Has to deal with experimental design and fractional factorials
STAT/ME 424 Homework
Due Dec 15 in lecture
1. Split a 25 factorial into four blocks of eight, confounding BCD and ACE with
block e?ects. Write out the factor-level combinations that go into each block.
2. Suppose that we divide a 28 factorial into 16 blocks of size 16 using ABCF,
ABDE, ACDE, and BCDH as de?ning contrasts. Find all the confounded
3. Individuals perceive odors at di?erent intensities. We have a procedure that
allows us to determine the concentration of a solution at which an individual
?rst senses the odor (the threshold concentration). We would like to determine
how the threshold concentrations vary over sixteen solutions. The thresholddetermining procedure is time consuming and any individual judge can only
be used to ?nd threshold concentrations for four solutions.
Each solution is a combination of ?ve compounds in various ratios. The sixteen
solutions are formed by manipulating four factors, each at two levels. Factor
A is the ratio of the concentration of compound 1 to the concentration of
compound 5. Factor B is the ratio of the concentration of compound 2 to the
concentration of compound 5, and so on.
We have eight judges. Two judges are assigned at random to each of the solution sets [(1), bc, abd, acd], [a, abc, bd, cd], [ab, ac, d, bcd], and [b, c, ad, abcd]. The
threshold concentrations are normalized by dividing by a reference concentration. The results are given below. 1 Judge
46 3 a
(1) 56034 a
61 (a) Analyze the data to determine how the factors a?ect the threshold concentration.
(b) Re-analyze them after taking logs. Does it matter whether you take common logs (base 10) or natural logs (base e)?
(c) What de?ciencies can you ?nd in the design? 2
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