# Any suggestions for a good undergraduate introductory textbook to statistics?

I am hoping you can give me some suggestions. I am teaching in a very diverse (made of minority groups) college and the students are mostly Psychology majors. Most students are fresh from high school but some of them are older returning students above 40. Most of the students have motivational problems and aversion to math. But I am still looking for a book that covers the basic curriculum: from descriptive to sampling and testing all the way to ANOVA, and all in the context of experimental methods. The department requires me to use SPSS in class, but I like the idea of building the analysis in a spreadsheet such as excel.

p.s. the other teachers use a book that I don't like because of the extensive reliance on computational formulae. I find using these computational formulas - rather than the more intuitive and computationally intensive formula that is consistent with the rational and basic algorithm- unintuitive, unnecessary and confusing. This is the book I refer to Essentials of Statistics for the Behavioral Sciences, 7th Edition Frederick J Gravetter State University of New York, Brockport Larry B. Wallnau State University of New York, Brockport ISBN-10: 049581220X Thank you for reading!

Statistics, by Freedman, Pisani, & Purves, originated from a popular and successful course taught at U.C. Berkeley. I have used it as an intro stats text for undergraduates, have borrowed some of its ideas when teaching graduate stats courses, and have given away many copies to colleagues and clients. There are many reasons for its popularity:

• Its narrative and its problems are driven by real case studies and actual data of obvious importance, rather than the made-up drivel found in so many texts. These are truly interesting and memorable, including the Salk polio vaccine trials, the 1936 Literary Digest poll debacle, the Berkeley graduate student discrimination lawsuit (hinging on Simpson's Paradox), Fisher's criticism of Mendel's pea results, and much more.

• It has extensive problems at three levels: at the end of each chapter subsection (of which there are hundreds), at the end of each chapter (over 30), and at the ends of major groups of chapters (about 4, I recall). These problems require minimal or no mathematics: they focus on potential misunderstandings that the authors, in their extensive experience, have found to arise among students.

• It focuses on statistical ideas and reasoning rather than mathematics.

• It uses (almost) no mathematical formulas. Quantitative relationships are usually expressed graphically and in words. (They are so clearly conveyed that when I first read this book, as a math graduate student entirely ignorant of statistics, I was able to reproduce all the underlying mathematical theory with no trouble.)

• It covers most of the traditional material, including the Binomial and Normal distributions, confidence intervals, z tests, t tests, chi squared tests, regression, and the minimum amount of probability and combinatorics needed to understand these.

Some potential drawbacks would include:

• No treatment of Bayesian statistics. This will make this book outmoded within a decade.

• No treatment of ANOVA (psychology students might miss this the most).

• No discussion of computing.

I believe the latter two are not critical: a good instructor can easily supply the ANOVA material and can teach as much or little computing as they might wish. Whether the omission of Bayesian statistics is important will depend on the instructor's tastes and aims.

Finally, I should note that although the mathematical demands are as small as one could possibly imagine, my pre- and post-testing of students indicates that people who come to the book with a disposition and habit of thinking quantitatively still get much more out of it than those who do not. Most of my students performed badly on pretests of mathematical knowledge (90% got failing grades), but those who also performed badly on pretests of critical thinking (Shane Frederick's Cognitive Reflection Test) exhibited markedly less improvement during the semester than others did. The pre and post tests both included the full 40-item CAOS test of fundamental concepts any introductory college-level stats course ought to include. The students in this class have consistently exhibited twice as much improvement as that reported in the CAOS literature; the students with poor cognitive reflection scores improved only an average amount (or failed to complete the course). I haven't the data to assign causes to this extra improvement, but suspect the textbook deserves at least some of the credit.

• whuber, based on your contributions to this site, I am convinced your students (if you are still teaching) are very lucky. – Michael Bishop Jan 23 '13 at 17:37

I read Freedman (almost the entire book) and OpenIntro Statistics (more than a third). Both of these books are quite good.

