Stat-Ease Blog

Existing data can yield valuable insights for immediate process or product improvement or point you in the right direction for a well-planned experiment. Here’s how to get that “happenstance” data into Stat-Ease software in a few clicks and put its powerful modeling, graphing and optimization tools to good use.

Original question from a pharmaceutics professor:

Answer from Stat-Ease:

Design-Expert® software (DX) provides handy and intuitive import tools to paste in existing data copied to the Windows clipboard, ideally from Excel. Stat-Ease® 360 (SE360) software offers additional capability to read Excel files for direct import. This tool can be accessed from the main screen.

I will now demonstrate importing via pasting data from your clipboard, doable with either DX or SE360.

Begin by copying data on all your inputs—process factors and/or mixture components—and outputs (the responses), including the names and units of measure, to the clipboard.

Next open your Stat-Ease software, click IMPORT DATA and then Paste from Clipboard as shown in Figure 1.

Then, via right clicks on rows and columns, identify or delete them. You will find this process to be very easy and intuitive.

For example, I imported a dataset from the U.S. Bureau of Labor Statistics that James Longley used to test regression software.* Next, as displayed in Figure 2, I began the process of identification by right clicking to the left of row 1 and making it the factor names.

After identifying the second row as units, I right clicked on the first column and set it as a numeric factor as shown in Figure 3.

From there I identified the other factors and the response. When all rows and columns were identified, I pressed Finish.

Stat-Ease software provides many helpful guard rails and niceties throughout the entire process of importing data and helping you model it. For example, if you forget to identify a row or column, the software will pop up an error. Also, it provides special treatment to inputs identified as mixture components—ensuring that they always add to a fixed total. After accomplishing the import, Stat-Ease software sets up the appropriate analysis—factorial, process response surface, mixture or combined mixture-process.

For a video demo of the process to import the Longley data, view my presentation on Evaluating and Exploiting Existing Data (gold or garbage?). As you will see, it is very easy to do. The video shows how Stat-Ease software’s powerful tools can then be deployed to mine the most from your existing data, making it easy to deploy regression tools to derive predictive models, generate compelling 3D and other graphics and search out desirable settings for the factors and/or components.

*“An Appraisal of Least Squares Programs for the Electronic Computer from the Point of View of the User,” Journal of the American Statistical Association, 62 (1967): 819-841.

When your designed experiments succeed a little too well, predicted percentages can creep past 100%, which is great for morale but terrible for credibility. A pharmaceutical research scientist ran into exactly this problem when fitting results for an encapsulation and asked Stat-Ease for a fix. The answer, courtesy of a chemical engineer's hard-won process development experience, involves one clever transformation and a rename button used with purpose.

Original question from a pharmaceutical research scientist:

Answer from Stat-Ease Consultant, Mark Anderson:

I came across this issue many times in my career as a chemical engineer doing process development aimed at maximizing yields. When my designed experiments succeed by pushing them up to near 100%, the confidence intervals on predicted results would range above 100%. This undermined credibility. Fortunately, Stat-Ease software provides a response transformation, called a “logit” (a combination of “logistic” and "digit,” pronounced “loh jit”), that prevents this from happening.

To apply this transformation, via the + key, add a new model for Encaps. Then select Logit and enter 0 and 100 for the lower and upper bounds, respectively.

Then click the Rename button to identify that this new analysis is in the logit scale. If transformations like this prove to be effective (as it did in your case, per your follow-up report), I advise a further renaming to say “**USE THIS**” or something along these lines, thus making it clear which model to apply when doing subsequent numerical optimization.

PS: For details on logit and other transformations, as well as special models, see this Help topic.

Ever run a mixture experiment where every component looks like a win, only to have the trace plot tell a different story? The following FAQ tackles that exact puzzle — why some ingredients can show a “negative” track in a trace plot even when they contribute positively overall. Stat-Ease consultant Mark Anderson breaks down the mixture-model math behind it using a simple sugar-sweetness example.

Original question from a chemist:

Answer from Stat-Ease:

“This is a peculiarity of the mixture models (also known as Scheffé polynomials). I created a similar example on a hypothetical mixture of 3 types of sugar by setting up an equation-only model: R = 1A + 2B + 3C. Then I generated a trace plot showing how the predicted response changes when you increase one component while keeping the ratios of the other components constant.

The plot shows the downward impact of A (sugar S1) on sweetness due to it having the lowest coefficient of the three ingredients. This is relative to the other ingredients, adding more of that specific component does not lower the response on its own. Component B (sugar S2) generates a flat track—it’s impact on sweetness is ‘middling.’ The most impactful ingredient is C (sugar S3), as evidenced by its upward track.

For another example showing the trace plot being put to good use, see the November 2024 blog Perfecting pound cake via mixture design for optimal formulation.

This is part 3 of an adaption from Mark Anderson’s 2023 YouTube webinar, "Do's & Don'ts for Screening Process Factors."

