Patrick Giuliano, Senior Analytical Technical Support Engineer, JMP (SAS)
Mason Chen, Black Belt Student, Stanford University OHS
Charles Chen, Master Black Belt / Continuous Improvement Expert, Applied Materials
Through JMP 16 outlier and quantile box plots (distribution), together with quantile range outlier and robust fit outlier detection (screening), we present comprehensive strategies to powerfully separate signal from noise in the presence of univariate response(s). We also propose that through practical analysis with the box plot, we can connect the Gauge R&R noise impact with location of the points most adjacent to the upper and lower fences. We use Monte Carlo sampling (random() function and instant columnfFormulas) to produce multiple distribution types (normal, uniform, peaked, bimodal) to validate the impact on the box plot and histogram together to detect normality violation failure modes.
We demonstrate that the box plot is a powerful visualization tool to judge the data distribution, unique to separate skewness from outliers. Graph Builder, one-way, GoF, and nonparametric hypothesis testing show that – since box plot is very weak to detect bimodality, kurtosis, or draw hypothesis test decisions (missing sample size effect) – both the histogram and box plot are needed to visualize normality. Together with descriptive statistics, the most powerful discrimination between different candidate distributions is presented. Finally, we synthesize and demonstrate our learning experience by formulating 17 thought-provoking quiz questions and answers to maximize the utility of the box plot for data-driven problem solving.
