A Graphical Tool for Detection of Outliers in Completely Randomized, Unreplicated 2k and 2k-P Factorials
Tony Cooper, PhD, Principal Analytical Consultant, SAS
Doug Sanders, Consulting Statistician
Cheryl Hild, Director of Quality, Aegis Sciences
With the increased awareness of statistical methods in industry today, many non-statisticians are implementing statistical studies and conducting statistically designed experiments (DOEs). With this increased use of DOE by non-statisticians in applied settings, there is a need for more graphical methodologies to support both analysis and interpretations of DOE results. In particular, there is a critical need for user-friendly means to investigate outlier effects of noise and active background variables in unreplicated DOEs. This paper presents a profoundly simple, yet effective methodology to identify outliers in unreplicated 2k and 2k-p factorial designs that integrates well-established, confirmatory statistical techniques with a simple graphical, exploratory tool. The best application of the method requires interactive and dynamic use of color codes and markers on graphs. This is particularly easy and powerful in JMP software. As always, industry is looking to find maximum information for the minimum outlay of resources. Many industries are leaning on unreplicated design where pure error terms will not be estimated. Pseudo-error terms can be used to estimate the significance of effects. This methodology extends the investigation to allow the experimenter to assess the consistency of the noise within the experiment. The method has been used extensively, allowing experimenters to interact with their data to avoid misleading analysis and discover additional clues about how their processes are operating.