Chapter 9. Supplemental Text Material
S9.1. Yates's Algorithm for the 3k Design
Computer methods are used almost exclusively for the analysis of factorial and fractional
designs. However, Yates's algorithm can be modified for use in the 3k factorial desig
Chapter 11. Supplemental Text Material
S11.1. The Method of Steepest Ascent
The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder model
k
y 0 i xi
i
1
and we wish to use this model to determine a path leading fro
Chapter 15. Supplemental Text Material
S15.1. The Form of a Transformation
In Section 3.4.3 of the textbook we introduce transformations as a way to stabilize the
variance of a response and to (hopefully) induce approximate normality when inequality
of va
Chapter 6. Supplemental Text Material
S6.1. Factor Effect Estimates are Least Squares Estimates
We have given heuristic or intuitive explanations of how the estimates of the factor
effects are obtained in the textbook. Also, it has been pointed out that i
Chapter 12 Supplemental Text Material
S12.1. The Taguchi Approach to Robust Parameter Design
Throughout this book, we have emphasized the importance of using designed
experiments for product and process improvement. Today, many engineers and scientists
ar
Chapter 7. Supplemental Text Material
S7.1. The Error Term in a Blocked Design
Just as in any randomized complete block design, when we run a replicated factorial
experiment in blocks we are assuming that there is no interaction between treatments and
blo
Chapter 8. Supplemental Text Material
S8.1. Yatess Method for the Analysis of Fractional Factorials
Computer programs are almost always used for the analysis of fractional factorial.
However, we may use Yates's algorithm for the analysis of a 2 k-1 fracti
Chapter 13. Supplemental Text Material
S13.1. Expected Mean Squares for the Random Model
We consider the two-factor random effects balanced ANOVA model
yij i j ( ) ij ijk
R1,22,a
|ij 1 b
S
|k 1,2, n
T
given as Equation (13.15) in the textbook. We list the
Chapter 10. Supplemental Text Material
S10.1. The Covariance Matrix of the Regression Coefficients
In Section 10.3 of the textbook, we show that the least squares estimator of in the linear
regression model y X
( X ) 1 X
X
y
is an unbiased estimator. W
Chapter 14. Supplemental Text Material
S14.1. The Staggered, Nested Design
In Section 14.1.4 we introduced the staggered, nested design as a useful way to prevent
the number of degrees of freedom from building up so rapidly at lower levels of
the design.