Stat-Ease Blog

We’ve designed Design-Expert® software to be flexible and user-friendly. For those of you who haven’t had a chance to fully explore its capabilities, here are some tips to help you navigate the software and find options that are useful for you:

• The all-new Design Wizard asks you a series of questions, and then directs you to a starting design! You may want to modify things from here, but it’s a great starting point.
• To access guidance specific to the screen that you are on (Screen Tips), click on the light bulb on the tool bar. The question mark brings up more general help.
• Use the Tab key when entering factor information. The tab will flow left to right across the factor information for the first factor, and then move to the second factor. No mouse is needed!
• You can change factor names or levels by right-clicking on either a factor or response column header and choosing Edit Info. This is a convenient way of editing design information rather than rebuilding the design.
• Insert or Delete a response (or factor) by right-clicking on a response or factor column header.
• On the Design Layout view (spreadsheet) right-click on the gray square to the left of any row to access features like Inserting/Deleting/Duplicating rows, or changing the Row Status to Verification/Highlight/Ignore.
• On a graph, you can change axis settings, number formats, graph features, colors, and more, by right-clicking on the graph and choosing Graph Preferences. On a contour plot, you can set the increments of the contour lines to specific values.

Has a low R² ever disappointed you during the analysis of your experimental results? Is this really the kiss of death? Is all lost? Let’s examine R² as it relates to factorial design of experiments (DOE) and find out.

R² measures are calculated on the basis of the change in the response (Δy) relative to the total variation of the response (Δy + σ)over the range of the independent factor:

Let’s look at an example. Response y is dependent on factor x in a linear fashion:

We run a DOE using levels x1 and x2 in Figure 1 (below) to estimate beta1 (β1). Having the independent factor levels far apart generates a large signal-to-noise ratio (Δ12) and it is relatively easy to estimate β1. Because the signal (Δy) is large relative to the noise (σ), R² approaches one.

What if we had run a DOE using levels x3 and x4 in figure 1 to estimate β1? Having the independent factor levels closer together generates a smaller signal-to-noise ratio (Δ34) and it is more difficult to estimate β1. We can overcome this difficulty by running more replicates of the experiments. If enough replicates are run, β1 can be estimated with the same precision as in the first DOE using levels x1 and x2. But, because the signal (Δy) is smaller relative to the noise (σ), R² will be smaller, no matter how many replicates are run!

In factorial design of experiments our goal is to identify the active factors and measure their effects. Experiments can be designed with replication so active factors can be found even in the absence of a huge signal-to-noise ratio. Power allows us to determine how many replicates are needed. The delta (Δ) and sigma (Σ) used in the power calculation also give us an estimate of the expected R² (see the formula above). In many real DOEs we intentionally limit a factor’s range to avoid problems. Success is measured with the ANOVA (analysis of variance) and the t-tests on the model coefficients. A significant p-value indicates an active factor and a reasonable estimate of its effects. A significant p-value, along with a low R², may mean a proper job of designing the experiments, rather than a problem!

R² is an interesting statistic, but not of primary importance in factorial DOE. Don’t be fooled by R²!

The third edition of DOE Simplified: Practical Tools for Effective Experimentation is now available. This comprehensive introductory text is geared towards readers with a minimal statistical background. In it, the authors take a fresh and lively approach to learning the fundamentals of experiment design and analysis. This edition includes a major revision of the software that accompanies the book (via trial download) and sets the stage for introducing experiment designs where the randomization of one or more hard-to-change factors can be restricted. It also includes a new chapter on split plots and adds coverage of a number of recent developments in the design and analysis of experiments.

P.S. There are still some copies of DOE Simplified, 2nd Edition available on clearance if you would like to learn the fundamentals of DOE while saving money.

If you haven't discovered Mark Anderson's Stats Made Easy blog yet, you may enjoy checking it out.  Mark offers a wry look at all things statistical and/or scientific from an engineering perspective. You will find posts on topics as varied as nature, science, sports, politics, and DOE.  His latest post, Conqueror paper dominates in flight test, involves fun with paper airplanes.  Take a look and feel free to share your comments. One is never too old for paper airplanes!