INVESTIGATING STATISTICAL CONCEPTS, APPLICATIONS, AND METHODS, Second Edition

Changes to the Second Edition:

There are two primary changes to the second edition

·         Reordering of topics

·         Updated technology instructions for both Minitab and R

Why did we reorder the topics?

We have continued the focus on asking students to consider an entire statistical investigation from beginning to end, and spiraling through that process in several different settings.  Originally we felt this would be best achieved by asking students to compare groups through randomized experiments. One limitation to this approach is students often became bogged down in study design issues and odds ratio vs. relative risk.  Our approach in the second edition is to begin with investigations that center around binomial outcomes and a coin tossing model.  We feel we have utilized compelling research questions while simplifying many of the details so students can focus on the overall statistical investigative process. We focus first on a binomial process, taking students immediately through tests of significance, confidence intervals, and power, and then reinforce these concepts through the normal approximation. We next transition to sampling from a finite population.

What is the overall format?

The second chapter then focuses on comparing two groups on a categorical response, distinguishing between comparing two population proportions and comparing two treatment probabilities. The scope of conclusions that can be drawn based on the study design is a constant focus.  Students again work through simulations, exact procedures, and normal approximations for statistical inference, culminating in inference procedures for odds ratios.

The third chapter parallels the process of the first two chapters but now focusing on comparisons for quantitative data, especially through randomized experiments. Some initial explorations allows students to explore issues with quantitative data and sampling distributions for the sample mean (these are fairly brief and can even be skipped). After exploration of randomization tests with a quantitative response, two-sample t-procedures are introduced, followed by matched-pairs designs.  These three chapters appear quite sufficient for a 10-week quarter.

Chapter 4 is an updated version of the previous Chapter 6, focusing on relationships between variables, culminating in Chi-Square, ANOVA, and Regression procedures. These chapters are fairly independent and can be done individually or in any sequence.  This chapter also incorporate several new applets. These applets are written in javascript, and so are much more portable (e.g., run on iPads).  They have a consistent formatting, allowing exploration of descriptive statistics, “scrambling” distributions of different choices of statistics, and output of more traditional test procedures.

We have also added an optional initial exploration focusing on the relative frequency interpretation of probability and use of simulation to investigate random outcomes.  Since last fall we have added back in a bit more mathematical exploration and more of this can be found in the homework exercises. The homework exercises now more some more investigation based questions with the old edition 1 exercises.

At the end of each chapter are 2-3 examples with detailed solutions applying the concepts from the chapter.  Some chapters include an appendix which incorporates additional calculation details or extends a concept further. You may also find you want to supplement some of the mathematical treatment of the ideas, either in class or through homework exercises.  Practice problems are given at the end of each section. These can be used to structure student activity outside of class, to begin class discussion and review, or as quiz problems.  The length of the practice problems is generally shorter than in the first edition.

An index is included in the materials and the pdf files include hyperlinks to glossary terms, data files, and applets.

What technology is used in the text?

We continue to incorporate Minitab commands into the text and hope we have done so in a way that does not disrupt the flow of the text.  Side-by-side with the Minitab commands we now also include instructors for using R.  Or you may select to have your students purchase a version that focuses primarily on only one of the packages. We have also developed a set of functions that can be easily imported into R through a workspace. In lieu of a GUI interface/menu driven environment, these “iscam functions” ask students to input certain parameters to run the R functions and often include a graphical display with the output in the R Session window. We are not intending for students to spend much time learning R, and indeed the R use is rather basic and preprogrammed, but to allow students to seamlessly allow the technology to perform the calculations so they make focus on and explore the statistical concepts. We also make use of several java applets throughout the course, especially for the simulations.  In many situations students will have a choice of all three technologies and may be instructive to rotate among them and compare the functionality and output.

General Notes:

We envision the materials as being very flexible in how they are used.  You may choose to lead students through many of the investigations together as a class, but we also encourage you to give students time to work through some questions on their own (or better in pairs) and then debrief with the students afterwards.  If you do have students work through investigations largely on their own, it’s very important to conduct a wrap-up discussion at the end of class, and/or at the beginning of the next class, in which you make clear what the “morals” of the investigations were.  In other words, summarize for students what they were supposed to have learned through the investigations and what they are responsible for knowing, making sure they are reading the additional exposition in the text as well.  These wrap-up discussion times are also ideal for inviting students’ questions, because they will have wrestled with the ideas enough to know what the issues are and where their understanding is shaky.  You may wish to collect students’ answers to just a few of the questions in an investigation to read over and give feedback before the next class session.  The practice problems are intended to provide students with basic review and practice of the most recent ideas between class periods.  This will help structure their time outside of class, and provide a way for you and the students to informally assess their understanding and provide feedback.  You may choose to collect and grade these as homework problems or use them more to motivate initial discussion in the next class period.  You can also consider including a “participation” component in your syllabus to include effort if your evaluation will be more informal.  If you are short on time, you may also wish to formal assign students to answer the first few questions of the next investigation before class to allow you to get to the “meat” of the investigation more efficiently during class.

You may also wish to supplement some of the material in the book, for example, bringing in recent news articles for discussion, or assigning data collection project assignments.  We think students will find the ISCAM investigations interesting and motivating, but there will also be time to share other examples as well.  Some students prefer to read through examples worked out in detail and we have provided at least one such example at the end of each chapter.  If you do bring in your own material, we do caution you to try to remain consistent with the text in terminology, notation, and sequencing of ideas.  Some of this material and sequencing may be new to you as the instructor and may take a while to get used to.  Keep in mind that the material you think is usually introduced at different points in the course will be coming eventually.

We have written the materials assuming students will have easy access to a computer, and we make increasing use of technology as the course progresses. We have taught the course with daily access to a computer lab, but believe it will also work with less frequent visits to a computer lab and/or more instructor demonstrations (using a computer projection system).  If the students do not have frequent access to computers during class, you may wish to assign more of the computer work to take place outside of class.  We do provide detailed instructions for all of the computer work (Minitab, Excel, java applets), but you may still want to encourage students to work together.  Even with heavy use of computers, it is also nice to have some days where you focus less on the computers to give students a chance to ask questions on the larger concepts in the material and even work a few calculations “by hand.”  Student will use a calculator on a daily basis as well.

The following elements will be found in each chapter:

Investigations: These are intended to be “covered” during the lecture period, either as note pages for the class to complete together or as worksheets for students to work on individually or in pairs. Often, a section can correspond to one 50-60 minute class period.  Each investigation provides a model write-up of the study conclusions.

Practice Problems: These are intended as quick reviews of the basic ideas and terminology of the previous investigation(s) and can often be assigned between class periods.

Examples: Each chapter contains at least one example worked out for students to see the solution approach in detail.

Chapter Summary and Technology Summary: These provide a review list of the main concepts covered in the chapter as well as the basic computer commands that will be used in subsequent chapters.