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Statistics 500 – Fall 2009
Solutions to Homework 4
1
1.
Diet plans – no SAS
(a)
Source
d.f.
Sum of
Squares
Mean
Square
F
Treatment
3
2272.80
757.60
34.33
Error
20
441.35
22.07
Total
23
2714.15
Note: remember that the total SS = treatment SS + error SS and total d.f. = treatment d.f. +
error d.f.
(b) 4 treatments.
Note: treatment d.f. = r – 1.
(c) There are 24 observations in total.
If all groups have the sample size, there are 6
observations per treatment.
Note: this only works if n’s are the same for all groups.
If the n’s were unequal, the
number observations in each group can not be determined from the ANOVA table.
(d)
8.10
33
.
34
999
.
0
,
20
,
3
=
>
=
F
F
. Therefore, we reject the null hypothesis that all means are
equal.
The pvalue is < 0.001. There is very strong evidence that at least one mean is
different.
2. Fixed or random effects.
(a) Schools are random.
There is no interest in a specific school.
(b) Schools are fixed.
You want to compare school A to each of the other 9 schools.
(c) Schools are random.
There is no interest in specific schools, but the variability among
schools within a curriculum will be an important part of the analysis.
Curriculum is fixed.
You want to estimate differences between specific curriculums.
3.
Bottle filling.
My SAS code, without extra run commands:
data bottle;
infile ‘c:/philip/stat500/data/bottle.txt’;
input fill machine;
/* can ignore other two variables */
proc boxplot;
plot fill*machine;
proc gplot;
/* hi resolution dot plots */
plot fill*machine;
proc
glm
;
class
machine;
model
fill = machine ;
lsmeans
machine /
stderr pdiff cl
;
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View Full DocumentStatistics 500 – Fall 2009
Solutions to Homework 4
2
estimate
'Contrast a'
machine
0.25
0.25

0.5

0.5
0.25
0.25
;
estimate
'Contrast b'
machine
0.5
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 Fall '08
 Staff
 Statistics

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