STATISTICS 402B
Spring 2016
Homework Set#7
1. Construct an experimental plan (1 rep only) for a 24 factorial (with factors A, B, C, and D) in four blocks
of four runs using ABD and ACD as block generators. (Must show work).
2. Consider a 27 factorial experiment to be carried out in incomplete blocks. The available block size is such
that, to obtain the experimental plan, 4 effects have to be selected for confounding in each replicate (i.e.,
4 block generators have to be used for confounding with blocks)
(a) What is the block size?
(b) What is the number of blocks per each replicate?
(c) What is the total number of effects that will be confounded with blocks in each rep?
(d) Assuming that the factors are denoted by A, B, C, D, E, F, and G, give an example of 4 effects
that you would use for confounding (i.e., 4 block generators) so that no main effects and 2-factor
interactions will be confounded (You are not required to construct the experimental plan).
(e) List all effects that will be confounded with blocks in the design proposed in part (d).
Hint: Use the table listing suggested block generators shown in the notes or the text.
3. In a 26 factorial experiment with factors A, B, C, D, E, and F, to be run in blocks of size 16, the experimenter
prefers to use a design with balanced confounding. Assuming that enough resources are available for doing
at least 5 replicates, explain how to construct a design for this experiment, indicating effects that will be
confounded in each replication. (Experimental plans for each replication is not required to be shown). Key
out an Anova table (showing SV, df, and percent information columns only) for the design you selected.
4. A 23 factorial experiment (factors A, B, and C) was carried out in blocks of size 4 and 5 replications were
obtained. The response is the variable Yield. The data are shown next page and available in the JMP
table homework7-4.jmp. Use JMP to provide answers to the following questions:
(a) Find the effect confounded in each replication.
(b) Provide a table of estimates of the factorial effects with their standard errors.
(c) Construct an analysis of variance table that inccludes F statistics and p-values. Add a column that
indicates relative percentage of information used in estmating each of the partially confounded effects.
(d) Interpret the results of this analysis. First, determine the effects that are significant. Then quantitatively explain the effect of each significant factor on the mean responses.
Hint: Set all factors A, B, and C as continuous variables except Rep and Block. Build a full factorial
model and add the terms Rep and Block(Rep). Note carefully that the values in the parameter estimates
table (both estimates and standard errors) must be multiplied by 2 to obtain the corresponding effects and
their standard errors. The analysis of variance table is exactly as it appears in the output from JMP.
1
Block 1
Treatment
Observation
a
8
b
9
c
8
abc
10
Block 2
Treatment
Observation
Treatment
Observation
(1)
5
(1)
4
ab
11
b
6
ac
8
ac
7
bc
6
abc
8
Treatment
Observation
Treatment
Observation
ab
7
(1)
6
bc
8
ab
11
a
5
abc
9
c
4
c
6
Treatment
Observation
Treatment
Observation
a
4
(1)
5
b
6
bc
7
ac
5
ac
8
bc
5
ab
12
Treatment
Observation
Treatment
Observation
a
7
a
3
abc
10
bc
4
b
8
abc
7
c
7
(1)
4
Treatment
Observation
ab
6
ac
9
b
8
c
7
Rep 1
Block 1
Rep 2
Block 2
Block 1
Rep 3
Block 2
Block 1
Rep 4
Block 2
Block 1
Rep 5
Block 2
Note: Need to present written answers to each part, with calculation shown for parts that you are required to do
hand computation. Use the JMP output to obtain numbers for answering other parts. Attach edited JMP output
when you use the JMP output to extract numbers as part of the analysis. The JMP data file homework7-4.jmp
is available to download.
Due Friday, April 22nd, 2016 (turn-in at the beginning of class)
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