IN THIS ISSUE
Vol. 23, No. 1 - Jan/Feb 2023
Dear Experimenter,

I am happy to share another answer or two from our statistical consulting team to frequently asked questions (FAQs) about design of experiments (DOE), as well as timely alerts for events, publications, and software updates. Check it out! Feel free to get back to me via [email protected] with further questions or comments: I would really appreciate hearing from you!

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

Sincerely,
Mark J. Anderson, PE, CQE
Engineering Consultant, Stat-Ease, Inc.
www.linkedin.com/in/markstat/


PS Quote for the day: The importance of models.
(Page down to the end of this e-zine to enjoy the actual quote.)
BLOGS
StatsMadeEasy Blog
My wry look at all things statistical and/or scientific with an engineering perspective.
Also, see the Stat-Ease blog for tips on making DOE easy. For example, a recent posting provides advice on “Augmenting One-Factor-at-a-Time Data to Build a DOE”. Take a look!
FAQ
How do I explain the y axis on a half-normal plot?

Original question from an Innovation Center Director:
“I attended your webinar on “Graphical Selection of Factorial Effects What’s In It for You”* and greatly appreciated it. I often give quality control workshops for manufacturers and, while the focus is primarily on SPC, I do a very cursory overview of DOE – mostly with the intent to encourage companies to take a more structured approach to experimentation and invest in formal training.

"I use Design-Expert in my demonstrations and can walk people (especially laypeople) through things reasonably well – except for the half-normal plots. I have your book DOE Simplified and it explains the plots well, though I’m still a bit unclear on the y axis.

"For example, as I recall (book isn’t in front of me right now) with 7 effects you simply divide 100% by 7, then take the midpoint of that (7.14) as the probability for your lowest ranked effect and then add 100/7 to get the cumulative probabilities for the remaining 6 effects. That’s straightforward enough. What I could use your help with is understanding the underlying assumption here for these essentially ‘equally spaced’ probability values.  In doing this, are we assuming that, if our effects are a random sample from a (standard?) normal distribution, they will fall roughly on a straight line. Those that violate that assumption are significantly ‘out of line?’ In cases where there are several duplicate values, the ranking doesn’t matter – but then why would a normal distribution be expected? Or is that when we would see some minor deviation from the line even for the trivial effects?

"Again, I’m mostly concerned with understanding this well enough that I can explain it to people with little to no statistical background. I’ve tended to zip past the half-normal plot in my workshops to get to the ANOVA and start talking about p values. Of course, the good students always ask me to back up and explain that plot and why I just went click, click and moved on!”

*See my webinar on graphical selection of factorial effects on the Stat-Ease YouTube channel.

Answer:
You got it: Divide the number of points to be plotted into 100, rank from low-to-high for the x-axis and plot each at the mid-point of their percentile for their y. It’s easier to consider a set of data with 10 numbers. Then each result represents 10% of the entire collection, thus they are plotted at the center of the increasing deciles, e.g., at 5% for the lowest value, then 15% for the next highest, and so on. The equal spacing works because of scaling of the y-axis based on normal probabilities (linear in Z score for full normal). Naturally, real data with duplicate values and all will deviate somewhat from normal, thus the line-up of near-zero effects will never be perfect.

See below for a slide on ‘fishing’ for effects via the half-normal that we present in our Modern DOE for Process Optimization workshop. For the benefit of DOE ‘newbies’, it adds dots on the bottom, draws out the curve and labels the vital few effects (the ‘keepers’—likely to be statistically significant and thus chosen as model terms) versus the “trivial many” effects (thrown into the pool for error estimation).
I advise embracing the half-normal plot as an initial selection tool, followed up with Pareto before diving into the daunting statistics on the analysis of variance (ANOVA). Also, if you then focus on the normal plot of residuals as the first diagnostic, this reinforces the use of these specialized graphs to see at-a-glance what, if anything, stands out.

(Learn more about half-normal plots for factorial-effect selection by enrolling in Modern DOE for Process Optimization.)
SOFTWARE ALERT
New features released for Design-Expert® and Stat-Ease® 360 software! (second notice)

The Stat-Ease development team ushered in a new era with version 22.0.1 of Design-Expert (DX) and Stat-Ease 360 (SE360) software: The beginning of time-based releases per the “release early, release often” approach of the modern software industry. See what’s new in this infographic.

Contact our Sales team now to purchase a license or lay out the path for an upgrade to these leading-edge statistical tools developed by the world-class team of Stat-Ease programmers, statisticians, and engineers.
EVENT ALERT
Do you need a speaker on DOE for a 2023 learning session within your company or professional society at regional, national, or international levels? If so, please get back to me. – Mark
WEBINAR ALERT
Free webinars Sign up now to take advantage
Click here to view the times, descriptions and registration links for all upcoming live webinars. Sign up now to advance your DOE know-how!
WORKSHOP ALERT
Sharpen up on DOE—Enroll before classes fill
You can do no better for quickly advancing your DOE skills than attending a Stat-Ease workshop. Our expert instructors provide you with a lively and extremely informative series of lectures interspersed by valuable hands-on exercises. Enroll early to ensure your spot!
See this web page for the complete schedule of upcoming Stat-Ease courses. To enroll in the workshop that suits you best, click Register on that webpage, or click here to contact us.
 
PS If you lead a group of 6 or more colleagues, save money and customize content via a private workshop. For a quote, please contact us
“Without models data would be only a meaningless stream of numbers.”
 

Erica Thompson, a statistician, a fellow at the London School of Economics, and author of Escape from Model Land: How Mathematical Models Can Lead Us Astray and What We Can Do About It
Stat-Ease, Design-Expert and Statistics Made Easy are registered trademarks of Stat-Ease, Inc.

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