# Advanced High School Statistics - 2nd Edition

David Diez, OpenIntro

Christopher Barr, Varadero Capital

Mine Çetinkaya-Rundel, Duke University

Leah Dorazio, San Francisco University High School

Copyright Year: 2019

Publisher: OpenIntro

Language: English

## Formats Available

## Conditions of Use

Attribution-ShareAlike

CC BY-SA

## Reviews

I've worked with a lot of statistics textbooks. I really like the organization of this text. It works logically from creating and organizing data to statistical summaries then to probability distributions and inference. There is a natural... read more

I've worked with a lot of statistics textbooks. I really like the organization of this text. It works logically from creating and organizing data to statistical summaries then to probability distributions and inference. There is a natural building of concepts. There are also often references to more complex statistical procedures, for instance when the conditions for a statistical procedure are not met. There are more topics shared than might be covered in a typical one semester offering of introductory statistics, but it is nice to have them available. In addition to the content, the text provides directions for different forms of technology including Casio and TI calculators, some Desmos connections, and even some results using R. There are connections to videos and other online tools that are also a benefit to this text.

As the text is now in the third edition, many errors from prior editions have been cleared up. Like many online tools, though, there are occasionally online links that no longer work.

I appreciate that the text seems to focus on current, technology focused methods of learning statistics. There are still connections to older practices, such as using tables and doing normal approximations for binomial distributions, the text does a nice job of emphasizing current methods. The data sets also seem to be relevant and often provided online so that they can be updated as needed.

I appreciate that the text focuses on the statistical procedures and concepts. As new terminology is introduced, it is clearly defined right away. The reading level seems appropriate for this level of course.

The concepts and terminology shared in the text were connected well both within different sections of the textbook but also within the exercises.

The primary chapters in the text would be typical to many introductory statistics texts. Each chapter is broken down into subsections with exercises that work within that section.

As already shared, the organization of the text seems very logical for introducing an emphasis on using data to answer questions, creating data, and then analyzing the data. I appreciate how techniques related to categorical data are separated from techniques related to numerical data.

While the illustrations in the book are rather simple, they do a good job of illustrating concepts. For instance, images of possible distributions from non-normal populations are clearly organized and displayed to point out the power of the central limit theorem.

The text reads well with proper grammatical structure and lack of overly technical language.

The text does provide data sets from a variety of situations.

This book offers many benefits by not only being well organized and well written, but also by providing excellently connected data sets, videos, illustrations, and directions for technology. There is also an alternative edition provided through My Open Math that has electronically graded exercises.

The entire text is easy to understand for beginners and it covers all needed subjects very well. An exception is that one-way and two-way ANOVA are not included, and these would be helpful for first year, second semester statistics students. read more

The entire text is easy to understand for beginners and it covers all needed subjects very well. An exception is that one-way and two-way ANOVA are not included, and these would be helpful for first year, second semester statistics students.

Overall, the material is correct with some minor problems (maybe typos), They are minor but can be confusing to students. A few examples are as follows: In some places, it should say "do not reject Ho" but it says "reject Ho". On page 412 the numbers used for SE are not correct, and it shows "n1" where it should be "n2"; and of course, the SE value is incorrect and the rest of the problem is wrong as a result.

Content and specific examples are all excellent choices. In my opinion, it will not be obsolete for a long. However, over time some numbers in examples and problems might become outdated (prices, etc.) but should be very easy to fix.

The TI 83/84 technology used in this text is obsolete. Also, when Excel output is used, "Excel" should be mentioned. I feel instructions for how to use 83/84 should be replaced with instruction for how to use Excel, because Excel is updated often and is available to most students without additional cost.

The way this text was written, it is easy for students to read and understand. Even if students have only taken a first term of algebra, they should be able to read and understand it.

Text is consistent all the way through.

Modularity is excellent. The way each chapter is divided into sections and subsections makes it easy for students. It is easy for students and teachers to communicate because they can easily refer to a specific subsection when discussing a question or an example.

