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2021 | Book

Statistical Design and Analysis of Biological Experiments

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About this book

This richly illustrated book provides an overview of the design and analysis of experiments with a focus on non-clinical experiments in the life sciences, including animal research. It covers the most common aspects of experimental design such as handling multiple treatment factors and improving precision. In addition, it addresses experiments with large numbers of treatment factors and response surface methods for optimizing experimental conditions or biotechnological yields.

The book emphasizes the estimation of effect sizes and the principled use of statistical arguments in the broader scientific context. It gradually transitions from classical analysis of variance to modern linear mixed models, and provides detailed information on power analysis and sample size determination, including ‘portable power’ formulas for making quick approximate calculations. In turn, detailed discussions of several real-life examples illustrate the complexities and aberrations that can arise in practice.

Chiefly intended for students, teachers and researchers in the fields of experimental biology and biomedicine, the book is largely self-contained and starts with the necessary background on basic statistical concepts. The underlying ideas and necessary mathematics are gradually introduced in increasingly complex variants of a single example. Hasse diagrams serve as a powerful method for visualizing and comparing experimental designs and deriving appropriate models for their analysis. Manual calculations are provided for early examples, allowing the reader to follow the analyses in detail. More complex calculations rely on the statistical software R, but are easily transferable to other software.

Though there are few prerequisites for effectively using the book, previous exposure to basic statistical ideas and the software R would be advisable.

Table of Contents

Frontmatter
Chapter 1. Principles of Experimental Design
Abstract
We introduce the statistical design of experiments and put the topic into the larger context of scientific experimentation. We give a non-technical discussion of some key ideas of experimental design, including the role of randomization, replication, and the basic idea of blocking for increasing precision and power. We also take a more high-level view and consider the construct, internal and external validities of an experiment, and the corresponding tools that experimental design offers to achieve them.
Hans-Michael Kaltenbach
Chapter 2. Review of Statistical Concepts
Abstract
We review the basic statistical concepts that we need in later chapters; most of the material is covered in a typical introductory statistics course. We introduce the normal and related distributions, estimators and confidence intervals, and hypothesis testing. We emphasize the role of effect sizes and estimation over dichotomous testing outcomes, and the importance of interpretation of results informed by subject-matter knowledge.
Hans-Michael Kaltenbach
Chapter 3. Planning for Precision and Power
Abstract
We provide an introduction into power analysis based on a two-sample problem with normally distributed errors. We consider the impact of balancing the size of treatment groups, and methods for increasing precision and power by blocking or sub-sampling that do not require increasing the sample size. We then discuss the determination of sample sizes to achieve the desired precision of a difference of means, and the problem of power analysis for testing such a difference based on the normal and the t-distribution. We also provide some practical shorthand formulas for quick approximate sample size calculations.
Hans-Michael Kaltenbach
Chapter 4. Comparing More Than Two Groups: One-Way ANOVA
Abstract
We introduce the analysis of variance framework for decomposing the variation in the data into a part explained by treatments and an unexplained residual part. We introduce several effect size measures and derive the F-test from basic principles. Further, we develop power analysis for the analysis of variance and provide ‘portable power’ methods suitable for quick approximate sample size determination. We also formally introduce Hasse diagrams for visualizing the logical structure of an experiment, and derive the specification of a suitable linear model from the experiment’s diagram. Finally, we briefly remark on the one-way analysis of variance with unbalanced data.
Hans-Michael Kaltenbach
Chapter 5. Comparing Treatment Groups with Linear Contrasts
Abstract
We introduce linear contrasts between treatment group means as a principled way for constructing t-tests and confidence intervals for treatment comparisons. We consider a variety of contrasts, including contrasts for estimating time trends and for finding minimal effective doses. Multiple comparison procedures control the family-wise error rate, and we introduce four commonly used methods by Bonferroni, Tukey, Dunnett, and Scheffé. Finally, we discuss a larger real-life example to demonstrate the use of linear contrasts and highlight the need for careful definition of contrasts to correctly reflect the desired comparisons.
Hans-Michael Kaltenbach
Chapter 6. Multiple Treatment Factors: Factorial Designs
Abstract
We discuss factorial treatment designs with more than one treatment factor and extend the analysis of variance framework to handle these designs. The variation is then decomposed into several contributions for the different treatment factors. A new type of effect is the interaction between factors, and we discuss its interpretation in detail. We consider linear contrasts and power analysis for factorial designs, and provide a more general discussion on the advantages of these designs and strategies for analyzing them. Problems arising in the analysis of variance for unbalanced data are briefly considered.
Hans-Michael Kaltenbach
Chapter 7. Improving Precision and Power: Blocked Designs
Abstract
Grouping experimental units by some property unrelated to the treatments can substantially increase precision and power without increasing the sample size. We discuss designs for such blocking, starting from the randomized complete block design up to different designs with replicated Latin squares. We also consider incomplete block design. We present methods for choosing and evaluating blocking factors and discuss fixed block factors and the interpretation of block-by-treatment interactions. We make extensive use of Hasse diagrams to discuss different variants of blocked designs. We introduce simple linear mixed models as an alternative to analysis of variance, particularly for incomplete block designs.
Hans-Michael Kaltenbach
Chapter 8. Split-Unit Designs
Abstract
In a split-unit design, different treatment factors are randomized on different unit factors: the design has more than one experimental unit. This leads to different precision of estimates and power of tests, but can have advantages when some treatments are more easily changed than others. We discuss the basic split-unit design in detail and introduce several related designs, such as a split-unit blocked on the whole-unit level, simple cross-over designs, and pretest-posttest designs.
Hans-Michael Kaltenbach
Chapter 9. Many Treatment Factors: Fractional Factorial Designs
Abstract
We present fractional factorial designs for multiple treatment factors on two levels, where effects are deliberately confounded to reduce the experiment size. These designs can be defined by one or more generators, which formally describe the confounding. Simple algebraic manipulations of the generators allow derivation of all effect aliases in a design. We discuss using fractional factorials with blocks, and we show how multiple generators can then be used to disentangle confounded effects. Screening experiments are an important application of fractional factorial designs; we also introduce Plackett–Burman designs for this purpose.
Hans-Michael Kaltenbach
Chapter 10. Experimental Optimization with Response Surface Methods
Abstract
Response surface methods provide a principled way of finding experimental conditions that maximize a response. They are based on sequential experimentation where we alternate between locally exploring the changes in response around a given condition, and determining a set of conditions that likely yields increasing response values. We consider central composite designs as a family of flexible experimental designs for exploration and building approximate models of the surface in the vicinity of a given condition. We illustrate these techniques using a real-life example, where we optimize the composition of a growth medium for yeast.
Hans-Michael Kaltenbach
Backmatter
Metadata
Title
Statistical Design and Analysis of Biological Experiments
Author
Hans-Michael Kaltenbach
Copyright Year
2021
Electronic ISBN
978-3-030-69641-2
Print ISBN
978-3-030-69640-5
DOI
https://doi.org/10.1007/978-3-030-69641-2

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