Raising the bar

About the book

The book covers the topics usually included in undergraduate Statistics courses: graphical and numerical description of data, probability, discrete and continuous variables and distributions, sampling and sampling distribution, estimation, hypothesis testing, simple regression, ANOVA, and maximum likelihood method. It is the philosophy that is unusual: we try to prove most facts, without sacrificing intuition. As a result, the reader can see the true motivation behind statistical constructions and the logical links between them.

The electronic (pdf) copy of the book is extremely easy to use on
electronic devices because it contains almost 400 hyperlinks. You can start reading the book from the middle. Whenever knowledge of the previous material is required, you will see a link which will take you to the relevant place in the text. After reading it, just press the back button in your pdf reader and continue reading where you took off.

Innovative features

• The main statistical phenomena and variables are modeled and illustrated in Excel. This allows the student to see how data is generated in real time. We think the conventional practice to provide ready datasets partially hides the random nature of data and the difficulty of data collection.
• The definition of the correlation coefficient is explained using the Euclidean geometry. Specifically, the correlation coefficient is the cosine of the angle between certain vectors. Its interpretation as a cosine makes obvious most of its properties.
• The normal distribution is defined in two steps. First, we define a standard normal variable. Then, a (general) normal variable is defined as a linear transformation of the standard normal. This way is easier to understand and apply than the traditional way of defining the normal variable using its density. Under the traditional approach, the students do not remember the Gaussian density and cannot extract the mean and variance of the normal distribution from its density.
• Analysis of Variance (ANOVA) is a complex and outdated topic. It is not worth studying a bunch of definitions and formulas just to be able to interpret one table. We think ANOVA should not be given at all or should be given with most proofs. Giving it with proofs reveals that ANOVA is just an application of regression analysis and allows the students to learn manipulations with summation signs (including double summations).
• The whole book is written with the view that the reader is preparing to take Econometrics. In particular, the book contains a chapter called "Bridge to econometrics".
• Usually Statistics texts are provided with statistical tables. In addition to taking dozens of pages, the tables are inconvenient to use. In a separate chapter we describe Excel and Mathematica statistical functions that allow one to do without statistical tables.

Foreword to "AP Stats and Business Stats"

During the last twenty-two years I have taught undergraduate, and graduate, Econometrics at three different American universities for hundreds of students. At the very beginning of my teaching career I was introduced to what seems to be a perennial problem for those teaching Econometrics, especially at the undergraduate level: the lack of adequate background knowledge in basic Statistics for those that enroll in our classes. The problem seems to persist in spite of a large and expanding number of textbooks that purport to address this problem, and to do so with a specific focus on statistical knowledge that is directly relevant to Econometrics. In fact, in my view, the problem is becoming more severe. Undergraduate students are being exposed to an enormous amount of material in introductory Statistics courses, but their ability to retain and gain a more in depth understanding of this material is decreasing. As a result, they arrive in my classes with a fragmented knowledge of Statistics that is skin-deep. Most of what they ''know" is either a simple ''appreciation" of fundamental concepts, or the result of rote memorization. Of course, neither, in isolation or combined, allows them to establish a springboard for a deeper understanding and learning of Econometrics.

There are multiple causes for this grim scenario, and their relative importance is certainly an object of debate. However, throughout the years I have come to believe that our predicament is largely a consequence of instructors, who teach material that is so weakened, so diluted, that it cannot be properly learned. As Spanos (1999, p.xviii) has aptly put it, instructors in undergraduate Statistics courses frequently find themselves

''...on the slippery declivity of unconsciously emasculating probability theory and statistical inference down to maize-porridge."

An analysis of the forces and incentives that have led to the unconscious (or conscious?) emasculation of class material is beyond the objectives of this foreword. However, as an instructor or student, you should be pleased to be holding this book. It is a commendable effort to stir us in a much better direction, where clarity, simplicity and conciseness do not come at the expense of rigor and precision.

Kairat Mynbaev has written (and tested) this book with a specific audience in mind, i.e., undergraduate students at Kazakh British Technical University (KBTU) who are taking qualifying Econometrics exams at the University of London, but it is obvious that its reach is much longer. Its content, organization and level justify its adoption as a textbook for introductory statistics for Econometrics in most American or European universities. The book's table of contents is somewhat standard, the innovation comes in a presentation that is crisp, concise, precise and directly relevant to the Econometrics course that will follow. I think instructors and students will appreciate the absence of unnecessary verbiage that permeates many existing textbooks.

Each of the main thirteen chapters is conveniently divided in a number of units that in most cases can be covered in a single class period. These in turn are laced with pedagogical exercises and examples that demonstrate the applicability and breadth of the concepts that are covered. Each chapter also contains a set of closing Questions that provide additional practice for the students. Definitions are clearly marked (boxed) throughout the text and important results are displayed in the form of ''properties" or solutions to exercises, which are always proved. I can't stress enough how important and desirable it is to make proofs part of the main text. They are the best representation of a chain of logical thinking and should be emphasized, not relegated to appendices or underplayed, as is now common practice in textbooks. Reading and developing proofs is the quintessence of mathematical reasoning and a critical exercise in disciplined learning and creativity. The sooner students are exposed to proofs, the better able they are to identify the critical arguments and assumptions necessary to get important results. They are also able to establish connections between seemingly disparate material, a critical part of learning and expanding knowledge.

Having read Professor Mynbaev's previous books and research articles I was not surprised with his clear writing and precision. However, I was surprised with an informal and almost conversational one-on-one style of writing which should please most students. The informality belies a careful presentation where great care has been taken to present the material in a pedagogical manner. This will be useful for both student and instructor.

I hope you will enjoy studying and teaching from this book as much as I have enjoyed reading it.

Carlos Martins-Filho
Professor of Economics
University of Colorado at Boulder
Boulder, USA

References

Spanos, A., 1999, Probability Theory and Statistical Inference: Econometric Modeling with Observational Data. Cambridge University Press, UK.

Where to buy

Hint. The paperback copy is available also on Amazon.com, BarnesandNoble.com, Ingram and probably in other places. The price on Lulu.com, to which the above button takes you, is the lowest. Besides, if you register on Lulu.com, you can avail yourself of further discounts.

Hint. The pdf copy is available only on Lulu.com.

Hint. For those of you who love free stuff here is the free 2010 version of the book:

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