I eventually found the book that came close to what I was looking for: Learning Statistics with R: A tutorial for psychology students and other beginners by Danielle Navarro. It is freely available online (legally) and you can also order a print version for about US $30 (see the book page for details). The main pros of this book are: • R implementations embedded in text as topics are introduced. R has built-in functions for most of the methods explained in the book. Where R doesn't have a built-in, the author has written her own function for it and made it available on CRAN under her lsr library, so your learning is quite complete. I personally found this to be the biggest plus point of this book. • The book is more comprehensive than Freedman and OpenIntro. Along with the basics, it covers topics like Shapiro-Wilk test, Wilcoxon test, Spearman correlation, trimmed means and a chapter on Bayesian statistics, to name a few. • The motivation behind each topic is explained clearly. There is also a good amount of history behind the topics, so you get to appreciate how a method was arrived at. • The book was written iteratively with feedback from readers and I believe the author is still improving upon the book. The only drawback is that the hard copy version is large and heavy! • +1 Thank you for a thoughtful and informative contribution! – whuber May 1 '16 at 17:52 • Thank you for your kind words. That is the greatest compliment I have got recently coming from one of the top contributors to this site! – arun May 2 '16 at 2:02 Thom Baguley, an outgoing editor of The British Journal of Mathematical and Statistical Psychology, published Serious Stats book that you could find useful. It relies on R rather than SPSS, though. I am suspicious of the books that are in their 7th edition. In my teaching experience, it means that the sections and problems were reshuffled so that the students would have to buy the latest edition to generate the cash flow for the publisher and royalties for the authors keep up with the course. Few serious, research level monographs have undergone a second edition by their authors, and any higher number is obviously an outlier. (Kendall's Library of Statistics is a notable exception, but I cannot really think of any other book that I know that would be in its third edition.) In my very strong opinion, Excel is a good tool for statistical analysis only when used by a Ph.D. statistician. Teaching undergraduate statistics with it will likely have disastrous consequences, and teaches little statistics as compared to using a modern package like R or Stata. Just try to produce a standardized residual vs. leverage regression plot in Excel, and compare it to one-liners in these packages. Stat majors would need to know the theory, so they would need to build these plots from scratch, but still using a statistical package rather than copy/paste the formulae around in Excel. Non-major undergrads need to get the feel for data analysis, and Excel obscures it, at best. • I can think of several good books that are in high editions; they aren't research monographs, they are textbooks, but that's what is being asked for. e.g. Tabachnick and Fidell is in its 6th edition – Peter Flom Jan 23 '13 at 15:34 • Tabachnik was on the very bottom of my list of multivariate books (amazon.com/Multivariate-statistics-books/lm/R3312L94GKFZD1). I see a niche for this particular book to be researchers who want to apply a method like discriminant analysis once, follow the formulae and be done with it and not touch statistics with a ten-feet pole until a dire need arises. But I would not recommend it; again, the age of taking a formula and implementing it in Fortran is way over, and with more convenient tools, modern books can afford looking more into understanding the methods and how they work. – StasK Jan 23 '13 at 15:52 • Another exception that proves the multi-edition rule is Freedman, Pisani, & Purves which is in its fourth edition. Somewhere (perhaps in the instructor's manual, maybe the preface) they note that the material is largely unchanged from the first, published some 35 years ago, but that instructors have asked for updated datasets. Thus it's possible to teach from any edition if you like--and old editions are widely available at hugely discounted prices. (I bought my first copy for 25 cents.) – whuber Jan 23 '13 at 16:14 • Thank you for taking the time to expand on your original comment! The book may be too hard for these students, and it will take a long time until the exam copy arrives. About Excel, I think excel is useful for viewing the application of the formula to the data, not as a tool of analysis. – Adam SA Jan 23 '13 at 18:02 Statistics Unplugged is a great book for introductory statistics. The author first introduces the logic of the statistical test and later gives the mathematical formula. This approach helps in digesting the new concepts. There are several examples throughout the book which are presented in the form of a problem required to be solved rather than a hypothetical statement and mathematical steps. How about The Statistical Sleuth by Ramsey and Schafer? I think this book gets at some important points without either a) Too much math or b) dumbing things down. I would suggest that an intro stats course for psychology and other social science types should emphasize how not to go wrong too much. A survey of methods would also be a good thing for undergrads to get. Check out the introductory statistics book, Making Sense of Data through Statistics: An Introduction (2014) by Dorit Nevo. It is written in an extremely accessible manner and is meant for undergraduate or graduate students in business and in the social sciences. The textbook makes use of examples meaningful to today’s students and is accompanied with Excel worksheets providing hands-on experience that reinforces the statistical concepts and techniques covered. Instructors are provided with supplementary teaching materials, including PPT lecture slides for each chapter, a Solutions Manual for all Unit Exercises and End-of-Chapter Practice sets, and a Test Bank. The book is sold in digital format only (.pdf), allowing for the very reasonable price of$19.95. Educators may register for free access to the book and teaching materials by signing up at the Legerity Digital Press Educator Preview portal.

