Mathematical Sciences: Building Designs for Collecting Better Data and Making Finer Conclusions

我们计划在几个常用的科学研究中确定最佳和有效的统计设计。这些领域包括但不限于主要效应的两水平因子设计和选定的两因素相互作用；分辨率为III及以上的两水平分数因子设计具有（弱）最小像差；比较生物利用度研究的重复测量设计。基于设计不佳的研究收集的数据的推断通常具有误导性，并且可能完全无效。好的科学需要好的数据，而好的数据只能来自统计设计的研究。该提案计划确定和建立统计上有效的设计/单位成本，以便更好地收集数据并做出有效的科学推断。我们的发现将立即应用于包括医学和工程在内的许多科学研究领域。我们计划解决美国FDA和许多美国行业的科学家向我们提出的设计问题。

We plan to identify optimal and efficient statistical designs in several commonly used scientific studies. These areas include, but not limite to, two-level factorial designs for main effects and selected two-factor interactions; resolution III and more two-level fractional factorial designs with (weak) minimum aberration; repeated measurements designs for comparative bioavaliability studies. Inference based on data collected via poorly designed studies is generally misleading and could be invalid altogether. Good science calls for good data and good data can come only through statistically designed studies. This proposal plans to identify and build statistically efficient designs/per unit cost so that better data can be collected and valid scientific inference can be made. Our discoveries will have immediate applications to many areas of scientific studies including medicine and engineering. We plan to solve design problems which have been posed to us by scientists at US FDA, and many US industries.