Question

In a two-factor study, the treatment means /1-tj are as follows: Factor A 250 288 Factor 8 265 273 268 270 269 269 a. Obtain the factor B main effects. What do your results imply about factor B? b. Prepare a treatment means plot and determine whether the two factors interact. How can you tell that interactions are present? Are the interactions important or unimportant? c. Make a logarithmic transformation of the /1-ij and plot the transformed values to explore whether this transformation is helpful in reducing the interactions. What are your findings?

Answer 1

a. By R, we have µ.1 = µ.2 = µ.3 = µ.4 = µ.. = 269. Since β j = µ. j − µ.., we have β1 = β2 = β3 = β4 = 0. The results imply that factor B has no main effects.

b. The treatment means plot is shown below:

The lack of parallelism between the two curves reflects interaction effects. The interactions are important since the height difference between the two curves changes drastically.

c. The transformed treatment means plot is shown below:

This transformation is not helpful in reducing the interactions.