Two-level factorial designs are highly effective for discovering active factors and interactions in a process, and are optimal for fitting linear models by simply comparing low vs high factor settings. Super-charge these classic designs by adding center points!
(Read to the end for a bonus video clip!)
There is an underlying assumption that the straight-line model also fits the interior of the design space, but there is no actual check on this assumption unless center points (the mid-level) are added to the design. Figure 1 illustrates how the addition of center points helps you detect non-linearity in the middle of the experimental space.
A center point is located at the exact mid-point of all factor settings. The example in Figure 2 shows a cookie baking experiment where the center point is replicated four times at the mid-point of 10 minutes and 350 degrees.
Multiple center points (replicates) should be randomized throughout the other experimental conditions to get an adequate assessment of whether the actual values measured at this point match what is predicted by the linear model. This is called a test for curvature. If the curvature test is significant, this is considered evidence that a quadratic or higher order model is required to model the relationship between the factors and the response. If the curvature test is not significant, then it is okay to assume that the linear model fits in the middle of the design space.
In Design-Expert® software, version 11, the curvature test is placed in front of the ANOVA when you have included center points in the design. This immediately shows you if the model is significant, and if the curvature is significant. As illustrated by the screen shot below (Figure 3), advice is provided to guide your next steps.
New to DX11, is the “Remove Curvature Term” button. If curvature is significant and you click on this button, then the regression modeling is done by using all the data, including the center points. Because the actual center points are not sitting in the middle of the design space, it is highly likely that the resulting model will be poorly fit and the lack of fit statistic will be significant. Then, click on “Add Curvature Term” to put the curvature effect back into the model, thus accounting for the information in the middle of the design space.
Ultimately, if curvature is significant, the recommendation is to augment the design to a response surface design to better model the relationship between the factors and the response. If curvature is NOT significant, then proceeding with the analysis is acceptable.
Bonus: Check out Mark’s 1-minute video on this topic: MiniTip 2 - Center points in factorials
Stat-Ease has moved approximately 1 mile north up to Broadway Place West. We are located on the top floor (foreground of photo). Our building is just off Hwy 36 and Industrial Blvd., east of downtown Minneapolis. Our new postal address is:
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Stat-Ease, Inc. and Ritme, scientific solutions hosted the 7th European DOE User Meeting & Workshop in Paris, France this past June. The DOE User Meeting was held at Le CNAM (the National Conservatory of Arts and Crafts) in the heart of Paris, close to the Louvre and Notre Dame. All agreed that this bi-annual event proved to be both informative and fun! The dinner cruise on the Seine was a highlight of the conference for all with gorgeous views of Paris landmarks and absolutely perfect weather. Vive la France!
Stat-Ease, Inc. and Ritme, scientific solutions invite you to attend the 7th European DOE User Meeting & Workshop in Paris, France this June 6–8. The DOE User Meeting will be held at Le CNAM (the National Conservatory of Arts and Crafts) in the heart of Paris, close to the Louvre and Notre Dame. This bi-annual event is always a favorite with attendees—both informative and fun! Besides the interesting presentations and learning opportunities, at this year's event in Paris you will have the opportunity to go on a dinner cruise on the River Seine in an all-glass boat, taking in the sights and sounds of this beautiful city!
The conference will include a pre-conference workshop on June 6, followed by the 2-day user meeting on June 7–8 with talks by DOE Experts, as well as practical case study applications by industry practitioners. We will explore the latest design of experiments (DOE) techniques, and demonstrate new features in Design-Expert software, version 11. In addition, you will have the opportunity to get help from DOE consultants on your own particular applications. Our expert trainers are offering a pre-meeting workshop on June 6th. Sign up for Practical DOE “Tricks of the Trade” and learn advanced DOE skills that you can take home and apply. This is your chance to network, increase your DOE knowledge, learn from others' successes and challenges—all while visiting the City of Lights!
You won't want to miss this fun and educational conference in Paris. For more details and to register for the 2-day meeting and/or workshop click here. We hope to see you in Paris!
Stat-Ease is collaborating with Dr. Pelton to help users who achieve experimental success better communicate their results. Enjoy this article on improving how you say what you say!
In Act 1, Scene 1 of Shakespeare’s tragedy King Lear, Lear asks his three daughters to proclaim their affection for him which the first two, Goneril and Regan, do with genuine warmth, but the third, Cordelia, does not. She rather coldly says that she loves her Majesty according only to her bond, no more nor less. He’s taken somewhat aback by her callous comment and responds by saying “How, how Cordelia! Mend your speech a little, lest it mar your fortunes.”
Shakespearean actors worth their salt know full well that it’s not only the meaning of the words they speak but the way they speak them that makes what they say worth listening to. They are keenly aware of how to use articulation, modulation, tempo, sound and pronunciation to affect their speech. They are elocutionists who, to paraphrase one dictionary’s definition, are masters in the art of speaking effectively in public.
