Minitab Output for Question Two
Figure 1: Boxplot of T3
Boxplot of T3
240
220
200
180
T3
160
140
120
100
80
60
60gBran
80gBran
fasting
treatment
laying mash
premolt
Output 1: Test for Equal Variances: T3 versus treatment
Bartlett's Test (Normal Distribution)
Test statistic = 6.73, p-value = 0.151
Levene's Test (Any Continuous Distribution)
Test statistic = 1.71, p-value = 0.188
Output 2: One-way ANOVA: T3 versus treatment
Source
treatment
Error
Total
S = 12.42
DF
4
20
24
Level
60gBran
80gBran
fasting
laying mash
premolt
SS
48355
3086
51440
MS
12089
154
R-Sq = 94.00%
N
5
5
5
5
5
Mean
206.16
110.69
112.85
88.63
86.37
Pooled StDev = 12.42
F
78.35
P
0.000
R-Sq(adj) = 92.80%
StDev
19.84
8.45
11.99
4.96
11.76
Individual 95% CIs For Mean Based on
Pooled StDev
-+---------+---------+---------+-------(--*-)
(--*--)
(--*--)
(--*--)
(--*-)
-+---------+---------+---------+-------80
120
160
200
Output 3: Grouping Information Using Dunnett Method
Level
premolt (control)
60gBran
fasting
80gBran
laying mash
N
5
5
5
5
5
Mean
86.37
206.16
112.85
110.69
88.63
Grouping
A
A
Means not labeled with letter A are significantly different from control level
mean.
Dunnett's comparisons with a control
Family error rate = 0.05
Individual error rate = 0.0153
Critical value = 2.65
Control = level (premolt) of treatment
Intervals for treatment mean minus control mean
Level
60gBran
80gBran
fasting
laying mash
Lower
98.96
3.49
5.65
-18.57
Center
119.78
24.32
26.48
2.26
Upper
140.61
45.15
47.30
23.08
-----+---------+---------+---------+---(----*----)
(----*----)
(-----*----)
(-----*----)
-----+---------+---------+---------+---0
40
80
120
Output 4: Hsu's MCB (Multiple Comparisons with the Best)
Family error rate = 0.05
Critical value = 2.30
Intervals for level mean minus largest of other level means
Level
60gBran
80gBran
fasting
laying mash
premolt
Lower
0.00
-113.57
-111.41
-135.63
-137.89
Center
93.30
-95.46
-93.30
-117.53
-119.78
Upper
111.41
0.00
0.00
0.00
0.00
Level
60gBran
80gBran
fasting
laying mash
premolt
+---------+---------+---------+--------(------------*--)
(-*-------------)
(--*------------)
(-*----------------)
(--*----------------)
+---------+---------+---------+---------140
-70
0
70
Output 5: Grouping Information Using Tukey Method
treatment
60gBran
fasting
80gBran
laying mash
premolt
N
5
5
5
5
5
Mean
206.16
112.85
110.69
88.63
86.37
Grouping
A
B
B C
C D
D
Means that do not share a letter are significantly different.
Tukey 95% Simultaneous Confidence Intervals
All Pairwise Comparisons among Levels of treatment
Individual confidence level = 99.28%
treatment = 60gBran subtracted from:
treatment
80gBran
fasting
laying mash
premolt
Lower
-118.96
-116.80
-141.02
-143.28
Center
-95.46
-93.30
-117.53
-119.78
Upper
-71.96
-69.81
-94.03
-96.28
---------+---------+---------+---------+
(----*----)
(---*----)
(---*----)
(----*----)
---------+---------+---------+---------+
-100
-50
0
50
treatment = 80gBran subtracted from:
treatment
fasting
laying mash
premolt
Lower
-21.34
-45.56
-47.82
Center
2.16
-22.06
-24.32
Upper
25.66
1.43
-0.82
---------+---------+---------+---------+
(---*----)
(----*---)
(----*----)
---------+---------+---------+---------+
-100
-50
0
50
treatment = fasting subtracted from:
treatment
laying mash
premolt
Lower
-47.72
-49.98
Center
-24.22
-26.48
Upper
-0.72
-2.98
---------+---------+---------+---------+
(----*----)
(----*---)
---------+---------+---------+---------+
-100
-50
0
50
treatment = laying mash subtracted from:
treatment
premolt
Lower
-25.75
Center
-2.26
Upper
21.24
---------+---------+---------+---------+
(----*---)
---------+---------+---------+---------+
-100
-50
0
50
Output 6: Grouping Information Using Fisher Method
treatment
60gBran
fasting
80gBran
laying mash
premolt
N
5
5
5
5
5
Mean
206.16
112.85
110.69
88.63
86.37
Grouping
A
B
B
C
C
Means that do not share a letter are significantly different.
Fisher 95% Individual Confidence Intervals
All Pairwise Comparisons among Levels of treatment
Simultaneous confidence level = 73.57%
treatment = 60gBran subtracted from:
treatment
80gBran
fasting
laying mash
premolt
Lower
-111.85
-109.69
-133.91
-136.17
Center
-95.46
-93.30
-117.53
-119.78
Upper
-79.07
-76.92
-101.14
-103.39
treatment
80gBran
fasting
laying mash
premolt
-------+---------+---------+---------+-(--*--)
(--*---)
(--*---)
(--*--)
-------+---------+---------+---------+--100
-50
0
50
treatment = 80gBran subtracted from:
treatment
fasting
laying mash
premolt
Lower
-14.23
-38.45
-40.71
Center
2.16
-22.06
-24.32
Upper
18.55
-5.68
-7.93
-------+---------+---------+---------+-(--*---)
(---*--)
(--*--)
-------+---------+---------+---------+--100
-50
0
50
treatment = fasting subtracted from:
treatment
laying mash
premolt
Lower
-40.61
-42.87
Center
-24.22
-26.48
Upper
-7.83
-10.09
-------+---------+---------+---------+-(--*--)
(---*--)
-------+---------+---------+---------+--100
-50
0
50
treatment = laying mash subtracted from:
treatment
premolt
Lower
-18.64
Center
-2.26
Upper
14.13
-------+---------+---------+---------+-(---*--)
-------+---------+---------+---------+--100
-50
0
50
Figure 2: Residual Plots for T3
Residual Plots for T3
Normal Probability Plot
Versus Fits
99
20
Residual
Percent
90
50
10
1
0
-20
-30
-15
0
Residual
15
30
100
125
150
Fitted Value
Histogram
200
Versus Order
6.0
20
4.5
Residual
Frequency
175
3.0
1.5
0
-20
0.0
-30
-20
-10
0
Residual
10
20
2
4
6
8 10 12 14 16 18 20 22 24
Observation Order
Figure 3: Normality Tests
Probability Plot of RESI1
Normal
99
Mean
StDev
N
AD
P-Value
95
90
Percent
80
70
60
50
40
30
20
10
5
1
-30
-20
-10
0
RESI1
10
20
30
-5.68434E-16
11.34
25
0.209
0.845