In a continuation of the experiments to investigate the eect of plant growth regulators and spear bud scales on spear elongation in asparagus, described in exercise 5 of Chapter 2, Yang-Gyu and Woolley (2006) conducted a 4×3 factorial experiment varying the concentration of the plant growth regulator CPPU in the solution, and the time the asparagus spears were dipped in the solution. The results are shown in the table below.

(a) Partition the sums of squares for CPPU concentration and dipping time into orthogonal polynomial contrasts. Partition the interaction of CPPU conc. by dipping time into linear×linear, quadratic×linear, cubic×linear, linear×quadratic, quadratic×quadratic, and cubic×quadratic. Pool (sum)
all sums of squares but the linear×linear portion to form an error sum of squares and use it to test the linear×linear part of the interaction and the polynomial contrasts you found for the main eects. Interpret your results.

(b) Use the Tukey1df function to test the signicance of the interaction.

(c) Based on the results you obtained in

(a) and

(b) would you recommend the additive model for this data?

Transcribed Image Text:

Dipping Time (sec) CPPU Conc. 30 60 90 0 (control) 92.5 92.9 91.3 0.5 ppm 97.8 94.9 101.3 1.0 ppm 97.0 98.5 101.6 10.0 ppm 103.4 102.9 98.6