We recommend that, before embarking on this high-level feature tour, you work through the in-depth “Two-Level Factorial” tutorial. That will fill you in on many details that we do not repeat so you can more quickly get the gist of the unique features provided by Design-Expert for design and analysis of two-level factorials done as a split plot.

Very often, experimenters set up two-level factorial designs with the best intentions of running them in random order, but they find that a given factor, such as temperature, cannot be easily changed. In this case, the analysis should be done by the split-plot method.

Split-plot designs originated in the field of agriculture where experimenters applied one treatment to a large area of land, called a “whole-plot,” and other treatments to smaller areas of land within the whole-plot—called “subplots”. For example, the whole-plot treatment might be fertilizer 1 vs. fertilizer 2, with the subplot treatment being seed type 1 through 8 (see picture below).

This example is based on a polymerase chain reaction—a biochemical technology that amplifies DNA for diagnosing hereditary diseases and other purposes. Due to equipment limitations, it is not convenient to fully randomize the treatments, so the biochemists chose a split-plot design. In this case the whole plots are actually plates that are subjected to varying conditions of time and temperature. The subplots fall into the wells within each plate, within which experimenters can randomly apply the remaining factors.

To bypass the design build without having to enter the names of all the factors, go to

**Help, Tutorial Data**and open**PCR.dxpx**. Rebuild via**File, New Design**and clicking**Yes**to “Use previous design info”. Then note the design specifications for this two-level-factorial split plot.Total factors: 9. These includes both the whole-plot (hard-to-change) and subplot (easy-to-change).

Hard-to-change (HTC) factors: 3. These are the three thermocycler (whole-plot) factors.

HTC factors laid out as: Full factorial (the default).

Groups per replicate: 8.

Runs per Group: 32. This specifies a 29-1 factorial design for all 9 factors, which is resolution IX. Note that the box changes green for any design that is Res V or better, meaning you can fit main effects and two-factor interactions (2FI).

Click

**Next**to see aliases (there are none of any consequence) and**Next**again to see the entries for factors. Note here that the HTC factors are labeled lowercase—a, b, and c; while the easy-to-change (ETC) factors are uppercase—E, F, G, H, and J (skipping past letter I due it being reserved as label for model intercept).

Click

**Next**to view the entry for the response and then, accepting the defaults for Signal/Noise ratio,**Next**again to view the Split-Plot Design Power. Note that lowered power for the HTC factors (a, b and c). This occurs due them being put into 8 groups (whole plots), which restricts randomization.

4) Click **Finish** to exit the design-building wizard and produce the
experimental plan (recipe sheet), pressing **OK** on the warning to reset factor
levels. Scrolling down you will see how this 256 run design is split up into 8
whole-plot groups. Then, via **File, New Design**, re-open **PCR.dxpx** to get the
results back.

Now having rebuilt the design and collected the data, continue this feature tour to see Design-Expert’s specialized tools for selecting effects from a two-level-factorial split-plot, as well as the programs statistical analysis, diagnostics and informative displays for assessing the final outcome.

Analysis is the same as for a factorial design in Design-Expert, except for one
key difference: The subplot and whole-plot effects are analyzed separately—each
getting its own half-normal plot. To get started on analyzing the Amplification
response, click the **R1-Amplification** node under the Analysis branch at the
left.

Click the

**Sub-plot Effects**tab, bypassing the transform options (none needed unless diagnostics indicate so later in the analysis process).Select the significant effects (those that stand out to the right) by clicking them as shown below.

Notice how the Pareto chart, at the right in this default side-by-side view [|], updates as you modify the half-normal effect selection.

Click the

**Whole-plot Effects**tab and press**Yes**when asked the question about hierarchy. As shown below, select the significant whole-plot effects not already chosen for hierarchy.

Click on the

**ANOVA (REML)**tab. The restricted maximum likelihood (REML) analysis is necessary to properly identify the significant effects and calculate p-values for split-plot designs. In this case, all the whole-plot and sub-plot terms are significant at the p < 0.05 level.Click on the

**Diagnostics**tab and analyze the diagnostics as you normally would. (For more details refer to the “Two-Level” Factorial tutorial, which goes into far more depth than this high-level feature tour.) There is one possible outlier (outside the red lines), but in a design with 256 runs, that is not unexpected, so leave that run in.The model graphs, numerical optimization and other post-analysis options work as they do for all two-level factorial designs in Design-Expert. Explore the graphs for conditions that maximize the “Amplification” response.

This concludes a quick pass through the two-level factorial tools provided by Design-Expert software for a split-plot experiments. Consider saving your results and then seeing via Numerical Optimization what the program recommends for achieving maximum optimization for the polymerase chain reaction (PCR). It is quite amazing what DOE can do with the proper tools!