Topics in the body text of this DOE FAQ Alert are headlined below (the expert ones, if any, delve into statistical details):

PS. Quote for the month: Pinning down mathematicians.

1: FAQ: How do you perform the calculations for interactions?

Original question from a U.S. Marine Corps Test Engineer:
“Mark, I have been working through the online DOE Simplified Launch Pad course* and I have a question in reference to material in slide 3.1-i.  How do you perform the calculations for two-factor interactions (2FIs)?  I see on page 47 of the text that you provide the equation to calculate the main effects, but I can't find explanation on how to calculate the 2FIs.  Can you please provide guidance?”

*(Contact me to see these materials for free.  Then decide whether to pay the modest fee for engaging Stat-Ease Consultants on answering questions, correcting answers to problems and so forth, in return for earning 1 Continuing Education Unit (CEU) for your professional re-certification and/or resume. —Mark)

Answer:
These calculations are detailed in the textbook excerpt posted here.  It turns out that for a two-factor design forming the square shown at the upper left of Fig 3-1, the interaction is simply the contrast of the diagonals, that is, the average of points 1 & 4 minus the average of points 2 & 3.  At three or more factors it gets too hard to explain interactions geometrically—better then to use the matrix in Table 3-4.  Then it's only a matter of contrasting the averages of pluses with averages of minuses in any given effect column.  For example, the BC effect is calculated by subtracting the Avg Minuses [(71+80+81+77)/4] from the Avg Pluses [(74+75+42+32)/4].  If I copied these numbers correctly, it results in the big negative result shown on the bottom of the BC column.

(Learn more about interactions by attending the two-day computer-intensive workshop Experiment Design Made Easy.  Click on the title for a description of this class and link from this page to the course outline and schedule.  Then, if you like, enroll online.)

2: FAQ: Can you use LSD bars across different factors, or should they only be used within the same factor to compare interactions?

Original question from a Senior R&D Associate:
“I am trying to analyze a design on Design-Expert® software and have a question about interpreting the results in the context of the LSD bars.  Can you use the LSD bars across different factors, or should they only be used within the same factor to compare interactions?  Also, are they only used for interaction of two factors, or can the LSD bars be used to analyze differences between main effects?”

Answer from Stat-Ease Consultant Brooks Henderson:
“Least-significant-difference (LSD) bars tell you if there is a difference between two means—in this case, two mean predictions modeled from your experimental data.  So, yes, you can use the LSD bars from factor to factor.  For instance, on the interaction plot shown below, you can see that there isn’t a significant difference between the two power levels (red = high and black = low), when the time is set at the low level of 4 (upper left LSDs on the plot).  That is because the red and black LSDs are overlapping.  However, there is a significant difference between the low and high power when the Time is set at the high level of 6 (right side of the plot) because the LSD bars are not overlapping.

Interaction Plot

The LSD bars help you statistically assess the difference between the predictions—represented by a square or triangle in Design-Expert.  When two factors appear on the same plot as they do for displaying the interaction, for example, the one above, then you can compare the LSD bars.

Also, yes, you can look at them from left-to right to analyze differences between main effects.  For example, the plot above exhibits a significant difference between the low and high level of time when the high power is used (red line).  However, there isn’t a significant difference due to Time at the low power (black line).”

(Learn more about LSD bars by attending the two-day computer-intensive workshop Experiment Design Made Easy.  Click on the title for a description of this class and link from this page to the course outline and schedule.  Then, if you like, enroll online.)

3: Info alert: Primer on “How Much Testing is Enough” plus case studies on applying DOE to measurement validation and coatings development

Along with Stat-Ease Consultant Pat Whitcomb, I authored a primer on “How Much Testing is Enough: How do we right-size tests?” that ITEA Journal published in their March 2014 issue.  The publication features a Design-Expert graph on the cover as you can see here along with an abstract of our article (scroll down).
Ethanol Producer magazine in its June 2014 issue features this detailing of how “Experiment Design Validates Measurement Technology.”

4: Book giveaway: Winners of free DOE and RSM Simplified books

(Sorry, due to the high cost of shipping, this offer applied only to residents of the United States and Canada.)

