In the experiment to compare four commercial brands of ravioli described in Chapter 2, it may be argued that ‘assessor’ should be regarded as a random-effect factor.

(a) Consider the case for this decision, and present the arguments for and against.

(b) If ‘brand’ is regarded as a fixed-effect term and ‘assessor’ as a random-effect term, how should ‘brand.assessor’ be regarded?

(c) Make these changes to the mixed model fitted to these data. Perform the new analysis, and interpret the results. Explain the effect of the changes on the SEs of differences between brands.

(d) Perform appropriate tests to determine whether the new random-effect terms are significant.