Resolution IV designs that detect two-factor interactions

In our training courses, we teach screening using a 9-factor, 20-run example for an arc-welding experiment. This case deploys a Resolution IV Minimum-Run Screening design. The significant effects are shown below:

This experiment reveals a significant two-factor interaction term (AB). The half-normal plot also indicates significance for both parents of AB—factors A and B. A resolution IV design aliases main effects only with three-factor or higher order effects that rarely occur, thus it is save to conclude in this case that factors A and B do indeed create main effects. But you must remain wary about the AB term. Here’s the catch: with resolution IV designs, two-factor interactions are aliased with other two-factor interactions. As shown in Figure 2, in this case, AB is aliased with eight other two-factor interactions.

The reason AB is listed on the half-normal plot instead of the other options is simply because the list is alphabetical. Perhaps it makes sense to the process experts that AB is indeed the proper choice. Or perhaps you feel confident that because both A and B were correctly identified, the interaction between the two is the most logical choice. But it is possible to have an interaction present even when the main effect terms do not show up as significant. Anyone who has ever encountered our software’s hierarchy warning has seen this phenomenon in action.

The consequence of getting this wrong in a screening design is that you may miss factors that are indeed consequential. For example, in the above list if CH was the correct interaction rather than AB, then you would miss carrying C and H forward from the screening design.

You can use a semifold design to validate the AB alias. This will add 50% more runs but will more confidently ensure the likelihood that you’re not missing something important from your screening effort. Figure 3 shows how to do so with Stat-Ease software.

In the next menu, selecting either A or B to fold on will be best given the goal ofresolving the AB interaction. In this case, a good choice will be J+ Edge Prep at the high level), because this factor at the plus setting generated significantly higher tensile strength for the welds. Figure 4 shows these entries in the semifold dialog box.

Inspecting the resulting alias structure shown in Figure 5, the semifolded design cleanly identifies not only main effects, but all the two-factor interactions involving factor A, including the AB term of interest.

The semifold increased the original 9 factor, 20 run design to 30 runs. Another option would be to use a resolution V design from the start to ensure all two-factor interactions could be estimated clear of any troublesome aliasing, for example, the minimum-run resolution V characterization design with 46 runs. So, for screening, there is a clear efficiency advantage to using resolution IV designs, even if there is an interaction term worthy of investigating further using a semifold augmentation.

For all DOE’s, it is important to evaluate a design for power–the ability of the design to identify factors impacting responses by a selected magnitude. This is mainly driven by the number of runs. For example. If you’re running a seven-factor resolution IV screening design to look for factor effects of 1.5 standard deviations, you will need at least 19 runs to have acceptable power. The standard geometric resolution IV design has only 16 runs and the minimum run screening design has only 14 runs. Both approaches will require adding a few more runs to satisfy the power requirements.

For fractional factorial designs–especially screening designs–it is also important to evaluate the design for aliasing. The lower the resolution, the more consequential the aliasing. The augmentation approaches discussed in the post can be helpful in addressing tricky aliasing issues that could otherwise limit the success of your screening effort.

When things don't go as planned, whether you've inherited a resolution III design or uncovered a suspicious interaction term, augmentation strategies like the foldover and Semifold offer practical paths forward without starting from scratch. Yes, these repairs cost additional runs, but they cost far less than drawing the wrong conclusions and carrying the wrong factors into your next phase of experimentation. A little upfront diligence in design selection, paired with a willingness to augment when the data demands it, is the surest route to a screening effort that sets your entire experimental program up for success.

This is part 2 of an adaption from Mark Anderson’s 2023 YouTube webinar, "Do's & Don'ts for Screening Process Factors."

Salvaging a Resolution III design

The first situation is when you violate the advice in our previous blog post and run a resolution III design for screening. Recall that a key assumption for screening is that you anticipate important factors will present a statistically significant main effect. But with a resolution III design, each main effect is aliased with one or more two-factor interactions. So if there are actually interactions present in the system, some or all of the main effects identified will be incorrect. Remember that screening with a resolution IV design keeps us away from this problem by aliasing main effects only with highly unlikely three-factor interactions.

If you didn’t know better and deployed a resolution III design for screening: no worries, resolve the issue by using a foldover design. This design augmentation doubles the original run count in a way that de-aliases the main effects from two factor interactions. The second block of data reverses every factor level (plus to minus and minus to plus) from the original design.

Let’s look at an 11-factor, resolution III, 16-run design for example. The alias structure is shown in Table 1 (interactions involving three factors or more not shown).

Notice that each main effect is aliased with multiple two-factor interactions.

By augmenting this bad design with a foldover (see Figure 1), you can de-alias the main effects from the two-factor interactions.

The new runs are put in a second block. This structure removes any shift in response that may occur from when you ran the first experiment, such as an increase or decrease due to differing ambient conditions.

Table 2 shows the new, improved, alias structure.

Note that it took 32 runs to get to the point where it’s confident that the main effects are properly assessed. It would have been far better off to start with a minimum-run screening design for 11 factors, requiring only 24 runs (including 2 runs to bolster it against outliers). However, in our scenario, this would be wishful thinking, since we cannot go back in time. Consider the foldover in this case to be a design repair to achieve the resolution IV needed to safely screen factors down to a vital few for further investigation.

Foldover augmentation also works to de-alias Plackett-Burman designs. Handy!