Here are three key steps to improving—or mending—your speech so you, too, can speak more effectively. Once you’ve read them and practiced the suggested exercises, you’ll be well on your way to becoming a more polished speaker and, who knows, even a proficient enough master to go on stage and play Goneril, Regan, Cordelia or Lear.
First: Variety above all else. You never want your voice to sound colorless, dull, passive or lifeless, so to give it character and make it interesting to listen to, change speeds, expand its range and play with dynamics. Which would you rather see, a river placidly and monotonously rolling along without anything in it to grab and hold your interest or one that’s alive with activities that catch your eye and make you want to stop and pay attention? The same with the voice and variety.
Also, pause, pause and pause yet again. You never want to run phrases together so that you prevent audiences from understanding, appreciating or enjoying what you’re saying. Silence is, indeed, golden so, to quote the great American raconteur Will Rogers, “never miss a good chance to shut up.” Actors and storytellers vary their voices and use silence to keep their audiences engaged and involved. Listen to your favorite actor or actress reciting a poem or reading a novel and you’ll hear what I mean. You’ll certainly be taken in by how they use their voices and pauses to hold your interest. Better yet, record yourself reading, say, A. E. Houseman’s short poem “When I was one and twenty” from “A Shropshire Lad” and listen to what you sound like when you play it back. Did you vary speed, range and dynamics and use pauses to make the poem come alive and be worth listening to, or did you merely go through the motions and read it without vocal inflection or pausing so it came across as boring, bland and, in a word, blah. Hopefully, the former.
When I was one-and-twenty
I heard a wise man say,
‘Give crowns and pounds and guineas
But not your heart away;
Give pearls away and rubies
But keep you fancy free.’
But I was one-and-twenty,
No use to talk to me.
When I was one-and-twenty
I heard him say again,
‘The heart out of the bosom
Was never given in vain;
‘Tis paid with sighs a plenty
And sold for endless rue.’
And I am two-and-twenty,
And oh, ‘tis true, ‘tis true.
You’ll find that, as you practice varying your voice and pausing, you, too, will turn into an actor or storyteller who’s more than adept at using variety and silence to persuade, influence, motivate, entertain or educate the people you’re talking to. So, vary away and shush.
Second: Enunciate, enunciate, enunciate. English is a hard, percussive language and, to speak it well, consonants need to be sharp and incisive. Many speakers of English, both native and foreign, don’t do this enough and, as a result, listeners all too often fail to understand what’s being said because speakers don’t pronounce their “b”s, “t”s, “v”s, “l”s, “m”s, “p”s or “d”s clearly, cleanly and consistently. So ask yourself which consonants you don’t articulate well and work on them. Try the following tongue twisters and see if they’ll help. As you go through them, notice how many consonants you miss—quite a few, I’ll wager.
Try them again making sure to enunciate the next consonant as emphatically as the one before and you’ll notice a marked improvement.
So, enunciate sharply and consistently and you’ll be better off for it.
Third: Handle with care. For your voice to be the expressive, compelling, engaging and appealing instrument you want it to be, it needs more than its fair share of TLC.
It is extremely fragile, though paradoxically quite strong, and can become damaged much more easily than people think it can without proper care. So, to speak well:
Also, avoid as much as possible:
To paraphrase W. H. Auden, “all (you) have is a voice,” so the more you take care of it and use it wisely, the more it will be able to do what you ask it to.
The British actress Dame Penelope Keith once said that when she went to school everyone had elocution lessons, not to sound posh but so they could be understood. Understanding, of course, is at the heart of any communication so it goes without saying that the more effectively and expertly you use variety, silence and diction to speak and the more you take care of what the composer Richard Strauss calls “the most beautiful instrument in the world (and the most difficult to play)”, the greater the impact of what you say will have on those listening to you. In short, just remember that what you say will only be as good as how you say it.
Dr. David Pelton has been a professional communicator for over 45 years and has taught courses in communication and communication-related subjects for a number of national and international training/development organizations including PetroSkills, Energy Delta Institute (The Netherlands), The Learning Tree (Malaysia), Integrative Learning & Consulting, Ltd. (Singapore), and the Oxford Management Centre (UK/UAE). He is currently President of Pelton Communications, LLC and holds degrees from Cornell University, The New England Conservatory of Music, and the University of Cincinnati. He has performed for, and spoken to, audiences in the United States, Central and Western Europe, Armenia, Azerbaijan, Russia, The Ukraine, Africa, The Middle East, and Southeast Asia. He has also taught at major US colleges and universities and has done voice over work and been an active seminar/workshop trainer/facilitator for businesses and organizations in California, Colorado, Illinois, Louisiana, Massachusetts, New York, Rhode Island, Texas, Virginia and in Angola, Canada, Australia, England, Germany, Holland, Ireland, Kazakhstan, Wales, the Czech and Slovak Republics, Benin, and Nigeria. Today he is a member of numerous training institutes and societies and enjoys a national and international reputation as a communications consultant, lecturer, trainer, and coach. He can be reached at email@example.com.