Question

just for part b c e

Consider the following experiment of the effects of eight factors on the taste of a 1985 Pinot Noir, as assessed by a panel of five experts. Each expert ranked the sixteen samples of wine, with rank "1" denoti the best and "16" the worst. The final outcome for a treatment- level combination is the average rank for that particular wine over all the experts, which we shall treat as a continuous outcome. Descriptions of the levels for these factors follow in the table below. The data for this experiment are contained in the file HW 9 Question 4.csv, as well as below Level Factor A: Pinot Noir Clone B: Oak Type C: Age of Barrel D: Yeast/skin contact E: Stems F: Barrel Toast G: Whole Cluster H: Fermentation Temperature Pommard Wadenswil Allier Old Troncais ew Champagne Montrachet None Light None All Medium 10% High Factor Run A BCDEFG H Outcome 9.6 31- +1- +1 +12.6 9.2 9.0 6 +11 +-1 -+ 15.0 -1 +15.0 8 +1 1-1 +115.2 +1 2.2 10 +1-1 +1 +1-1 +1- 7.0 8.8 12 +1 - --+1 13-1-1 +1 +1--1 +1 +1 4.6 2.4 19.2 15 oint) (a) What is the formal name for this design? ints) (b) Provide a set of generators that define this design, and describe how the design matrix is constructed on the basis of these generators. ints) (c What is the defining contrast subgroup for this experiment? Why is it important? ints) (d) How many independent aliasing relations exist in this design? How many words are in any given aliasing relation? ints) (e) State the factorial effects aliased with ME(A), and those aliased with INT (A, B), in this experiment. Explain the reasoning you used to identify the aliased factorial effects. ints) (f) A main effect or two-factor interaction is clear if none of its aliases are main effects or two-factor interactions. A main effect or two-factor interaction is strongly clear if none of its aliases are main effects, two-factor interactions, or three-factor interactions. Which main effects and two-factor interactions are clear in this experiment? Which are strongly clear? ints) (g) Provide the estimates of all the main effects and two-factor interactions as obtained by fitting the corresponding linear regression model (excluding higher-order interactions) to this data. Are there any ambiguities with respect to these estimates? ints) (h) Construct a half-Normal plot to screen for the active factorial effects. Are there any ambiguities in your final conclusions on active effects? Why or why not?

Answer 1

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