Applied Univariate, Bivariate, and Multivariate Statistics

This book is designed for upper level undergraduate and graduate students. Though the intended target is very clear, the book is very challenging, especially for upper level undergraduate students. As a teacher who teaches statistics, I found it sometimes difficult to understand. In this review, I will mainly discuss Chapter 3, Chapter 4, Chapter 8 and Chapter 9 in order to get my ideas across, but many of my comments can be similarly applied in the other chapters.

First of all, I like the idea of having a companion website. This website can definitely help students to use the software better.

Second, the choice of topics is often strange. Consider Section 2.9, “Essential Mathematics: Precalculus Calculus and Algebra.” Students taking this course will probably already have a solid background in Calculus I and Algebra. If the author insists in adding this part, I would recommend putting it at the beginning, as “preparation.” In Chapter 3, the author uses half a page to explain the simple definition of a “z-score”. Some information can be delivered in class, so there is no need for writing everything down; alternatively, the author could include a glossary.

Third, the author should cover more information and motivation. The missing definitions make the book very hard to follow. For example, Chapter 3 begins with the topic “normal distribution.” The author doesn’t provide any information about how to use normal distribution and why we need to learn the normal distribution. These two questions are common questions that students would normally have at the early stage of learning a new topic. In this case, students could be easily lost. The next topic after “normal distribution” is “Chi-Square” in Section 3.2. Such a change in topic is a surprise to me, because there are so many things that need to be covered before introducing “Chi-Square”, such as “skewed distributions” (introduced in Section 3.10), “2 way tables”, “one way tables”, “null and alternative hypothesis”, “degrees of freedom” (introduced in Section 3.9), etc. The author doesn’t deliver explanations related to any of the definitions mentioned above. And he doesn’t tell us why we need Chi-square distribution. In Chapter 4, the author doesn’t explain the difference between “between-group” and “within-group”. These two definitions are actually confusing — I always need to spend some time to explain them and give examples to my upper level classes.

The order of the content sometimes makes the book tough to read, as noted above for chapter 3. There are numerous other places with the same issue. The “sample and population mean vector” in Chapter 3, for instance, can actually be moved to Chapter 2. Same situation applies to Section 3.17 (covariance and correlation).

Some information outlined in the book is not complete. In Section 3.17, for example, the author provides several examples of correlations, but he only reveals the answers without explaining their meaning. The author does not discuss if a correlation is strong or weak. Furthermore, all the examples have positive correlation, but the correlation can be a negative number. The author should have given an example of this.

Sometimes the information listed in the book is misleading. One example is in Chapter 4: on page 178, the statement “there is at least one difference of the null hypothesis” should include four situations: (a) \(\mu_1\neq\mu_2,\mu_1=\mu_3\), (b) \(\mu_1=\mu_2,\mu_1\neq\mu_3\), (c) \(\mu_1\neq\mu_2, \mu_2=\mu_3\), and (d) \(\mu_1\), \(\mu_2\) and \(\mu_3\) all different. This is not what is listed in the book.

Another example is in Chapter 8, when it comes to the predicted value \(y_i’\) and the observed value \(y_i\). I think the author wanted to say that \(y_i=y’_i + e_i\), with \(e_i\) representing the errors, and the linear regression line would be \(y_i’=a+bx_i\). On page 339, however, where is the “\(e_i\)” after the calculation? Why does the formula become \(y_i’=a+bx_i+e_i\)? The author needs to explain that.

Last but not the least, the author should provide more examples and more detailed steps in the examples. I was trying to look for some useful examples in section 3.2, since the author already skipped so many important definitions. I didn’t find any except those instructions about how to use the related software. I do understand that proficiency using software is required in statistics. I believe, as a teacher, that we should teach them how to do the problem by hand first. Using the software is supplementary. Similarly, in chapters 10, 11, and 12, the author could start with an example and have it solved in steps. It is more important to teach students how to solve problems than simply knowing how to use the software.

Because the author gave so many examples computed using software, I was surprised when I didn’t find many homework exercises that can be solved by using software. There are a lot of theory based problems. At this point, I became confused about this book’s intention. Was the book designed for those students who are going to industry? Or was the book designed for those students who are going have an academic job? No matter which target audience the author are aiming at, I believe the homework exercises should be more practical. It also would be better to have some projects included.

I do like the selection of examples. All them seem to use real data, which can help students better understand the real world. But the author does not go deep enough when he explained the examples.

Summing up, I don’t think I would recommend this book or use it class. To my mind, the author concentrates too much on using software and neglects teaching students to solve problems by hand. I would also need more preparation time to fill in the missing definitions and motivation.

Mengyi Ying is Assistant Professor of Mathematics at the University of North Georgia.