Building from our successful 2019 analytics conference, co-hosted by Stat-Ease and Camo Analytics, we are once again partnering to bring you a full week of technical skills education! Start with the 2-day Experiment Design Made Easy workshop on March 9-10, focusing on factorial design of experiments (DOE). These highly efficient designs help you discover those key factors and interactions that bring about breakthrough achievements in this new year! Follow this up with the 3-day Multivariate Data Analysis – Level 1 workshop on March 11-13, where you will learn how to use methods such as Principle Components Analysis (PCA) and Partial Least Squares (PLS) to identify important relationships between variables. In both courses, learn to use top-notch graphical visualization to effectively communicate your results!

These courses have something for everyone – you do not need any prior experience to get significant value from them! They are designed for individuals working in R&D, product development, process optimization, and others from a wide variety of industries.

Our highly-experienced instructors will guide attendees through these powerful tools, with a high level of interactivity along the way. They provide hands-on instruction, with all topics illustrated by practical exercises using Design-Expert® and Unscrambler software packages.

Click on the links above for more information about either workshop. Register for either one, or both for additional savings. Early Bird and multi-student discounts may be available. Contact workshops@statease.com if you have questions. We look forward to seeing you!

Don't forget to check out our 8th European DOE Meeting, held in Groningen, Netherlands in 2020.

**European DOE Meeting**

- Co-sponsored by Stat-Ease, Inc. (USA) and Science Plus Group (Netherlands)
- Date: June 18-19, 2020 (Save the Date!)
- Location: Het Kasteel, Groningen, Netherlands
- Theme: “Make the Most from Every Experiment”

Do you have a story to tell? Share your design of experiments (DOE) success with us. We invite you to submit an abstract to speak at the 2020 European DOE Meeting.

Stat-Ease and Science Plus Group are partnering together to host the premier conference on the practical applications of design of experiments. Topics feature using the tools of factorial design, response surface methods, and mixture design to solve business problems.

The 2020 European DOE Meeting is the perfect venue to learn how others are using these statistical techniques to dramatically impact the bottom line. Industries include, but are not limited to: pharmaceutical, medical device, electronics, food science, oil and gas, chemical processes, aerospace, etc. Presentation length: approximately 25 minutes.

The program committee is looking for presentations that:

- Describe real-world problems solved by implementing DOE.
- Illustrate a successful DOE using Design-Expert® software, including what breakthroughs were made and lessons learned.
- Showcase business results achieved using DOE and Design-Expert.
- Inspire others to use DOE.

Speakers (one per presentation) will be given discounted registration rates.

The conference will include a pre-conference short-course, keynote speakers, and some fun evening events.

Abstracts must include:

- Author Name
- Affiliation
- Phone number
- Mailing address
- Email address
- Abstract – limited to 1 page

Submit abstracts (up to 1 page) to the program committee at conference@statease.com

Submission Deadline: February 15, 2020

Disclaimer: I’m not a statistician. Nor do I want you to think that I am. I am a marketing guy (with a few years of biochemistry lab experience) learning the basics of statistics, design of experiments (DOE) in particular. This series of blog posts is meant to be a light-hearted chronicle of my travels in the land of DOE, not be a textbook for statistics. So please, take it as it is meant to be taken. Thanks!

As I learn about design of experiments, it’s natural to start with simple concepts; such as an experiment where one of the inputs is changed to see if the output changes. That seems simple enough.

For example, let’s say you know from historical data that if 100 children brush their teeth with a certain toothpaste for six months, 10 will have cavities. What happens when you change the toothpaste? Does the number with cavities go up, down, or stay the same? That is a simple comparative experiment.

“Well then,” I say, “if you change the toothpaste and 6 months later 9 children have cavities, then that’s an improvement.”

Not so fast, I’m told. I’ve already forgotten about that thing called *variability* that I defined in my last post. Great.

In that first example, where 10 kids got cavities. That result comes from that particular sample of 100 kids. A different sample of 100 kids may produce an outcome of 9, other times it’s 11. There is some variability in there. It’s not 10 every time.

[Note: You can and should remove as much variability as you can. Make sure the children brush their teeth twice a day. Make sure it’s for exactly 2 minutes each time. But there is still going to be some variation in the experiment. Some kids are just more prone to cavities than others.]

How do you know when your observed differences are due to the changes to the inputs, and not from the variation?

It’s called the F-Test.

I’ve seen it written as:

Where:

s = standard deviation

s2 = variance

n = sample size

y = response

ӯ (“y bar”) = average response

In essence, this is the amount of variance for individual observations in the new experiment (multiplied by the number of observations) divided by the total variation in the experiment.

