ST512
Quiz 3 SSII-2010
1. A poultry scientist was studying various dietary additives to increase the rate at which chickens gain weight.
One of the potential additives was studied by creating a new diet which consisted of a standard basal diet
supplemented with varying amounts of the additive (0, 20, 40, 60, 80, 100). There were sixty chicks available
for the study. Each of the six diets was randomly assigned to ten chicks. At the end of four weeks, the feed
efficiency ratio, feed consumed (gm) to weight gain (gm), was obtained for the sixty chicks. An analysis of
variance table is presented below with the estimated coefficients for the corresponding linear model.
Class Level Information
Class
Levels
Additive
Values
6
0 20 40 60 80 100
Number of Observations Read
Number of Observations Used
60
60
Dependent Variable: FeedEffRatio
Source
DF
Sum of
Squares
Mean Square
F Value
Pr > F
Model
5
66.85993333
13.37198667
440.32
<.0001
Error
6*9=54
1.63990000
0.03036085
Corrected Total
59
R-Square
Coeff Var
Root MSE
FeedEffRatio Mean
0.976060
6.272309
0.174266
2.778333
Parameter
Intercept
Additive
Additive
Additive
Additive
Additive
Additive
Let
68.49983
Estimate
0
20
40
60
80
100
4.790000000
-3.349000000
-2.596000000
-2.418000000
-2.237000000
-1.470000000
0.000000000
B
B
B
B
B
B
B
Standard
Error
t Value
Pr > |t|
0.05510764
0.07793397
0.07793397
0.07793397
0.07793397
0.07793397
.
86.92
-42.97
-33.31
-31.03
-28.70
-18.86
.
<.0001
<.0001
<.0001
<.0001
<.0001
<.0001
.
y 0 , y 20 , y 40 , y 60 , y80 , y100 denote the sample treatment means.
(A) Fill in blanks in above table of Analysis of Variance.
(B) Write the lineal model for this experiment.
(C) Compute, if possible, the t test associated with
y 0 - y100 t=
-42.97 .
Compute y 40 = 2.372 and its standard error = sqrt(0.03036085/10)= 0.0551
(E) Write the predicted value for FeedEffRatio when Additive level is 60.
(D)
yˆ Add 60  4.79  2.237  2.553
July 22, 2010
Page 1
ST512
Quiz 3 SSII-2010
(F) The graph plot of the least squares means is presented next, with leverage and Cook’s D plots
for residual checking and validation of the Anova Assumptions. Please write a few lines with
your findings after inspecting these graphs.
July 22, 2010
Page 2
ST512
Quiz 3 SSII-2010
There is an observations that seems to be fairly influential, with an
standardized residual value of -8 and a Cook’s D value of 0.5, which results
on a residual distribution skewed to the left. It should be important to run
again the analysis without this observation and analyze any change on the
parameter estimated values
2.
I have a completely randomized design with 3 treatments (drug A, B,
and C) and 5 replicates of each. Here are some sums of squares (SSq) and F
tests for some contrasts:
A versus B
SSq = 22.5
F = 4.5
B versus C
SSq = 202.5 F = 40.5
A vs. avg. of B,C
SSq = 187.5 F = ____
C vs. avg. of A,B
SSq = _____
Contrast
A
B
C
SSq
F
A vs B
-1
1
0
22.5
4.5
B vs C
0
-1
1
202.5
40.5
37.5
A vs avg(B, C)
-2
1
1
187.5
367.5
73.5
C vs avg(A, B)
-1
-1
2
(A)
Compute
-
(B)
Fill in blanks
Each contrast have 1 df.
F = (Contrast MS)/MSE
MSE = 22.5/4.5 = 5
A vs B and C vs avg(A, B) are orthogonal
C vs avg(A, B) SS = 390 – 22.5 = 367.5
3.
4.
the treatment sum of squares.
B vs C and A vs (B, C) are orthogonal
Treatment have 3-1= 2 df.
Treatment SS = 202.5 + 187.5 = 390
Give an example of a one-way ANOVA (Completely Randomized design),
indicating:
a.
Response,
b.
treatment factor,
c.
experimental units,
d.
number of repetitions,
e.
Error Df, and
f.
(Research) Question of interest, why do you run this
experiment?
Please comment the following form Cottingham et al. paper
July 22, 2010
Page 3