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Title: Errors in statistical decision making Chapter 2 in Applied Statistics in Agricultural, Biological, and Environmental Sciences

item Garland-Campbell, Kimberly

Submitted to: Book Chapter
Publication Type: Book / Chapter
Publication Acceptance Date: 9/9/2016
Publication Date: N/A
Citation: N/A

Interpretive Summary: In agricultural and environmental research experiments, the data that is collected is subject to uncertainty from variation from environmental and measurement factors. When this data is analyzed, this uncertainty is taken into account and modeled. The resulting distributions are used to predict answers to the research questions. Decisions that are made based on these analyses are subject to error. These errors can be classified as false positives, false negatives, or the wrong direction. This chapter explores the methods that can be used to design experiments and while making sure to take all the error into account. The chapter includes examples, true false questions, and an exercise to further reinforce the concepts discussed in the chapter.

Technical Abstract: Agronomic and Environmental research experiments result in data that are analyzed using statistical methods. These data are unavoidably accompanied by uncertainty. Decisions about hypotheses, based on statistical analyses of these data are therefore subject to error. This error is of three types, Type 1 (alpha) is a false positive, Type 2 (beta) is a false negative and Type 3 (gamma) is directional. Type 1 and Type 2 errors both prevalent but, often, only the Type 1 error is controlled when experiments are designed. Statistical decisions are therefore subject to more error than is usually acknowledged. The goal of this chapter is to explore the consequences of that error and uncertainty in the context of null hypothesis testing and the use of the normal distribution; methods that are usually taught in introductory statistics courses. Concepts to be discussed include effect size, non-central distributions, and power analysis. Two examples are analyzed, one illustrates methods to obtain the minimum average error for an experimental design and the other illustrates the effect of a split plot design and linear field trends on estimates of error variance. The following best practices are recommended: keep experiments simple; determine a relevant effect size for the treatments to be tested prior to conducting the experiment; benchmark against similar experiments; determine a range of suitable ratios of Type 1(alpha) and Type 2 (beta) error; define costs of each variable in the experimental design; determine the optimal error of an experiment under various experimental design scenarios; and conduct a power analysis.