Now that, by itself, does not mean much to me (see disclaimer above!). But I was told to think of it as the ratio of signal to noise. The top part of that equation is the amount of signal you are getting from the new condition; it’s the amount of change you are seeing from the established mean with the change you made (new toothpaste). The bottom part is the total variation you see in all your data. So, the way I’m interpreting this F-Test is (again, see disclaimer above): measuring the amount of change you see versus the amount of change that is naturally there.

If that ratio is equal to 1, more than likely there is no difference between the two. In our example, changing the toothpaste probably makes no difference in the number of cavities.

As the F-value goes up, then we start to see differences that can likely be credited to the new toothpaste. The higher the value of the F-test, the less likely it is that we are seeing that difference by chance and the more likely it is due to the change in the input (toothpaste).

*Trivia*

**Question**: Why is this thing called an F-Test?

**Answer**: It is named after Sir Ronald Fisher. He was a geneticist who developed this test while working on some agricultural experiments. “Gee Greg, what kind of experiments?”. He was looking at how different kinds of manure effected the growth of potatoes. Yup. How “Peculiar Poop Promotes Potato Plants”. At least that would have been my title for the research.

Graduate students are frequently expected to use design of experiments (DOE) in their thesis project, often without much DOE background or support. This results in some classic mistakes.

- Designs that were popular in the 1970’s-1990’s (before computers were widely available) have been replaced with more sophisticated alternatives. A common mistake –
*using a Plackett-Burman (PB) design for either screening purposes, or to gain process understanding for a system that is highly likely to have interactions*. PB designs are badly aliased resolution III, thus any interactions present in the system will cause many of the main effect estimates to be biased. This increases the internal noise of the design and can easily cause misleading and inaccurate results. Better designs for screening are regular two-level factorials at resolution IV or minimum-run (MR) designs. For details on PB, regular and MR designs, read*DOE Simplified*. - Reducing the number of replicated points will likely result in losing important information. A common mistake –
*reducing the number of center points in a response surface design down to one.*The replicated center points provide an estimate of pure error, which is necessary to calculate the lack of fit statistic. Perhaps even more importantly, they reduce the standard error of prediction in the middle of the design space. Eliminating the replication may mean that results in the middle of the design space (where the optimum is likely to be) have more prediction error than results at the edges of the design space! - If you plan to use DOE software to analyze the results, then use the same software at the start to create the design. A common mistake –
*designing the experiment based on traditional engineering practices, rather than on statistical best practices.*The software very likely has recommended defaults that will make a better design that what you can plan on your own. - Plan your experimentation budget to include confirmation runs after the DOE has been run and analyzed. A common mistake –
*assuming that the DOE results will be perfectly correct!*In the real world, a process is not improved unless the results can be proven. It is necessary to return to the process and test the optimum settings to verify the results.

The number one thing to remember is this: Using previous student’s theses as a basis for yours, means that you may be repeating their mistakes and propagating poor practices! Don’t be afraid to forge a new path and showcase your talent for using state-of-the-art statistical designs and best practices.

If you read my previous post, you will remember that design of experiments (DOE) is a systematic method used to find cause and effect. That systematic method includes a lot of (frightening music here!) statistics.

[I’ll be honest here. I was a biology major in college. I was forced to take a statistics course or two. I didn’t really understand why I had to take it. I also didn’t understand what was being taught. I know a lot of others who didn’t understand it as well. But it’s now starting to come into focus.]

Before getting into the concepts of DOE, we must get into the basic concepts of statistics (as they relate to DOE).

Basic Statistical Concepts:

**Variability**

In an experiment or process, you have inputs you control, the output you measure, and uncontrollable factors that influence the process (things like humidity). These uncontrollable factors (along with other things like sampling differences and measurement error) are what lead to variation in your results.

**Mean/Average**

We all pretty much know what this is right? Add up all your scores, divide by the number of scores, and you have the average score.

**Normal distribution**

Also known as a bell curve due to its shape. The peak of the curve is the average, and then it tails off to the left and right.

**Variance**

Variance is a measure of the variability in a system (see above). Let’s say you have a bunch of data points for an experiment. You can find the average of those points (above). For each data point subtract that average (so you see how far away each piece of data is away from the average). Then square that. Why? That way you get rid of the negative numbers; we only want positive numbers. Why? Because the next step is to add them all up, and you want a sum of all the differences without negative numbers getting in the way. Now divide that number by the number of data points you started with. You are essentially taking an average of the squares of the differences from the mean.

That is your variance. Summarized by the following equation:

\(s^2 = \frac{\Sigma(Y_i - \bar{Y})^2}{(n - 1)}\)

In this equation:

**Yi** is a data point**Ȳ** is the average of all the data points**n** is the number of data points

**Standard Deviation**

Take the square root of the variance. The variance is the average of the squares of the differences from the mean. Now you are taking the square root of that number to get back to the original units. One item I just found out: even though standard deviations are in the original units, you can’t add and subtract them. You have to keep it as variance (s2), do your math, then convert back.