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).
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.
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!