-----Original Comments-----
From: John Cornell, author of "Experiments with Mixtures"
(available via Stat-Ease e-commerce site for DOE textbooks at http://www.statease.com/prodbook.html).

"I generally look forward to reading the monthly DOE FAQ Alert by Stat-Ease that you e-mail me because they are very informative. The most recent alert, March 2006, however, contained a response to the FAQ (#1) "Why a p-value is not provided for variance from blocks" where you say "Since blocking restricts randomization (by design), it violates the assumption of independence. Thus it wouldn't be proper statistically to perform the F-test." Then you proceed to give an engineering rule of thumb. (See http://www.statease.com/news/faqalert6-03.html.)

As one who spent 37 years as a statistical consultant in an agricultural experiment station, I helped literally hundreds of clients set up and analyze data collected from randomized complete block designs (RCBD’s). In a majority of the cases, the clients were the ones who suggested blocks be used to remove a source of variation that otherwise would be included in and perhaps inflate the magnitude of "error" in the analysis of variance table. I might also add that the more knowledgeable clients would generally ask if it was possible to determine whether or not anything was gained by blocking. That is when I used a formula that allowed me to estimate the relative efficiency of the RCBD compared with that to be expected from a completely random design (CRD). This formula for b blocks and t treatments is

(1) Eff(RCBD to CRD) = [(b-1)MSBlks + b(t-1)MSE]/(bt-1)MSE

where MSBlks and MSE are the block and error mean squares, respectively, in the analysis of variance table for the RCBD. If the degrees of freedom, (b-1)(t-1) for the RCBD error are less than 20, it is important to consider the loss in precision resulting from fewer degrees of freedom with which to estimate the error mean square of the RCBD experiment as compared to the CRD. This is accomplished by multiplying the quantity in (1) by the precision factor

(2) PrFac = {[(b-1)(t-1)+1][t(b-1)+3]}/{[t(b-1)+1][(b-1)(t-1)+3]}

so that the adjusted relative efficiency of the RCBD to the CRD is
(1) times PrFac (2).

It doesn't take a rocket scientist to see from (1) that the efficiency of the RCBD to the CRD increases the more significantly different blocks are (or MSBlks is) since MSBlks lies in the numerator of (1). Should you wish to see a proof of (1), the textbook by Cochran, W. G. and G.M. Cox (1957) "Experimental
Designs," 2nd. Ed., John Wiley & Sons, Inc., New York, Chapter 8, is a good source. I suspect it was just an oversight on Robert O. Kuehl’s part to suggest "There is little interest in formal inferences ... of a computer program," but then he probably never had to provide an answer to the question, "Was anything gained by blocking?" as I had to many times.

I hope this helps to clear up the question, "Mighten I learn something from an F-test of Blocks in the ANOVA of a RCBD?" My answer is "Yes, Indeed." So with this information in mind, why don't you provide a p-value for the client? For the more significantly different blocks are, the greater the gain in setting up the design as a RCBD rather than a CRD.

If you have any questions about the above, please let me know. Once again, keep the DOE FAQ alerts coming for I believe they serve the public nicely.

All the very best,"

John A. Cornell
Professor Emeritus of Statistics, University of Florida

2ND NOTICE: Stat-Ease contract-trainer Carl McAfee will give an invited paper at the National Plastics Exhibition (NPE) on June 19-23 in Chicago. His talk on "Case Studies and Technical Perspectives on TPEs/TSRs: The Paradigm Shift" features Design-Expert and its capabilities as a tool for innovation and positive change. The NPE is one of the largest venues in the country — over 80,000 attendees last year. See http://www.npe.org/ for details.

2ND NOTICE: Stat-Ease Consultant Pat Whitcomb will be one of the featured speakers on "Approaching Product Design Systematically and Strategically" — offered June 23-24 in Orlando before the Annual Meeting and Food Expo of the Institute of Food Technologists (IFT). For information on the preconference class, in which Pat will detail application of screening, full factorial, response surface (RSM) and mixture designs, see http://www.am-fe.ift.org/cms/?pid=1000277.

Click http://www.statease.com/events.html for a list of appearances by Stat-Ease professionals. We hope to see you sometime in the near future!

"Experiment Design Made Easy" will be presented on June 6-8 in San Jose, California. If you work in western USA and need to master the basics of DOE, do not miss this opportunity for a computer-intensive workshop by a Stat-Ease statistical consultant.

(If you are a corporate technical professional, please pass this news on to your business people!) Quickly identify those factors which affect your sales and marketing results. Learn how they interact and apply that knowledge to make breakthrough increases in sales and profits. Attend the one-day "Crash Course on DOE for Sales & Marketing" in Chicago on June 22. See the course description and links to the syllabus and online enrollment at http://www.statease.com/clas_smdoe.html.

Stat-Ease also presents Mixture Design for Optimal Formulations this month — June 13-15 at its Minneapolis training facility. Don't miss this chance to enhance your chances of discovering the ideal recipe that puts your product ahead of the pack.

See http://www.statease.com/clas_pub.html for schedule and site information on all Stat-Ease workshops open to the public. To enroll, click the "register online" link on our web site or call Stat-Ease at 1.612.378.9449. If spots remain available, bring along several colleagues and take advantage of quantity discounts in tuition, or consider bringing in an expert from Stat-Ease to teach a private class at your site. Call us to get a quote.