PSTAT 120A: Introduction to Probability
Chapter 5: Continuous Random variables
Pierre-Olivier Goffard
University of California at Santa Barbara
Department of Statistics and Applied Probability
goffard
480
Exercises
Table 14.20
Data for the sugar beet experiment
Block I
Levels of
N, P, K
Yield
211
2575
120
2472
200
2411
002
2403
010
2220
021
2252
101
2295
112
2362
222
2434
Block II
Levels of
N, P, K
478
Exercises
Table 14.17
Correct analysis of variance for the dye experiment
The SAS System
General Linear Models Procedure
Dependent Variable: Y
Source
Model
Error
Corrected Total
Source
BLK
A
B
C
A
14.5
Table 14.12
Design d1 for a 23 experiment confounding F1 F2 G1 and design d2 for a
2
32 experiment confounding G2 H; G2 H 2
Design
d1
Table 14.13
Block
I1
II1
Block
I
I1 II2
II
I1 III2
III
II1 I2
14.4
473
Designing Confounded Asymmetrical Experiments
We can use this idea only when the numbers of levels of all factors are powers of the same
prime number. For all of the other examples mentioned
14.3
14.3
Designing Using Pseudofactors
471
Designing Using Pseudofactors
14.3.1
Confounding in 4p Experiments
A treatment factor F with four levels coded 0, 1, 2, 3 can be represented by two factors
472
Chapter 14
Table 14.8
Confounding in General Factorial Experiments
42 experiment in 4 blocks of 4, confounding three
degrees of freedom (F1 G1 , F1 F2 G2 , F2 G1 G2 ) from FG
Block
I
II
III
IV
14.
470
Chapter 14
Table 14.7
Confounding in General Factorial Experiments
Analysis of variance for the dye experiment
Source of
Variation
Block
A
AL
AQ
B
BL
BQ
C
CL
CQ
AB
AC
BC
Error
Total
Degrees of
Fre
14.2
469
Confounding with Factors at Three Levels
To normalize the contrasts, one would divide AL by
ci2 /(rbc)
2/9 and divide AQ
by
ci2 /(rbc)
6/9.
The sum of squares for testing the hypothesis that
14.2
Confounding with Factors at Three Levels
467
confound either a main effect or a two-factor interaction. However, the three-factor interactions are also thought to be negligible, so one possible c
466
Chapter 14
Confounding in General Factorial Experiments
to be confounded. If the pair (Az1 B z2 P zp ; A2z1 B 2z2 P 2zp ) is chosen for confounding
together with the pair (Ay1 B y2 P yp ; A2y1 B 2
14.2
465
Confounding with Factors at Three Levels
Block I:
Block II:
Block III:
Treatment combinations with L
Treatment combinations with L
Treatment combinations with L
a1 + a2
a1 + a2
a1 + a2
0 (mod
14.2
Table 14.2
Confounding with Factors at Three Levels
463
Groups of treatment combinations
corresponding to orthogonal interaction
contrasts in a 32 experiment
(AB; A2 B 2 )
00
01 02+
10
11+ 12
20+
479
Exercises
(b) Calculate the normalized contrast estimate for Linear A Linear B, using the
method outlined in Section 14.2.4.
(c) Compute the sum of squares for testing the hypothesis that the Line
481
Exercises
8. Consider a 22 32 design confounding AB, (CD 2 ; C 2 D), and (ABCD 2 ; ABC 2 D).
(a) Give the designnamely, list the treatment combinations block by block.
(b) Describe how to randomiz
PSTAT 120A: Introduction to Probability
Chapter 3: Conditional Probability
Pierre-Olivier Goard
University of California at Santa Barbara
Department of Statistics and Applied Probability
[email protected]
Principle of counting
Permutations, arrangements and combinations
PSTAT 120A: Introduction to Probability
Chapter 1: Combinatorics
Pierre-Olivier Goard
University of California at Santa Barbara
Depart
A must have three pivot columns. (See Exercise 30 in Section 1.7, or realize that the equation Ax = 0
has only the trivial solution and so there can be no free variables in the system of equations.) S
15.2
Table 15.8
493
Fractions from Block Designs; Factors with 2 Levels
1
fraction
4
of a 25 experiment and data from the sludge
experiment.
Levels of
A, B, C, D, E
00010
00111
01001
01100
10001
10100
492
Chapter 15
Fractional Factorial Experiments
1
design obtained by confounding ABD, ACE, and BCDE will give a 4 fraction in which
CD is not aliased with main effects.
1
A list of useful 4 fractions
15.2
491
Fractions from Block Designs; Factors with 2 Levels
1
one block for the 4 fraction, specically the block that satises
a1 + a 2 + a 4
1 (mod 2) and a3 + a4 + a5
0 (mod 2).
The treatment combin
490
Chapter 15
Fractional Factorial Experiments
Contrast Estimate
T
0.4
0.2
0.0
b
-0.2
Figure 15.1
Soup experiment:
normal probability
plot of contrast
estimates
b
-0.4
1.8 T
1.4
1.0
b b
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