Errata

Errata for Mathews, Design of Experiments with MINITAB
(Changes and additions since 25 April 2009 are in bold font.)

Errata - Textbook

p. 38, In Section 3.2 title, replace R with sigma.
p. 50, In Figure 3.9, reject H0 region in far left tail shouldn't be shaded.
p. 52, In Example 3.9, change two instances of t to z. New text should read "The p value for the test is given by the area under the z distribution to the left of x_bar = 78.2 or z = -0.82:"
p. 54, In Section 3.5.2 title, replace s with sigma.
p. 61, In Example 3.13, put 1/7[ ] around summation inside of square root
p. 61, In Example 3.13, change from 9 to 7 df and change p value from 0.037 to 0.044.
p. 74, In Acceptance Interval for One mean, sigma unknown, mu NE mu0 case, insert minus sign in front of left end of interval, i.e. -t sub alpha/2 < ...
p. 74, In Test Statistic for One variance case, replace x squared with chi squared.
p. 77, Replace z sub pi with z sub p sub i.
p. 81, In Figure 3.28, last test, replace "vs mu = 500" with "vs < 500".
p. 82, 3rd line from top, replace "so again we must conclude that mu NE 500" with "so we must reject Ho: mu = 500 in favor of HA: mu < 500."
p. 109, In Figure 4.6, change axis label from CC(5-1) to CC(2^(5-1)).
p. 111, Omit first sentence of Example 4.7.
p. 128, Misplaced comma. Change "After the experiment design, has been chosen a sample-size calculation ..." to "After the experiment design has been chosen, a sample-size calculation ..."
p. 166, Remove space between (1 - alpha) and 100% on 2nd line before Equation 5.25.
p. 175, In Table 5.5, fill in block numbers: 1, 1, 1, 2, 2, 2, ..., 6, 6, 6.
p. 196, In Example 6.2 change 3-2 = 2 to 3-1 = 2.
p. 201, Change "Notice that the row and column sums add up to zero." to "Notice that each of the rows and columns sums to zero."
p. 212, In last line of solution to Example 6.7, change affect to effect.
p. 218, In Figure 6.5, columns A and B in Data Display are incorrect. Correct values are A={1,1,1,1,2,2,2,2,3,3,3,3} and B={1,1,2,2,1,1,2,2,1,1,2,2}.
p. 236, Equation 7.5, Change equals signs to approximately equals signs and add explanatory footnote. Make same same change in other places. See comments below.
p. 246, In Figure 7.3, Two-Way ANOVA Table With Interaction, replace "Part # Op" with "Part * Op".
p. 258, In Example 7.11, the power should be P = 1 - 0.448 = 0.552.
p. 287, In Eq. 8.26, in the upper (right side) limit of the compound inequality for beta(1), change - sign to + sign.
p. 309, after Eq. 8.49, change t_sub_b2 to t_sub_b_sub_2 in two places.
p. 322, Omit "Stat> " from "Stat> Calc> Calculator".
p. 340, 3rd line from end of solution to Example 8.31, replace b with beta sub 1 in "... a narrower confidence interval for b than ..."
p. 369, Table 9.2, in the first column of p-values only, delete the p-value associated with A (0.022) and move all of the other p-values in this column up one row. The p-value for AC should be 0.222 when you're done. Add the p-value for BC: 0.451.
p. 440, In Figure 11.3d, add "-20B^2" to title.
p. 481, Add "= p" to title.
Back cover, 4th line from bottom of About the Author, change misspelled last name "Matthews" to "Mathews ".

Errata - CD
Example Problem Data/Chapter 05.xls: Values for Example 5.1 are not data - they are a list of the two-factor interactions.
Example Problem Data/Chapter 08.xls: Data for Example 8.29 is missing. Data for Example 8.30 is mislabeled as 8.29.
Example Problem Data/Chapter 10.xls: Data for Example 10.8 is mislabeled as data from Problem 10.5.
Example Problem Data /Chapter 11.xls: Data for Example 11.9 is missing and data for Problem 15 is not required.

