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STA 8200 — Design of Experiments for Research Workers
Lab 3 – Due Friday, October 1
Example:
As part of the production of a liquid medication, the producer, a large pharmaceutical
company, mixes batches of medication in large vats. To determine the degree to which
their product is consistent from batch to batch, the company takes a random sample of
ﬁve batches from a month’s production. From each batch four samples were obtained and
for each sample, an important characteristic of the medication was measured, yielding
the data below.
Batch
1
2
3
4
5
3.2 2.6 3.4 4.2 1.8
3.8 2.9 3.9 4.4 2.3
3.5 2.8 3.3 4.3 1.9
3.0 2.0 3.1 4.2 2.1
The ﬁle “drug.sas” contains a SAS program for analyzing these data with a oneway
random eﬀects ANOVA model. Copy this program from the public data directory to
your home directory and run the program in SAS.
•
drug.sas illustrates the use of both PROC GLM and PROC MIXED to implement the
oneway random eﬀects ANOVA model. First, we use PROC GLM:
•
To test
H
0
:
σ
2
a
= 0, the hypothesis that there is no batchtobatch variability we use
F
=
MS
A
/MS
E
= 2
.
987
/
0
.
0918 = 32
.
53 (p.2 of the output). Comparing this statistic
to its distribution,
F
(
a

1
,N

a
) =
F
(4
,
15) gives a
p

value of less than 0.0001, so we
reject the null hypothesis and conclude that there is signiﬁcant batchtobatch variability.
•
To estimate the variance components: We estimate the withinbatch variance (the error
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 Fall '08
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