ST512
Quiz 4
SSII-2010
1) I have a 2x2 factorial with factors A and B in a completely randomized
design
a1b1
30
Treatment means
a1b2
a2b1
24
10
a2b2
16
Each of these is a mean of 10 observations.
The error mean square is MSE=90.
a) The mean
y11 has standard error ______
b) Compute the main effect of factor A _____
______
and its standard error
c) Compute a sum of squares for testing each
of these null hypotheses:
i) H0: There is no effect of A averaged over the levels of B. SSq =
_______
ii)
July 29, 2010
H0: The effect of A is the same at the high level of B as at the
low level.
SSq = _______
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ST512
Quiz 4
SSII-2010
2) An experiment is done to see how long it takes for floor finishes to wear through to
expose the bare wood. The treatments are the 6 combinations of factors W and C. Factor
W is type of wood flooring at two levels P=pine and O=oak. Factor C is the number of
coats of a polyurethane finish applied to the wood. It is at three levels 1, 3, and 5 coats.
One board with each treatment is prepared then these six boards are attached to a
horizontal surface to form a six board “floor”. A machine that simulates wear passes
across this “floor” over and over again until all boards are worn down to the bare wood.
For each board, the experimenter records the pass number Y on which the wood is
exposed.
He does these in sets of six because there is some concern that the pressure exerted by
the machine may vary slightly from run to run. He feels these things may affect wear
from replicate to replicate, but he is certain that these replicate effects do not interact with
the treatments.
The entire process is repeated 4 times in all and these are the totals (of 6 Ys each) for
his 4 replicates:
Block
Total
1
990
2
960
3
1050
4
1200
The corrected total sum of squares for all of his Y values is 21,729.
a) The replicates here are blocks. Would you have known this from the description of the
experiment or did I need to tell you? Briefly explain. You need to recognize a blocked
experiment from the description of the experiment as requested.
b) Compute the block (rep) sum of squares.
c) How many observations (Y values) did the experiment have?
The treatment totals can be laid out in a table. They are
coats
WOOD
1
3
OAK
720
624
PINE
672
600
Totals
1296
1320
5
840
744
1584
Totals
2184
2016
4200
d) Complete the degrees of freedom and sums of squares for this analysis of variance table.
Source
Blocks(reps)
Treatments
Error
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df
Sum of Squares
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ST512
Quiz 4
SSII-2010
e) Break the treatment sum of squares down into sums of squares for wood type, for
coatings and for interaction wood and coating and give the respective degrees of freedom.
Source
Blocks
W (Wood)
C (Coating)
W*C
Error
df
Sum of Square
MS
F
f) Give the F test ___ for testing the null hypothesis that the difference in wear between Oak
and Pine is the same for all levels of Coats.
g) Compute a sum of squares ______ for testing the null hypothesis that the difference in
wear between Oak and Pine is the same with 3 coats as it is with 5 (ignoring what
happens with one coat)
July 29, 2010
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ST512
Quiz 4
SSII-2010
3) Give an example of a 2 by 2 factorial experiment in a randomized complete block design. Present the
layout of one of the blocks. Identify the following,
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
Response,
Blocking factor, explain.
experimental units,
number of repetitions,
factor A
factor B
Error Df, and
(Research) Question of interest, why do you run this
experiment?
4)
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