The May-June DOE FAQ Alert announced a drawing for a free DOE (1 copy) or RSM (5) Simplified that were either slightly used after being exhibited or flawed immaterially to an extent that they could not be sold. The co-authors—Pat Whitcomb and me—signed them.  After a great deal of calculating, the two of us came to the conclusion that one’s odds of winning were nil by not entering this drawing. ; )

Several dozen readers took our advice by simply replying to their e-mailed DOE FAQ Alert by May 26 that they’d be happy to win a book.  Here are the lucky ones:

• DOE Simplified— Manufacturing Engineer Larry McCulloch
• RSM Simplified— Senior Research Scientist Randy Bishop, Ph. D.
• RSM Simplified— Magnetic Separation Consultant Joseph Wernham
• RSM Simplified— Senior Chemist Ramez Boshra, Ph.D.
• RSM Simplified— Pharma and Fine Chemical Consultant Pete Bonk, Ph.D.
• RSM Simplified— Continuous Improvement Project Manager (Coatings) Aaron Osysko

Congratulations to these winners and better luck next time to the rest of you.

P.S. Consider as a companion to the DOE Simplified book our audiovisual (voiced-over Powerpoint presentation) Launch Pad described here.  Watch this for free and then consider whether to pay a modest fee for engaging Stat-Ease Consultants on answering questions, correcting answers to problems and so forth in return for earning 1 CEU.

5: Events alert: Come to talks by Stat-Ease Consultants and stop by our exhibits at conferences in Boston, and Linz, Austria

Consultant Brooks Henderson will moderate a round-table discussion on “Using Split-Plot Designs for Efficient Experimentation” at the Joint Statistical Meetings (JSM) 2014 and he, along with Marketing Director Heidi Hansel Wolfe, will exhibit the new version of Stat-Ease software at Booth 216 during the August 2-7 conference in Boston.  See details on JSM here.

Consultant Pat Whitcomb will give a talk on “Split Plots Pros and Cons” at the European Network for Business and Industrial Statistics (ENBIS) in Linz, Austria, September 22-24—see the meeting site here.  If you make it to ENBIS, please stop by the Stat-Ease table to talk with Pat about our new version 9 of Design-Expert software.

Click here for a list of upcoming appearances by Stat-Ease professionals.  We hope to see you sometime in the near future!

6: Workshop alert: Experiment Design Made Easy and Factorial Split-Plot Designs for Hard-to-Change Factors workshops coming to San Francisco!

All classes listed below will be held at the Stat-Ease training center in Minneapolis unless otherwise noted.  If possible, enroll at least 4 weeks prior to the date so your place can be assured.  Also, take advantage of a $400 discount when you take two complementary workshops that are offered on consecutive days.

• Experiment Design Made Easy (EDME)
  
  • September 29-30, San Jose, CA
• December 9-10*
  
  
• Factorial Split-Plot Designs for Hard-to-Change Factors (FSPD)
  
  • October 1 (half day), San Jose, CA
    
    
• Response Surface Methods for Process Optimization (RSM)
  • December 11-12*

*Take both EDME and RSM in the same week to earn $400 off the combined tuition!

• Mixture Design for Optimal Formulations (MIX)
• November 4-5**
  
  
• Advanced Formulations: Combining Mixture & Process Variables (MIX2)
• November 6-7**

** Take both MIX and MIX2 to earn $400 off the combined tuition!

See this web page for complete schedule and site information on all Stat-Ease workshops open to the public.  To enroll, scroll down to the workshop of your choice and click on it, or call Rachel at 612-746-2038.  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. Once you achieve a critical mass of about 6 students, it becomes very economical to sponsor a private workshop, which is most convenient and effective for your staff.  For a quote, e-mail [email protected].

I hope you learned something from this issue. Address your general questions and comments to me at: [email protected].

Please do not send me requests to subscribe or unsubscribe—follow the instructions at the end of this message. Sincerely,

Mark

Mark J. Anderson, PE, CQE
Principal, Stat-Ease, Inc.
2021 East Hennepin Avenue, Suite 480
Minneapolis, Minnesota 55413 USA

PS. Quote for the month—Pinning down mathematicians:

 
"If you ever hear a mathematician say something ‘exists,’ ask if they can actually find it.”

—Derek Bingham, Simon Fraser University (from Joint Research Conference, June 2014 talk on “Space Filling Experimental Designs Using Lattices”)

Trademarks: Stat-Ease, Design-Ease, Design-Expert and Statistics Made Easy are registered trademarks of Stat-Ease, Inc.

Acknowledgements to contributors:
—Students of Stat-Ease training and users of Stat-Ease software
—Stat-Ease consultants Pat Whitcomb, Shari Kraber, Wayne Adams and Brooks Henderson
—Statistical advisor to Stat-Ease: Dr. Gary Oehlert
—Stat-Ease programmers led by Neal Vaughn
—Heidi Hansel Wolfe, Stat-Ease sales and marketing director, Karen Dulski, and all the remaining staff that provide such supreme support!

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