Topics are arranged in an appropriate order.

This text has no interface issue throughout. Graphs and charts and output of technology are arranged well.

No grammatical errors were found.

There are no cultural issues at all.

I believe it is a simple task to fix all minor problems in the ebook and perhaps to add one- and two-way ANOVA. For the hard copy, an "errata sheet/pamphlet" with corrections and perhaps material for one-and two-way ANOVA could be distributed. And then corrections and additions could appear in the next edition.

I highly recommend removing TI 83/84 and instructions and replacing with Excel instructions.

I would give the book a 4.5 score here if possible. The coverage of confidence intervals and hypothesis testing of population proportions and means is adequate but could have more material. I would like to see more homework exercises in each... read more

I would give the book a 4.5 score here if possible. The coverage of confidence intervals and hypothesis testing of population proportions and means is adequate but could have more material. I would like to see more homework exercises in each section. The index is complete.

I found almost no errors/typos and they were not conceptual errors.

The real-world examples and content are relevant and up-to-date and I do not see that these will become obsolete. Any updates made to the text should be easily implemented.

This book is very easy to read and follow. I really like the checkpoints and examples. The answers do not show up until the reader clicks on them.

The terminology and framework is consistent. The definitions and terminology do not differ from standard, accepted probability and statistics definitions and terminology.

Each section in the chapter could be assigned as an individual reading assignment. The sections are complete but concise and easy to read and follow.

I really don't see the presentation of the topics could be improved. Everything is laid out clearly and in order.

The text is laid out perfectly. There is a table of contents column on the left that is always visible, showing the sections and appendices so the text is easy to navigate. There is no distortion of images/charts or display features. All images/charts have a zoom-in feature. Again, I really like how the checkpoints and examples are laid out requiring the reader to click on them to get the full answer. It gives the reader the opportunity think about the concept first.

I found no grammatical errors.

The text is not offensive or culturally insensitive and includes a variety of races, ethnicities and backgrounds.

The short videos that accompany the text are outstanding and really help motivate the material in the text. The power point slides are excellent as well. The only thing that I would like to see is more homework exercises.

This textbook contains the main components necessary to cover the average beginner course in statistics. It doesn’t provide a staggered introduction to statistical concepts but rather jumps right in with demonstrating how statistics can be used in... read more

This textbook contains the main components necessary to cover the average beginner course in statistics. It doesn’t provide a staggered introduction to statistical concepts but rather jumps right in with demonstrating how statistics can be used in an applied setting. As a standalone the books covers several topics but not in depth it is just enough for a survey course. The real strength of this text is in the video overviews and the informational slides. These supplementary materials allow students greater insight into the content with applied or real life examples. The authors also include examples of how to interpret the numerical findings as well as considering assumptions with the various tests.

I have not detected any obvious errors in the content.

The content is current and includes examples from current topics like stem cell research. The examples vary and are not within the same discipline (e.g., medical, psychological, political, etc.) and they are not aligned with one single software package like R, SPSS, or Excel therefore the text can be used across the natural and social sciences with a variety of computing tools.

This is written in a very straightforward manner and doesn’t over complicate the content by exhausting the reader with too many definitional terms. The authors provides the minimum of what the reader needs to know in order to follow the examples and conduct the exercises. The added use of figures is applauded as it helps develop the reader’s ability over the course of the textbook to visualize the data and distributions.

The text is written in a consistent voice.

The text is easily divisible to coincide with the assignment of multiple interacting units. The subsections can be switched around or reorganized to match the instructors own preferred organization of the content as the units are mostly self-sustaining (except for those with extended examples).

The organization is not like a typical stats textbook where the content is structured by type of statistical test or type of research question. Instead the organization further confirms the data-centric perspective of this text by focusing for the most part on the type of data that the student has and what tests can be done within that limited range. It is a slightly different flow and I find it interesting and logical.

There were no interface issues or navigation problems with the downloaded pdf version. Charts and figures loaded and resized easily.

