Collaborative research: OPUS: Permutational Biometry: Synthesizing the Analytics of Data Analysis in Ecology and Evolution

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In this project, the investigators will synthesize their work in statistical theory. The analysis of biological data has long been accomplished using standard (parametric) statistical methods. However, these tools lack solutions for many complex questions. As an alternative, resampling of data using computers provides a general procedure that can replace traditional methods in cases where they are insufficient. These new methods have the potential to provide a tool for biologists that is less restrictive than traditional tests. A full-length book will be produced and made freely available providing broad impacts. Web-based tutorials demonstrating all topics in the book will also be provided. Both products will leverage existing software the investigators have developed and distributed freely to the scientific community.By synthesizing 25 years of permutation-based analytics they have developed, the investigators will arrive at an entirely new philosophy for performing data analysis in the biological sciences. This new paradigm results from the union of their methods in four interrelated areas: 1) Resampling of Residuals in a Permutation Procedure (RRPP), 2) permutation-based effect sizes, 3) permutation-based pairwise comparisons, and 4) permutation-based evaluation of independent or correlated datasets. The result will be a biometric perspective that emphasizes both hypothesis testing and biological signal strength determination, where the generation of empirical sampling distributions enables both components simultaneously. The approach is both univariate and multivariate, and can be used to evaluate trends in independent, or correlated observations. When complete the synthesis will provide a comprehensive learning platform, that combines thorough explanation of permutational analytics, and integrates this emerging statistical perspective with hands-on tutorials that utilize existing software for implementation. This advance has the potential to transform how biologists conduct their research, as the RRPP synthetic paradigm provides analytical tools that are capable of addressing hypotheses that parametric procedures cannot.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.