The Statistical Analysis of Small Data Sets

About this book

We live in the era of big data. However, small data sets are still common for ethical, financial, or practical reasons. Small sample sizes can cause researchers to seek out the most powerful methods to analyse their data, but they may also be wary that some methodologies and assumptions may not be appropriate when samples are small. The book offers advice on the statistical analysis of small data sets for various designs and levels of measurement, helping researchers to analyse such data sets, but also to evaluate and interpret others' analyses.

The book discusses the potential challenges associated with a small sample, as well as the ways in which these challenges can be mitigated. General topics with strong relevance to small sample sizes such as meta-analysis, sequential and adaptive designs, and multiple testing are introduced. While the focus is on hypothesis tests and confidence intervals, Bayesian analyses are also covered. Code written in the statistical software R is presented to carry out the proposed methods, many of which are not limited to use on small data sets, and the book also discusses approaches to computing the power or the necessary sample size, respectively.

Contents

1. General principles
2. Note on permutation and bootstrap tests
3. A single sample of continuous data
4. Comparing continuous data across levels of one or more factors
5. Correlation and regression
6. Binomial data
7. Multinomial data
8. Sequential analysis and adaptive designs
9. Meta-analysis
10. Multiple testing
11. Bayesian analysis

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Biography

Professor Markus Neuhäuser graduated with a doctorate from the Faculty of Mathematics of the Technical University of Munich (Germany). He was then a postdoctoral fellow in Mathematics at universities in Germany, Austria, and Switzerland, among them the Georg-August-University Goettingen (Germany) and the University of Vienna (Austria). He is currently a Professor of Statistics at the Koblenz University of Applied Sciences, Germany. His research interests focus on group and representation theoretic aspects of harmonic analysis with applications in the construction of efficient networks and time-frequency analysis with applications in many disciplines of the natural sciences; among them, the most prominent is signal processing. Other research interests include combinatorics and number theory.

Professor Graeme Ruxton FRSE is a zoologist known for his research into behavioural ecology and evolutionary ecology. Ruxton received his PhD in Statistics and Modelling Science in 1992 from the University of Strathclyde. His studies focus on the evolutionary pressures on aggregation by animals and predator-prey aspects of sensory ecology. He researched visual communication in animals at the University of Glasgow, where he was a professor of theoretical ecology. In 2013 he became a professor at the University of St Andrews, Scotland. Ruxton has published numerous papers on antipredator adaptations, along with contributions to textbooks. In 2012 Ruxton was elected a Fellow of the Royal Society of Edinburgh.