Preface xi The linear algebra middle road. Linear models (regression and ANOVA) are treated using a geometric, vector-based approach. A more common approach at this level is to intro- duce these topics without referring to the underlying linear algebra. Such an approach avoids the problem of students with minimal background in linear algebra but leads to mysterious and unmotivated identities and notions. Here I rely on a small amount of linear algebra that can be quickly re- viewed or learned and is based on geometric intuition and motivation (see Appendix C). This works well in conjunction with R since R is in many ways vector-based and facilitates vector and matrix operations. On the other hand, I avoid using an approach that is too abstract or requires too much background for the typical student in my course. Brief Outline The first four chapters of this book introduce important ideas in statistics (dis- tributions, variability, hypothesis testing, confidence intervals) while developing a mathematical and computational toolkit. I cover this material in a one-semester course. Also, since some of my students only take the first semester, I wanted to be sure that they leave with a sense for statistical practice and have some useful statistical skills even if they do not continue. Interestingly, as a result of designing my course so that stopping halfway makes some sense, I am finding that more of my students are continuing on to the second semester. My sample size is still small, but I hope that the trend continues and would like to think it is due in part because the students are enjoying the course and can see “where it is going”. The last three chapters deal primarily with two important methods for handling more complex statistical models: maximum likelihood and linear models (including regression, ANOVA, and an introduction to generalized linear models). This is not a comprehensive treatment of these topics, of course, but I hope it both provides flexible, usable statistical skills and prepares students for further learning. Chi-squared tests for goodness of fit and for two-way tables using both the Pearson and likelihood ratio test statistics are covered after first generating em- pirical p-values based on simulations. The use of simulations here reinforces the notion of a sampling distribution and allows for a discussion about what makes a good test statistic when multiple test statistics are available. I have also included a brief introduction to Bayesian inference, some examples that use simulations to investigate robustness, a few examples of permutation tests, and a discussion of Bradley-Terry models. The latter topic is one that I cover between Selection Sun- day and the beginning of the NCAA Division I Basketball Tournament each year. An application of the method to the 2009–2010 season is included. Various R functions and methods are described as we go along, and Appendix A provides an introduction to R focusing on the way R is used in the rest of the book. I recommend working through Appendix A simultaneously with the first chapter especially if you are unfamiliar with programming or with R. Some of my students enter the course unfamiliar with the notation for things like sets, functions, and summation, so Appendix B contains a brief tour of the basic
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