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