Homework Problems, page v (Preface), third paragraph: Delete "With respect to homework problems, " and capitalize the following "t".
Homework Problems, p. 14, Problem 22: Missing reciprocal operation. Change "F_alpha,... = F_1-alpha,..." to "F_alpha,... = 1 / F_1-alpha,..." in two places.
Homework Problems, p. 22, Problem 5.3: There are twelve observations per treatment instead of eight as stated.
Homework Problems, p. 26: Copy Problem 7 into Chapter 7 problems where it's more appropriate.
Homework Problems, p. 48, Problem 10.10: Change the subscript on the 2^(6-1) design from IV to VI.
Homework Problems, p. 56, Problem 11.11: In Answer a), change 3^5 to 3^k.

Classroom Exercises and Labs, p. 15: Missing period in Problem 4. Should read "... until the clay stops flowing. Then measure the ...".

Corrections to Equations for E(F)
A liberty that I took with notation in the book was caught by Rolf Turner. Rolf thought that the issue was serious enough to justify changes in the next printing and after considering his case and the simplicity of the changes he's proposed, I agree with him. For readers with limited theoretical statistics background this issue is subtle and not of consequence.

The issue has to do with expected value calculations for ANOVA F statistics. The first instance of the problem appears in Equation 7.5 on page 236. The problem, which Rolf eloquently describes below, is that under the usual conditions E(F) is only approximately equal to E(MS(A)) / E(MS(epsilon)). For practical purposes, the use of the approximation is justified in this case but to avoid misleading advanced readers it is worth changing the equals signs in the offending equations to approximately equals signs. There are one or more such changes required on the following pages: 236, 237, 238, 241, 242, 253, 256, 257, 259, 260, 261, 262, 263, 267, 268, 270, 343.

Rolf and I negotiated the following explanation for the approximately equals signs which I hope we can include as a footnote on the bottom of page 236 in future printings:

"The expected value of a ratio is never equal to the ratio of the expected values, however, in this instance this operation yields an adequate approximation."

Paul Mathews, 23 August 2005

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E-mail from Rolf Turner:

Hi. I recently purchased a copy of your book (with a view to its possible use in a course on DOE that we offer here). Let me say to start with that I really like the book. It treats important ideas in a clear and comprehensible way, gives practical and useful advice, and has good examples of practically everything.

HOWEVER! I noticed fairly quickly an error that really bugs me. The first place that the error occurs (as far as I can discern; there may be earlier instances that I haven't spotted) is on page 236. You say:

E(F) = E(MS(A)) / E(MS(epsilon)) (7.5)

This is simply NOT TRUE!!! The expected value of a ratio is NEVER (except in trivial cases) equal to the ratio of the expected values. Expected value is a linear function; but ratios are ***not*** linear combinations!

Now you may say that this is not an egregious error, and indeed it is not, at least from certain points of view.

(a) This is the way we "think about" E(F); what is F going to be "like" if the null hypothesis is true? What will F tend to be "like" if the null hypothesis is false?

(b) The assertion is ***approximately*** true; since MS(A) and MS(epsilon) are independent (under the usual assumptions) it is true that:

    E(F) = E(MS(A)) * E(1/MS(epsilon))

And then applying the so-called "delta method" --- i.e. using a first order Taylor expansion --- one can say that:

    E(1/MS(epsilon)) ***approximately*** equals 1/E(MS(epsilon))

This works since E(MS(epsilon)) is not equal to 0. Hence:

    E(F) ***approximately*** equals E(MS(A)) / E(MS(epsilon))

On the other hand, even if the error is not particularly egregious, it is indeed an ERROR and could be misleading and could give the
uninitiated wrong ideas and lead them into making more serious errors.

It seems to me that it would not be difficult to amend the exposition on page 236 along the lines of (a) and (b) above, and then use the notation:

E(F) approximately = E(MS(A)) / E(MS(epsilon))

(using the double wavy line symbol for "approximately =") there and thereafter. You could thereby preserve clarity, conciseness, and usefulness of exposition without sacrificing truth or accuracy.

I hope you will make an adjustment along these lines for the next edition of your book, and that you will include a note about this matter in your on-line errata.

Cheers,

Rolf Turner (rolf@math.unb.ca)