Exam 1 Review
Chapter 1
Probability: a measure of how many likely an event is to occur
o Prob = 1, event will happen
o Prob =0, will not happen
Population: all individuals who are of interest to a r
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5.6
Checking the Equal Variance Assumption
113
2
2
ratio of the largest of the v treatment variance estimates to the smallest, smax /smin , does
not exceed three. The rule of thumb is suggested by sim
112
Chapter 5
Checking Model Assumptions
zit
T
3
2
b
b
b
b
1
0
-1
-2
b
b
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b
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b
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-3
b
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b
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bb
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Figure 5.6
E
Megaphone-shaped
110
Chapter 5
Checking Model Assumptions
zit
T
3
2
b
1
0
b
b b
b
-1
-2
b
b
b
b
b
b
b
b
b
b
b
-3
Figure 5.4
E
Residual plot for the
battery experiment
5
10
15
Run Order
the plot were to exhibit a stron
5.6
Checking the Equal Variance Assumption
111
2
If an analysis is conducted under the assumptions of model (3.3.1) when, in fact, the
error variables are dependent, the true signicance levels of hypo
5.5
109
Checking Independence of the Error Terms
zit
T
3
2
1
0
-1
-2
Figure 5.3
Residual plot after
data correction for the
battery experiment
b
b
b
b
b
b
b
b
b
b
b
b
b
b
b
-3
E
1
2
3
4
Battery type
v
5.3
Checking the Fit of the Model
107
residuals for treatment 2 seems a little larger than the spread for the other three treatments.
This could be interpreted as a sign of unequal variances of the er
108
Chapter 5
Checking Model Assumptions
zit
T
3
2
1
0
-1
b
b
b
-2
Figure 5.2
Original residual plot
for the battery
experiment
b
b
b
b
b
b
b
b
bb
b
b
-3
1
2
E
3
4
Battery type
and +2, and approximate
104
Chapter 5
Checking Model Assumptions
the adequacy of the model can be checked. Even if a pilot experiment has been used to
help select the model, it is still important to check that the chosen mod
5
Checking Model Assumptions
5.1 Introduction
5.2 Strategy for Checking Model Assumptions
5.3 Checking the Fit of the Model
5.4 Checking for Outliers
5.5 Checking Independence of the Error Terms
5.6 C
643
Exercises
7. Consider the following mixed model:
+ i + Bj + Ck + m + (B)ij + ()im
Yij kmt
i
+ (B)j m + (C)km + (B)ij m + ij kmt ,
1, . . . , a, j 1, . . . , b, k 1, . . . , c,
m
1, . . . , d, t
1
639
Exercises
Table 17.15
SAS analysis of variance for the ice cream experiment
The SAS System
General Linear Models Procedure
Dependent Variable: MELTTIME
Sum of
Mean
Source
DF
Squares
Square F Value
638
Chapter 17
Random Effects and Variance Components
Plot of Z*ORDER.
Figure 17.6
Plot of the
standardized residuals
against order of
observation for the ice
cream experiment
The SAS System
Legend: A
636
Chapter 17
Table 17.13
Random Effects and Variance Components
SAS program for the temperature experiment
DATA TEMPR;
INPUT THERM SITE SUBJ TIME;
LINES;
1 1 1 62.16
1 2 1 61.53
: : :
:
3 2 4 304.58
17.10
Using SAS Software
635
The SAS System
Plot of AVCONT*NSCORE. Symbol is value of BALE.
Figure 17.5
Normal probability
plot of the
standardized
treatment averages for
the clean wool
experiment
2 +
17.10
Table 17.14
637
Using SAS Software
SAS analysis of variance for the temperature experiment
The SAS System
General Linear Models Procedure
Source
SUBJ
THERM
SITE
THERM*SITE
SITE*SUBJ
Type III Exp
632
Chapter 17
Random Effects and Variance Components
However, for illustration purposes, we ask whether the average time taken for these three
digital thermometers to register is the same whether use
634
Chapter 17
Random Effects and Variance Components
The SAS System
Plot of Z*PRED. Symbol is value of BALE.
Figure 17.4
Residuals versus
predicted values for
the clean wool
experiment, excluding
the