Analyzing a DOE with a Dispersion response and many Reps

---

•  Most designed experiments (DOEs) seek to shift a mean response, but a few aim to minimize the dispersion of a response, using the standard deviation (STD) of replicates at each condition. Obtaining sufficient statistical power is often a challenge; dozens of replicates may be needed to detect a substantial reduction in dispersion.

• In the problem which motivated this example many replicates were feasible.  A two-level factorial DOE studied a highly automated gage for measuring the axial strength of a mass-produced metal object. After 30 replicates per condition had been collected, the question arose whether to calculate one standard deviation estimate per condition (based on 30 raw data), two standard deviation estimates per condition (15 raw data each), three standard deviation estimates (10 each) etc.? 

• A Monte Carlo simulation showed that the best arrangement of the raw data are often one that approximately balances the number of dispersion estimates and the dispersion subgroup size per each condition (e.g., five standard deviation estimates of subgroup size 6) for all but the most severely skewed raw data distributions. 

• This website provides free access to a simulator which may be used by the reader to explore a variety of two-level factorial DOEs, as needed. This enables experimenters in any subject domain to design such DOEs with sufficient power, while making best use of the raw data.

• This Monte Carlo simulator estimates the power to detect a stated difference between standard deviations. The Simulator allows you to investigate 2 to 7 factors from a variety of data distributions including Normal, Beta, Exponential, Gamma, Largest Extreme Value, Logistic, Smallest Extreme Value, and Weibull.

• This is an application designed to work in Minitab versions 20, 21 and above. It uses a custom dialog box to select the simulation parameters and then run a Minitab Macro with the selected parameters.

1. Follow the first video below 

to see how to download and extract files.

2. Follow the Second video to see 

how to run the Minitab Application.

3. Watch the third video to see an example.