Applications of statistical experimental designs to improve statistical inference in weed management

Abstract

In a balanced design, researchers allocate the same number of units across all treatment groups. It has been believed as a rule of thumb among some researchers in agriculture. Sometimes, an unbalanced design outperforms a balanced design. Given a specific parameter of interest, researchers can design an experiment by unevenly distributing experimental units to increase statistical information about the parameter of interest. An additional way of improving an experiment is an adaptive design (e.g., spending the total sample size in multiple steps). It is helpful to have some knowledge about the parameter of interest to design an experiment. In the initial phase of an experiment, a researcher may spend a portion of the total sample size to learn about the parameter of interest. In the later phase, the remaining portion of the sample size can be distributed in order to gain more information about the parameter of interest. Though such ideas have existed in statistical literature, they have not been applied broadly in agricultural studies. In this article, we used simulations to demonstrate the superiority of the experimental designs over the balanced designs under three practical situations: comparing two groups, studying a dose-response relationship with right-censored data, and studying a synergetic effect of two treatments. The simulations showed that an objective-specific design provides smaller error in parameter estimation and higher statistical power in hypothesis testing when compared to a balanced design. We also conducted an adaptive experimental design applied to a dose-response study with right-censored data to quantify the effect of ethanol on weed control. Retrospective simulations supported the benefit of this adaptive design as well. All researchers face different practical situations, and appropriate experimental designs will help utilize available resources efficiently.

Nonlinear Regression Modelling: A Primer with Applications and Caveats

“…In addition to the nonlinear regression methods and examples provided here, interested readers may wish to more fully explore topics such as further heteroskedastic (variance function) modelling, bioassay and synergy modelling (Lee et al 2007 ; Lynch et al 2016 ; Sims and O’Brien 2011 ; Straetemans et al 2005 ; Tallarida 2000 ; Wheeler et al 2006 ; White et al 2019 ), multivariate, compartmental, and generalized nonlinear models, related experimental design considerations (Kim et al 2021 ; O’Brien et al 2010 , O’Brien and Silcox 2021 ), and additional curvature examples (Seber and Wild 1989 ). Other notable recent application fields include the use of high-throughput dose response methods to evaluate compounds as potential antiviral drugs to treat COVID-19 patients (Chen et al 2022 ) and modelling to assess enzymatic activity in viral proteins comparing SARS-CoV with SARS-CoV-2 (O’Brien et al 2021 ).…”

Cost hierarchies and the pattern of product cost cross-subsidization: Extending a computational model of costing system design

“…Combined with the 200 randomly generated production environments (NUMB_FIRMS) described in Anand et al [ 13 ], we obtained 712,800 observations overall. We conduct this balanced design of our experiment for both the original and replicated models [ 44 ].…”

A comparison of tests for homoscedasticity using simulation and empirical data

“…The difficulty in selecting the appropriate statistical test is even more evident in biological and agricultural experiments that are conducted both in the laboratory and in the field. These experiments often have deviations from the assumptions of normality, homoscedasticity and independence, due to the small and unequal number of samples (Kim et al, 2021), skewed distributions (Webster and Lark, 2019), spatial dependence (Rossoni and Lima, 2019;Yamamotto et al, 2022) the use of untreated controls (Raudonius, 2017) and unbalance designs (Lix et al, 1996;Parra-Frutos, 2013).…”