A Distribution-Free Multi-Factorial Profiler for Harvesting Information from High-Density Screenings

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Data screening is an indispensable phase in initiating the scientific discovery process. Fractional factorial designs offer quick and economical options for engineering highly-dense structured datasets. Maximum information content is harvested when a selected fractional factorial scheme is driven to saturation while data gathering is suppressed to no replication. A novel multi-factorial profiler is presented that allows screening of saturated-unreplicated designs by decomposing the examined response to its constituent contributions. Partial effects are sliced off systematically from the investigated response to form individual contrasts using simple robust measures. By isolating each time the disturbance attributed solely to a single controlling factor, the Wilcoxon-Mann-Whitney rank stochastics are employed to assign significance. We demonstrate that the proposed profiler possesses its own self-checking mechanism for detecting a potential influence due to fluctuations attributed to the remaining unexplainable error. Main benefits of the method are: 1) easy to grasp, 2) well-explained test-power properties, 3) distribution-free, 4) sparsity-free, 5) calibration-free, 6) simulation-free, 7) easy to implement, and 8) expanded usability to any type and size of multi-factorial screening designs. The method is elucidated with a benchmarked profiling effort for a water filtration process.