 100 g/bu 200 g/bu 400 g/bu 13.2 16.0 7.8 21.0 12.4 12.6 14.4 14.8 12.8 14.8 20.0 19.1 17.2 13.0 15.8 15.8 13.0 14.0 17.0 18.0 14.0 23.6 27.0 26.0 14.2 14.0 19.6 21.1 21.6 17.0 18.0 22.0 15.0 22.2 20.2 25.0 20.0 24.4 23.2 18.2 Solve the problem as a Bayesian one-way ANOVA. Use STZ constraints on treatment effects. (a) Do different concentrations of MgNH PO, affect the average attained height of chrysanthemums? Look at the 95% credible sets for the differences between treatment effects. (b) Find the 95% credible set for the contrast /1 - /2 - /3 + /4