I have yet to detect major grammatical issues.

The text does not appear obviously offensive or culturally insensitive.

The text is written clearly and the examples are very applied. There are no frills, just good briefly covered content. While this is written for an advanced high school course it could easily be used for college or even beginner Master-level courses. It is also a good resource for those needing a refresher on how to interpret data findings or consider the limitations related to the nature of their data. This text is straight to the point and covers a good range of content.

## Table of Contents

1 Data collection

- 1.1 Case study
- 1.2 Data basics
- 1.3 Overview of data collection principles
- 1.4 Observational studies and sampling strategies
- 1.5 Experiments

2 Summarizing data

- 2.1 Examining numerical data
- 2.2 Numerical summaries and box plots
- 2.3 Considering categorical data
- 2.4 Case study: malaria vaccine (special topic)

3 Probability

- 3.1 Defining probability
- 3.2 Conditional probability
- 3.3 The binomial formula
- 3.4 Simulations
- 3.5 Random variables
- 3.6 Continuous distributions

4 Distributions of random variables

- 4.1 Normal distribution
- 4.2 Sampling distribution of a sample mean
- 4.3 Geometric distribution
- 4.4 Binomial distribution
- 4.5 Sampling distribution of a sample proportion

5 Foundation for inference

- 5.1 Estimating unknown parameters
- 5.2 Confidence intervals
- 5.3 Introducing hypothesis testing
- 5.4 Does it make sense?

6 Inference for categorical data

- 6.1 Inference for a single proportion
- 6.2 Difference of two proportions
- 6.3 Testing for goodness of fit using chi-square
- 6.4 Homogeneity and independence in two-way tables

7 Inference for numerical data

- 7.1 Inference for a mean with the t-distribution
- 7.2 Inference for paired data
- 7.3 Inference for the difference of two means

8 Introduction to linear regression

- 8.1 Line fitting, residuals, and correlation
- 8.2 Fitting a line by least squares regression
- 8.3 Inference for the slope of a regression line
- 8.4 Transformations for skewed data

A Exercise solutions

B Distribution tables

C Distribution Tables

D Calculator reference, Formulas, and Inference guide

## Ancillary Material

## About the Book

We hope readers will take away three ideas from this book in addition to forming a foundationof statistical thinking and methods.

- (1) Statistics is an applied field with a wide range of practical applications.
- (2) You don't have to be a math guru to learn from real, interesting data.
- (3) Data are messy, and statistical tools are imperfect. But, when you understand the strengths and weaknesses of these tools, you can use them to learn about the real world.

**Textbook overview**The chapters of this book are as follows:

- 1. Data collection. Data structures, variables, and basic data collection techniques.
- 2. Summarizing data. Data summaries and graphics.
- 3. Probability. The basic principles of probability.
- 4. Distributions of random variables. Introduction to key distributions, and how the normal model applies to the sample mean and sample proportion.
- 5. Foundation for inference. General ideas for statistical inference in the context of estimating the population proportion.
- 6. Inference for categorical data. Inference for proportions using the normal and chisquare distributions.
- 7. Inference for numerical data. Inference for one or two sample means using the t distribution, and comparisons of many means using ANOVA.
- 8. Introduction to linear regression. An introduction to regression with two variables.

Instructions are also provided in several sections for using Casio and TI calculators.

## About the Contributors

### Authors

**David Diez** is a Data Scientist at OpenIntro.

**Christopher Barr** is an Investment Analyst at Varadero Capital.

**Dr. Mine Çetinkaya-Rundel** is the Director of Undergraduate Studies and an Associate Professor of the Practice in the Department of Statistical Science at Duke University. She received her Ph.D. in Statistics from the University of California, Los Angeles, and a B.S. in Actuarial Science from New York University’s Stern School of Business. Her work focuses on innovation in statistics pedagogy, with an emphasis on student-centered learning, computation, reproducible research, and open-source education.

**Leah Dorazio**, Statistics and Computer Science Teacher, San Francisco University High School