Applied statistics in agricultural, biological, and environmental sciences

Authors: Yeater, Kathleen; VILLAMIL, MARIA - University Of Illinois

Submitted to: Soil Science Society of America Special Publication Book Chapter
Publication Type: Book / Chapter
Publication Acceptance Date: 12/3/2015
Publication Date: 9/28/2017
Citation: Yeater, K.M., Villamil, M.B. 2017. Applied statistics in agricultural, biological, and environmental sciences. Soil Science Society of America Special Publication Book Chapter. P. 371 - 400. https://doi.org/10.2134/appliedstatistics.2015.0083.
DOI: https://doi.org/10.2134/appliedstatistics.2015.0083

Interpretive Summary: Agronomic research often involves measurement and collection of multiple response variables in an effort to understand the more complex nature of the system being studied. Multivariate statistical methods encompass the simultaneous analysis of all random variables measured on each experimental or sampling unit. Many agronomic research systems studied are, by their very nature, multivariate; however, most analyses reported are univariate (analysis of one response at a time). The objective of this chapter is to use a hands-on approach to familiarize the researcher with a set of applications of multivariate methods and techniques for the agronomic sciences: principal components analysis, multiple regression, and discriminant analysis. We use an agronomic data set, a subset of the data collected for the “Yield Challenge” program, established by the Illinois Soybean Association in collaboration with researchers from the University of Illinois in 2010. We provide the reader with a field guide to serve as a taxonomical key, a list of relevant references for each technique, a road map to our work, as well as R code to follow as we explore the data to assess quality and suitability for multivariate analyses. We also provide SAS code. The chapter illustrates how multivariate methods can capture the concept of variability to better understand complex systems. Important considerations along with advantages and disadvantages of each multivariate tool and their corresponding research questions are examined.

Technical Abstract: Agronomic research often involves measurement and collection of multiple response variables in an effort to understand the more complex nature of the system being studied. Multivariate statistical methods encompass the simultaneous analysis of all random variables measured on each experimental or sampling unit. Many agronomic research systems studied are, by their very nature, multivariate; however, most analyses reported are univariate (analysis of one response at a time). The objective of this chapter is to use a hands-on approach to familiarize the researcher with a set of applications of multivariate methods and techniques for the agronomic sciences: principal components analysis, multiple regression, and discriminant analysis. We use an agronomic data set, a subset of the data collected for the “Yield Challenge” program, established by the Illinois Soybean Association in collaboration with researchers from the University of Illinois in 2010. We provide the reader with a field guide to serve as a taxonomical key, a list of relevant references for each technique, a road map to our work, as well as R code to follow as we explore the data to assess quality and suitability for multivariate analyses. We also provide SAS code. The chapter illustrates how multivariate methods can capture the concept of variability to better understand complex systems. Important considerations along with advantages and disadvantages of each multivariate tool and their corresponding research questions are examined.