# Experimental methods in agriculture

*Update: v. 1.1 (2023-12-06), compil. 2023-12-13*

# Introduction

This is the website for the book “Experimental methods in agriculture”, where we deal with the organisation of experiments and data analyses in agriculture and, more generally, in biology. Experiments are the key element to scientific progress and they need to be designed in a way that reliable data is produced. Once this fundamental requirement has been fulfilled, statistics can be used to summarise and explore the results, making a clear distinction between ‘signal’ and ‘noise’ and, hence, reaching appropriate conclusions.

In this book, we will try to give some essential information to support the adoption of good research practices, with particular reference to field experiments, which are used to compare, e.g., innovative genotypes, agronomic practices, herbicides and other weed control methods. We firmly believe that the advancement of cropping techniques should always be based on the evidence provided by scientifically sound experiments.

We will follow a ‘learn-by-doing’ approach, making use of several examples and case studies, while keeping theory and maths at a minimum level; indeed, we are talking to agronomists and biologists and not to statisticians! However, we will not totally remove theory: we think that being able to do some simple hand-calculations is the best way to master the process of data-analysis.

This website is (and will always be) free to use, and is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. It is written in RMarkdown with the ‘bookdown’ package and it is rebuilt every now and then, to incorporate corrections and updates. This is necessary, as R is a rapidly evolving language.

## Aims

This book is not written aiming at completeness, but it is finely tuned for a 6 ECTS introductory course in biometry, for master or PhD students. It is mainly aimed at building solid foundations for starting a job in the research field and, eventually, to be able to tackle more advanced statistical material.

## How this book is organised

In the first two Chapters we will deal with the experimental design: we need to be able to distinguish good from bad experiments. One key aspect is that our experimental results are only a sample from a universe of possible results and we can never be totally sure that such a sample fully reflects the characteristics of the whole universe. Hence, uncertainty is an unavoidable component of science, which we need to tackle by ensuring that the experimental methods are as reliable as possible.

In Chapter 3 we will show how we can describe the experimental results, based on some simple stats, such as the mean, median, chi square value and Pearson correlation coefficient. In chapter 4 we will introduce some simple models, which we can use to describe the results of our experiments. Of course, the observed data come as the result of deterministic and stochastic processes and, therefore, we will also describe some stochastic models, with particular reference to the Gaussian Density function.

In Chapters 5 and 6 we will talk about statistical inference and Formal Hypothesis Testing. We will describe the basic concepts of confidence intervals, P-levels and error types and we will introduce t-tests and chi-square tests.

From Chapter 7 to Chapter 12 we will talk about the ANOVA, that is one of the most widely used techniques of data analysis. We will show one-way and two-ways ANOVA models and we will also introduce more complex designs, such as the split-plot and strip-plot. Chapter 13 and 14 will be devoted to describe, respectively, linear and nonlinear regression models. In the Chapters from 7 to 14, we will always start from a motivating example, so that the readers can have an idea of the experimental situation, before diving into the details. In the final chapter 15, we will provide exercises for all book chapters, which should help the readers to practice with what they have learned, while reading the book.

## Statistical software

In this book, we will work through all the examples by using the R statistical software, together with the RStudio environment. We selected such software for a number of reasons: first of all we like it very much and we think that it is a pleasure to use it, once the initial difficulties have been overcame! Second, it is freeware, which is fundamental for the students. Third, in recent years the software skills of students in master degree or PhD programmes have notably increased and writing small chunks of code is no longer a problem for most of them. Last, but not least, we have seen that some experience with R is a very often required skill when applying for a job. We should acknowledge that R and RStudio are two wonderful pieces of software and we are very much indebted to the whole community who is working to ensure their wide availability and freeware nature.

R is characterised by a modular structure and its basic functionalities can be widely extended by a set of add-in packages. As this is mainly an introductory course, we decided to stick to the main packages, which come with the basic R installation. However, we could not avoid the use of a few very important packages, which we will indicate later on. Of course, it is necessary to state that many of the tasks we perform in this book could be as well (or even better) performed by using additional packages, such as those included in the relatively new ‘tidyverse’ package. We should also mention that this book was built by using the ‘bookdown’ package and it is hosted on the blog ‘www.statforbiology.com’, which is built by using the ‘blogdown’ package. We will not use these two packages during the course, but we should mention that they are really useful.

We will not assume any prior knowledge, and we will start from the very beginning. In order to help the readers, we also provide a very gentle introduction to R as an appendix.