The Weber data, Exercise 9.7, is a 2 × 2 × 5 factorial in a randomized complete block design with r = 2 blocks. Make the data unbalanced by assuming that the two highest concentrations (80 and 100) of...

The Weber data, Exercise 9.7, is a 2 × 2 × 5 factorial in a randomized complete block design with r = 2 blocks. Make the data unbalanced by assuming that the two highest concentrations (80 and 100) of herbicide B could not be used at the high temperature (55◦ C). (Call all treatment factors class variables.) Include block effects, treatment main effects, and treatment interaction effects in the model. Use PROC GLM to analyze the data and obtain the simple and least squares treatment means.

(a) Which sums of squares will you use for testing hypotheses about the treatment effects? Explain why you choose the particular set you do.

(b) Which least squares means are nonestimable? Explain why these particular means are nonestimable. Do the results of the analysis let you simplify the model so that all relevant means are estimable?

(c) Summarize the results with tables of relevant least squares means and their standard errors.

Exercise 9.7

Use the means model reparameterization on a randomized complete block design with b = 2 and t = 4. As discussed in the text, this reparameterization leaves zero degrees of freedom for the estimate of error. However, experimental error can be estimated as the blockby-treatment interaction sum of squares. Define K for the means reparameterization so that the sum of squares obtained from Q is the error sum of squares.