The Foundations of Statistics: A Simulation-based Approach

Statistics and hypothesis testing are routinely used in areas that are traditionally not mathematically intensive (such as linguistics). In such fields, when faced with experimental data in any form, many students and researchers tend to rely on commercial packages to carry out statistical data anal [...]
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Statistics and hypothesis testing are routinely used in areas that are traditionally not mathematically intensive (such as linguistics). In such fields, when faced with experimental data in any form, many students and researchers tend to rely on commercial packages to carry out statistical data analysis, often without acquiring much understanding of the logic of the statistics they rely on. As a consequence, results are often misinterpreted, and users are rarely able to flexibly apply techniques relevant to their own research -- they use whatever they happen to have learned from their advisors, and if a slightly new data analysis situation arises, they are unable to use a different method. A simple solution is to teach the fundamental ideas of statistical hypothesis testing without using too much mathematics. This book provides a non-mathematical, simulation-based introduction to basic statistical concepts, and encourages readers to try out the simulations themselves using the source code and data provided (the freely available programming language R is used throughout). Since the exercises provided in the text almost always require the use of previously introduced programming constructs, diligent students will acquire basic programming abilities as a "side effect," helping to give them the confidence necessary for carrying out more sophisticated analyses. The book is intended for advanced undergraduate and graduate classes in any discipline, although the focus is on linguistics and cognitive science. It is designed for self-instruction; however, the book has also regularly been used in undergraduate and graduate courses taught at the University of Potsdam, Germany. TOC:1. Getting Started.- 2. Randomness and Probability.- 3. The Sampling Distribution of the Sample Means.- 4. Power.- 5. Analysis of variance (NOVA).- 6. Bivariate Statistics and Linear Models.- 7. An Introduction to Linear Mixed Models. A. Random Variables.- Index.- References.