Preface
The thought of writing a textbook in my late 50’s seemed rather strange. Why now? What has yet to be said about statistics that cannot wait to be reiterated by a group of relative unknowns. Why this book? All good questions that I am not sure I can answer right now. What I can answer is that the world does need more, better, more interactive statistics (aka stats) books. The world needs more people who can think critically about data and the world needs more people who can communicate their findings in a clear and concise manner. This book is an attempt to address these needs - with your help. We hope you join us on this journey.
The work here represents an important change in the licensing and distribution of textbooks. Let us provide some context. Some years ago, one of us (PEM) wrote a book with his colleagues on missing data (McKnight et al. 2007). The book was a labor of love that we delivered to the publisher only to find our work was no longer ours to give away. Errors in the code, typos in the text, and other issues were no longer ours to fix. So the book stays in its final, flawed state. Editing a text like that takes too much time and energy. Instead, we figured a text that was available to all to edit and use as they see fit would be a much better approach, given our desire to shape the content over time. So here we are with another statistics textbook, but one that really is unique. We will get to that uniqueness shortly.
Why another statistics book?
The corrolary to adage “if it ain’t broke, don’t fix it” is “if it is broke, fix it.” We believe that statistics education is broken. Books are too expensive for the general public, immediately outdated upon publication, and often too dense for the average reader. We need a new approach to statistics education. An approach that involves the learners. We have an open text. Our efforts here are to preserve some of what we learned and hope many others will join us in this effort. We hope to provide a text that is readily available and focused on the points necessary for students to achieve our collective goals - to master statistics.
What we have ain’t working. Often, people repeat themselves when they feel as if they were not heard. We educators, students, and graduates feel unheard when it comes to statistics. Those who teach statistics often feel like we are teaching the unteachable. Students struggle to meet the requirements of even the most basic statistics course. Statistics today requires some facility with math - at a minimum, arithmetic and algebra; for advanced students, integral calculus, linear algebra, and an understanding of probability density functions are extremely helpful. How do we educators address that requirement when our students come from many backgrounds and few possess the requisite knowledge to master this material? Well, we don’t know but what we are doing is not fixing the problem.
Unfulfilled promises. The outcomes from our efforts are not all that impressive either. Students who take statistics courses often fail to grasp the material sufficiently to be considered knowledgeable about statistics. How could anyone grasp material that is beyond their scope of knowledge? Faculty in the social sciences have an even greater challenge. We must educate our students to a proficiency level that allows them to be educated consumers of the scientific literature. Without that knowledge, our graduates have little hope in discerning between science and nonsense.
Unrealistic expectations abound. Many of these students need to be able to conduct research and communicate their findings. Doing so requires content knowledge beyond just statistics. Thus, we have a delicate balance to strike between teaching statistics and teaching the content of our disciplines.
We commonly see students failing to grasp rudimentary concepts. The failures come from all parties. We educators use the same methods repeatedly expecting different results. Lectures followed by labs and homework produce rather poor results in student learning outcomes; forget about far transfer. Students fail to grasp the material because they tend not to read effectively and regularly while also avoiding application whenever they can. Read, play, and learn - our primary outcomes of interest. We want students to assume their responsibilities in learning; we educators need to assume responsibility for providing better tools. Here is our attempt to both focus on realizable outcomes and provide better tools. Students and educators alike can come together to produce the best possible outcomes for all involved. Read, play, and learn.
Reading
Most students stop reading the assignments because the assigned readings are often TOO dense and too tangential to their interests. The biggest obstacle is accessibility and readability. Texts that require students to lug around are less likely today to be used let alone read. We need material that is readily available to all users regardless of medium. A website works well for conveying this material provided the information “bits” are small and focused. Students gladly read if the material is readily available and focused on the points necessary for them to achieve their goals - often a grade. Some students, however, find mastery more to their liking. Regardless, both types of students need to read and read often. We hope to provide a text that is readily available and focused on the points necessary for students to achieve our collective goals.
Playing
Playful engagement. Students need to play with statistics. You may think you hate numbers but give us some time to convince you otherwise. Heck, half the fun in statistics is seeing, controlling, and imagining the things that you could do with these tools. Predict the stock prices of your favorite brand, the outcome of a sporting event, or the outcome of a relationship. These are just a few of the types of applications you can “play” with while learning these concepts. We want students to play with the data, the tools, and the concepts. That want comes with an expectation that such playful engagement produces thoughtful data analysts that desire to understand more from the data.
Learning
We all learn by doing. We want students to learn statistics by reading a little introductory material on a concept (see one), playing with the concept (do one), and then applying the concept to a real-world problem (teach one). We hope to provide a text that is readily available and focused on the points necessary for students to achieve our collective goals. Again, mastery is our goal.
What makes this book unique?
If we are successful in this attempt, we will eliminate the need for graduate statistics text books. We want students to read, play, and learn. We want students to assume their responsibilities in learning; we educators need to assume responsibility for providing better tools. Here is our attempt to both focus on realizable outcomes and provide better tools. Students and educators alike can come together to produce the best possible outcomes for all involved. Read, play, and learn.
We wrote this book for you - the budding stats enthusiast
This book is for anyone who needs to make sense of data and has been told, or has told themselves, that they are “not a math person.” That includes graduate students in the social and behavioral sciences, researchers who would rather check the analyses in a paper than take them on faith, and curious readers who simply want to think more clearly about numbers. You do not need calculus or linear algebra to begin. You need curiosity, a little patience, and a willingness to run the code and see what happens. If you have ever wanted to know not just which button to press but why, you are the reader we had in mind.
Structure of the book
The book builds from the ground up. The early parts cover the basics: variables, distributions, central tendency, and dispersion; the move from describing a sample to making inferences about a population; and the twin questions of reliability and validity that decide whether a measurement is worth anything. The middle of the book develops the general linear model, the single framework that unifies correlation, t-tests, regression, and ANOVA, and then extends it to latent-variable models (factor analysis, latent classes, and item response theory). The later parts step outside the normal-curve comfort zone with resampling, robust methods, and Bayesian inference; teach the craft of displaying data honestly in graphs and tables; and close with real case studies from our own published work, where every judgment call is on the table. You can read straight through or jump to what you need. Each chapter stands on its own and points to the others.
How to read/use the book
Our approach is simple: see one, do one, teach one. Read a short introduction to a concept (see one), run and change the code yourself (do one), and then explain it to someone else or apply it to your own data (teach one). Every analysis in this book is live R code, printed right where it runs, so you can copy it, change a number, and watch the result move. Do not just read the code; run it.
Key ideas are set off in highlighted boxes like this one:
A statistic is any number you compute from data, such as a mean, a proportion, or a correlation. Much of this book is about which statistic answers which question, and how confident you can be in the answer.
The larger heading and the 🔑 mark a key term or idea worth remembering — when you see that box, slow down. Occasional first-person asides (marked “PEM”) add a little context from the classroom. The book also has a light and a dark reading mode; use whichever is easier on your eyes, with the toggle at the top of the page.
Software information and conventions
We use R throughout, published through Quarto, the open system that turns our text and code into this website. R is free, open source, and the common language of modern statistics; you can install it from CRAN, and we recommend the free RStudio or Positron editor to work in it. When a chapter needs an add-on package, it says so and loads it at the top of the relevant code. Most of the code uses only base R and a few common packages (ggplot2 for graphics, for example), so you can reproduce nearly everything with a standard installation. Code appears in monospace, results follow directly beneath the code that produced them, and everything you see is reproducible: run the same code and you will get the same answer.