The Sensory Measurement data comes from Wu & Hamada 2009. The design is a CRD with a 510 factorial treatment design and n= 3 replications per treatment; both Items and Observers are random effects factors.

a) Give a suitable model for this experiment.

(b) State the testable null hypotheses (in terms of population parameters, of course) for an ANOVA.

(c) Obtain the appropriate ANOVA table with the assistance of R. If there are problems with Rs

output, fix them!

(d) Concisely interpret the results of the ANOVA. Include key evidence (value of F test statistic with associated d.f. and p-value) with each conclusion as appropriate.

(e) Estimate each of the variance components in the model, and calculate the proportion (or percentage each contributes to the sum of the (estimated) variance components.

perform in r

Table 3.12 Sensory Data, Measurement System Assessment Study Operator Item 1 2 3 4 5 1 4.9 4.5 5.3 5.3 6.3 5.3 5.5 5.7 wino i w 4.4 3.3 4.7 4.7 4.9 4.6 2 5.9 3 2.4 4 5 4.3 4.3 4.1 6.0 4.9 6.0 2.4 3.9 1.9 7.4 7.1 6.4 5.7 5.8 5.8 2.2 3.0 2.1 1.2 1.3 0.9 4.2 3.0 4.8 8.0 9.0 8.9 5.0 5.4 2.8 3.3 4.0 3.4 4.5 4.2 4.7 2.3 2.8 2.6 6.4 5.9 6.9 5.4 5.4 6.1 1.7 2.1 1.1 1.2 0.8 1.1 4.5 4.7 4.7 9.0 6.7 8.1 3.9 3.4 4.1 2.5 3.0 3.9 8.2 7.9 7.1 6.3 5.7 6.0 2.4 1.8 3.3 1.5 2.4 3.1 4.8 4.5 4.8 8.6 7.7 9.2 4.8 5.0 5.2 6 6.3 3.1 2.7 4.6 6.8 7.3 7.0 6.1 6.2 7.0 3.4 4.0 3.3 0.9 1.2 1.9 4.6 4.9 4.8 9.4 9.0 9.1 5.5 4.9 3.9 1.3 2.2 6.0 6.1 6.7 5.9 6.5 4.9 1.7 1.7 2.1 0.7 1.3 1.6 3.2 4.6 4.3 8.8 7.9 7.6 3.8 7 8 9 10 4.6 5.5 Table 3.12 Sensory Data, Measurement System Assessment Study Operator Item 1 2 3 4 5 1 4.9 4.5 5.3 5.3 6.3 5.3 5.5 5.7 wino i w 4.4 3.3 4.7 4.7 4.9 4.6 2 5.9 3 2.4 4 5 4.3 4.3 4.1 6.0 4.9 6.0 2.4 3.9 1.9 7.4 7.1 6.4 5.7 5.8 5.8 2.2 3.0 2.1 1.2 1.3 0.9 4.2 3.0 4.8 8.0 9.0 8.9 5.0 5.4 2.8 3.3 4.0 3.4 4.5 4.2 4.7 2.3 2.8 2.6 6.4 5.9 6.9 5.4 5.4 6.1 1.7 2.1 1.1 1.2 0.8 1.1 4.5 4.7 4.7 9.0 6.7 8.1 3.9 3.4 4.1 2.5 3.0 3.9 8.2 7.9 7.1 6.3 5.7 6.0 2.4 1.8 3.3 1.5 2.4 3.1 4.8 4.5 4.8 8.6 7.7 9.2 4.8 5.0 5.2 6 6.3 3.1 2.7 4.6 6.8 7.3 7.0 6.1 6.2 7.0 3.4 4.0 3.3 0.9 1.2 1.9 4.6 4.9 4.8 9.4 9.0 9.1 5.5 4.9 3.9 1.3 2.2 6.0 6.1 6.7 5.9 6.5 4.9 1.7 1.7 2.1 0.7 1.3 1.6 3.2 4.6 4.3 8.8 7.9 7.6 3.8 7 8 9 10 4.6 5.5