Here is a list of books. Puzzles/riddles are a great way to instil an interest in what mathematics/statistics can do. Real life examples help too.

• I added the post notice because answers that rely solely on a link are likely to become invalid in the future when the link rots. At least summarize or highlight some of the books on the list. Are you familiar with any of them? – whuber Jan 23 '13 at 16:10
• BTW, in reviewing this list I notice it focuses on probability exclusively. Probability is not the same as statistics! – whuber Jan 23 '13 at 16:55

I have been a TA, observer, or student in a lot of courses involving quantitative methods for psychology, with SPSS as the main program. In all cases it has seemed to me that students have gravitated towards Field (2013), irrespective of whether the course coordinator has mentioned this book or not. In numerous cases students have ignored a recommended textbook and read Field's textbook instead.

I'm not properly competent to assess the rigour of the explanations in the book, and nor am I aware of any research on learning outcomes. However, I can say that this book is comprehensive, cheap (where I'm from anyway), and popular with students. The author's writing style relies a great deal on personal anecdotes, which will grate with some readers. However, I've found that at least as many students enjoy it. I seemed to run into a lot of typos and other issues in the early editions, but by the fourth edition most of these seem to be weeded out.

So, Field (2013) is my recommendation, since:

1. I've seen psychology students engage with it and enjoy reading it.
2. Even if you recommend another book, it's quite likely that some students will use Field (2013) anyway. This can then create administration issues within your course.
3. The book is popular and the author is still relatively young, so it's likely that there will be further editions and improvements.
4. If you later decide that you want to use R instead, you can transition pretty seamlessly to Field, Miles, and Field (2012), which uses most of the same examples. @jeremy-miles is a frequent contributor to this site.

Field, A. (2013). Discovering statistics using IBM SPSS statistics. Sage.
Field, A., Miles, J., & Field, Z (2012). Discovering Statistics Using R. Sage.

• See the comment of @whuber in a thread discussing inaccurate and misleading advice in this book "Skimming pages here and there in the SPSS book provides insight into some of the really confused questions we get on this site: I think they must come from readers of that book. It is full of errors, misinformation, and outright confabulation." stats.stackexchange.com/questions/157217/… – Nick Cox Aug 12 '16 at 7:28
• The author's sense of humour divides people drastically. Juvenile, gross and disgusting are some of the negative verdicts. – Nick Cox Aug 12 '16 at 7:32

Statistics for College Students and Researchers: Grasping the Concepts, Paperback 2010, ISBN-13 : 978-1453604533 is perhaps the easiest and most comprehensive stat book for college students. "grasping the concepts and the logic of Statistics. Formulas do not lead to understanding, they actually prevent it. This book takes you through elementary, intermediate and advanced Statistics with only five simple formulas! Descriptive and inferential Statistics. t-test, one-way analysis of variance (ANOVA), two-way ANOVA, repeated measures, factorial designs unlimited, complex split-plot designs.". Unbelievable? Yes... I got the book, the description at amazon is correct. The author is a psychologist/medical anatomist, so examples come from these areas. Apparently these are his lectures. Concepts are developed through funny stories. Yes, five simple formulas all the way through ANOVA. ANOVA summary tables become redundant, although all example cases use them.

http://onlinestatbook.com/index.html is a very nice source with simulations and videos