The following summary quantities were computed from an experiment involving four levels of nitrogen (A), two times of planting (B), and two levels of potassium (C) ("Use and Misuse of Multiple Comparison Procedures," Agronomy J., 1977: 205-208). Only one observation (N content, in percentage, of corn grain) was made for each of the 16 combinations of levels.
SSA = .22625 SSB = .000025 SSC = .0036
SSAB = .004325 SSAC = .00065
SSBC = .000625 SST = .2384.
a. Construct the ANOVA table.
b. Assume that there are no three-way interaction effects, so that MSABC is a valid estimate of (2, and test at level .05 for interaction and main effects.
c. The nitrogen averages are x̅1.. = 1.1200, x̅2 .. = 1.3025, x̅3.. = 1.3875, and x̅4.. = 1.4300. Use Tukey's method to examine differences in percentage N among the nitrogen levels (Q.05,4,3 = 6.82).