Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Two
Two
-Way ANOVA Example
-Way ANOVA Example
= 170.53 -
= 170.53 -
162.6006 = 7.9294
162.6006 = 7.92945.0139
(4.1
(4.12 + 3.9
2
+ 3.9
2
2
+ 4.3
+ 4.3
2
2
+…+ 2.32 + 2.518
+…+ 2.3
2
+ 2.518
2
2
)
)
-
-
18
18
(54.1)
(54.1)2
2
SS
SS
Total
Total
=
=
= 167.6144 -
= 167.6144 -
162.6006 = 5.0139
162.6006 = 5.01392.1811
SS
SS
(A)
(A)
=
=
(54.1)
(54.1)2
2
9
9
(31.8+ 15.6
(31.8
2
2
+22.3+ 17.8
+22.3
2
2
)
)
-
-
= 167.7817 -
= 167.7817 -
162.6006 = 2.1811
162.6006 = 2.1811
SS
SS
(B)
(B)
=
=
18
18
(54.1)
(54.1)2
2
6
6
(20.7
(20.7
2
2
+ 15.62
2
+ 17.82
2
)
)
-
-
Use the Data to complete these
Use the Data to complete these
calculations:
calculations:
= 169.93 -
= 169.93 -
-
162.6006 -
162.6006 -
-
5.0139 -
5.0139 -
-
2.1811 = .1344
2.1811 = .1344
.1344
SS
SS
(AB)
(AB)
=
=
18
18
(54.1)
(54.1)2
2
3
3
(12.3
(12.3
2
2
+ 9.22
+ 9.2
2
+ … 7.52)
+ … 7.50.1344
2
)
-
-
-
-
SSA
SSA
-
-
SSB
SSB
SSE = Total SS -
SSE = Total SS -
SSA -
SSA -
SSB -
SSB -
SS(AB)
SS(AB)
= 7.9294 -
= 7.9294 -
-
5.0139 -
5.0139 -
-
2.1811 -
2.1811 -
-
.1344 = .6000
.1344 = .6000
.6000
MS
MS
(A)
(A)
=
=
= 5.0139
= 5.0139
1
12
5.0139
5.0139
MS
MS
(AB)
(AB)
=
=
= 0.0672
= 0.0672
22
0.1344
MSE =
MSE =
= 0.0500
= 0.0500
12
12
0.6000
0.6000
MS
MS
(B)
(B)
=
=
= 1.0906
= 1.0906
2
2.1811
2.1811
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