Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Treatment A
Treatment A
5, 7, 6, 7, 6
5, 7, 6, 7, 6
Treatment B
Treatment B
2, 0, 1, -2, 2
2, 0, 1, -2, 2
Treatment C
Treatment C
1, 0, -2, -3, 0
1, 0, -2, -3, 0
31
31
3
3
-4
-4
5
5
5
5
5
5
Total (
Total (
)
)
n
n
Total
Total
30
30
15
15
SS
SS
Total
Total
= (5MS
= (52 + 72
2
+ 72
2
+ 6² +…+ (-3)² + 0= 68.6
+ 6² +…+ (-3)² + 0= 68.6
2
+…+ (-3)² + 0= 68.6
2
+ 02) -
2
) -
= 162
= 162
15
15
(30)2
(30)2
2
Source
d.f.
SS
MS ~ Variance
Machine
Error
TOTAL
162
162
137.2
137.2
SS
SS
Machine
Machine
=
=
= 137.2
= 137.2
5
5
(31)2
(31)2
2
15
15
(30)2
(30)2
2
5
5
(3)2
(3)2
2
5
5
(-4)
(-4)
-4)
4)2
2
+
+
+-
+-
-
-
24.8
24.8
SSd.f.
SSMSE =
ErrorTotol
Error
= 162 -
= 162 -
137.2 = 24.8
137.2 = 24.8
2
2
d.f.
d.f.
Machine
Machine
= 3 -
= 3 -
-
1 = 2
1 = 2
14
14
d.f.
Totol
= 15 -
= 15 -
-
1 = 14
1 = 14
12
12
d.f.
d.f.
Error
Error
= 14 -
= 14 -
2 = 12
2 = 12
68.6
68.6
MS
machine
machine
=
=
= 68.6
2
2
137.2
137.2
2.067
2.067
MSE =
= 2.067
= 2.067
12
12
24.8
24.8
The Calculated F statistic =
The Calculated F statistic =
2.067
2.067
68.6
68.6
= 33.2
= 33.2
The Critical value for F
The Critical value for F
(
(
= 0.05, 2, 12)
= 0.05, 2, 12)
= 3.89
= 3.89
Since the calculated value for F (33.2) exceeds the critical
Since the calculated value for F (33.2) exceeds the critical
value of F (3.89), the null hypothesis is rejected. There is
value of F (3.89), the null hypothesis is rejected. There is
sufficient evidence that a statistically significant difference
sufficient evidence that a statistically significant difference
exists in the average output of the three machines.
exists in the average output of the three machines.
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