Nested Factorial Design 1
Factor A (MACHINE) : 3 Machine (A, B, C) fixed
Factor B (SPINDLE) : 2 Spindle for each machine (1, 2) fixed
Var (COMPNT) : 4 Components from each spindle random
Obs MACHINE SPINDLE COMPNT
1 A 1 12
2 A 1 9
3 A 1 11
4 A 1 12
5 A 2 8
6 A 2 9
7 A 2 10
8 A 2 8
9 B 1 14
10 B 1 15
11 B 1 13
12 B 1 14
13 B 2 12
14 B 2 10
15 B 2 11
16 B 2 13
17 C 1 14
18 C 1 10
19 C 1 12
20 C 1 11
21 C 2 16
22 C 2 15
23 C 2 15
24 C 2 14
Nested Factorial Design 2
Factor A (MACHINE) : 3 Machine (A, B, C) fixed
Factor B (SPINDLE) : 2 Spindle for each machine (1, 2) fixed
Var (COMPNT) : 4 Components from each spindle random
-------------------------------------------------------------------------------
| MACHINE |
|-----------------------------------------------------------------------------|
| A | B | C |
|-------------------------+-------------------------+-------------------------|
| SPINDLE | SPINDLE | SPINDLE |
|-------------------------+-------------------------+-------------------------|
| 1 | 2 | 1 | 2 | 1 | 2 |
|------------+------------+------------+------------+------------+------------|
|COMPONENT (4|COMPONENT (4|COMPONENT (4|COMPONENT (4|COMPONENT (4|COMPONENT (4|
|REPLICATES) |REPLICATES) |REPLICATES) |REPLICATES) |REPLICATES) |REPLICATES) |
|------------+------------+------------+------------+------------+------------|
| Y(IJ) | Y(IJ) | Y(IJ) | Y(IJ) | Y(IJ) | Y(IJ) |
|------------+------------+------------+------------+------------+------------|
| 44.00| 35.00| 56.00| 46.00| 47.00| 60.00|
-------------------------------------------------------------------------------
Nested Factorial Design 3
Factor A (MACHINE) : 3 Machine (A, B, C) fixed
Factor B (SPINDLE) : 2 Spindle for each machine (1, 2) fixed
Var (COMPNT) : 4 Components from each spindle random
The GLM Procedure
Class Level Information
Class Levels Values
MACHINE 3 A B C
SPINDLE 2 1 2
Number of observations 24
Nested Factorial Design 4
Factor A (MACHINE) : 3 Machine (A, B, C) fixed
Factor B (SPINDLE) : 2 Spindle for each machine (1, 2) fixed
Var (COMPNT) : 4 Components from each spindle random
The GLM Procedure
Dependent Variable: COMPNT
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 5 99.5000000 19.9000000 13.52 <.0001
Error 18 26.5000000 1.4722222
Corrected Total 23 126.0000000
R-Square Coeff Var Root MSE COMPNT Mean
0.789683 10.11126 1.213352 12.00000
Source DF Type I SS Mean Square F Value Pr > F
MACHINE 2 55.75000000 27.87500000 18.93 <.0001
SPINDLE(MACHINE) 3 43.75000000 14.58333333 9.91 0.0004
Source DF Type III SS Mean Square F Value Pr > F
MACHINE 2 55.75000000 27.87500000 18.93 <.0001
SPINDLE(MACHINE) 3 43.75000000 14.58333333 9.91 0.0004
Nested Factorial Design 5
Factor A (MACHINE) : 3 Machine (A, B, C) fixed
Factor B (SPINDLE) : 2 Spindle for each machine (1, 2) fixed
Var (COMPNT) : 4 Components from each spindle random
Plot of RESID*YHAT. Legend: A = 1 obs, B = 2 obs, etc.
RESID |
|
2.25 + A
|
2.00 +
|
1.75 +
|
1.50 + A
|
1.25 + A
|
1.00 + B A A
|
0.75 +
|
0.50 + A
|
0.25 + A A
|
0.00 + A B B
|
-0.25 +
|
-0.50 + A
|
-0.75 + B A
|
-1.00 + A A
|
-1.25 +
|
-1.50 + A
|
-1.75 + A
|
-2.00 + A
|
--+---------+---------+---------+---------+---------+---------+---------+-
8.75 9.75 10.75 11.75 12.75 13.75 14.75 15.75
YHAT
Nested Factorial Design 6
Factor A (MACHINE) : 3 Machine (A, B, C) fixed
Factor B (SPINDLE) : 2 Spindle for each machine (1, 2) fixed
Var (COMPNT) : 4 Components from each spindle random
Plot of NSCORE*RESID. Legend: A = 1 obs, B = 2 obs, etc.
|
|
2.0 +
| A
|
|
|
1.5 + A
|
|
R | A
a |
n 1.0 + A
k |
|
f | C
o |
r 0.5 + A
|
V | B
a |
r | B
i 0.0 +
a |
b | C
l |
e | A
-0.5 +
R | C
E |
S |
I | A
D -1.0 + A
|
| A
|
|
-1.5 + A
|
|
|
|A
-2.0 +
|
-+-------------+-------------+-------------+-------------+-------------+-
-2 -1 0 1 2 3
RESID