Stat 4210
Spring 2011
TakeHome Assignment 2 Solutions
Answer all of the following questions clearly and completely.
While I like to see SAS
code and computer output when it is an important part of the answer, do not turn code or
printout that you do not refer to.
Be sure to perform the usual residual analysis.
Each
part of each question is worth three points and is graded according to the rubric contained
in the syllabus.
This assignment is due on Wednesday, February 23.
1: Do exercise 3.19 on page 69 of the textbook.
Hint
:
Write out the Source of Variation
and degrees of freedom portions of the ANOVA table and consider the precision of
estimates of parameters.
The partial ANOVA table for a 3x3 Latin Square design is
Source
df
Treatment
2
Rows
2
Columns
2
Error
2
Total
8
There are only 2 degrees of freedom that can be used to estimate the residual variance.
Consequently, the estimate will not be very precise.
A solution is to replicate the
experiment to create more degrees of freedom for estimating the residual variance.
2: Do exercise 3.20 on page 69 of the textbook.
Source
df
SS
MS
Fvalue
Pvalue
Rows
5
150
150/5 = 30
30/5 = 6
0.0015
Columns
5
200
200/5 = 40
40/5 = 8
0.0003
Treatments
5
5 x 10 = 50
10
10/5 = 2
0.1225
Error
20
500 – (150+200+50) = 100
100/20 = 5
Total
35
500
In a 6x6 Latin Square, the Rows, Columns and Treatments each have 5 degrees of
freedom.
The total degrees of freedom value is 35 (6x6 – 1).
Consequently, the Error
degrees of freedom value is 20.
Because the Pvalue for the Treatments is 0.1225, do not reject the null hypothesis of no
treatment effect.
In addition, the rather large Fvalues for Rows and Columns indicate
that blocking was useful for both the Row and Column factors.
Given numbers are shown in
bold
.
The other calculations are indicated.
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View Full Document3: Do exercise 3.25 on page 71 of the textbook.
Notes
: 1) In part (a), do not compare
your result with the result of exercise 3.23.
Do use a post hoc test, if appropriate, to
decide which motor oil results in the best mean mileage.
2) To answer part (b) of the
exercise, you do not have to do exercise 3.23.
Just answer whether treating the drivers as
a blocking variable turned out to be a good idea.
a)
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 Spring '11
 Vanbrackle
 residual variance, motor oil

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