Introduction

There have been numerous and significant innovations to introductory statistics texts in the last decade or two. These have generally been very positive changes to a "traditional" introductory text that had remained relatively static since the 1950's, and is seriously inadequate for today's environment. Despite these positive changes, however, we feel that the introductory text still has a long way to go to successfully meet the needs of current students and their subsequent employers. We have therefore tried to combine the best of recent innovations, and in some cases go beyond them to create a truly unique approach. The purpose of this discussion is to highlight how our approach is different from some of the other innovative texts on the market today. Instructors can then decide for themselves whether they are in conceptual agreement with this approach or not, which will help them decide if this text is appropriate for them. We acknowledge that it will not be suitable for everyone. Further elaboration on our philosophy can be found in the text preface, also included on this website.

Some key reforms that have been made previously, and with which we wholeheartedly agree, are:

• Emphasizing conceptual understanding versus formulas.
• Using real data rather than artificial examples and exercises.
• Considering the topic of data quality in addition to data quantity.
• De-emphasizing formal probability theory and hypothesis testing.
• Fostering experiential learning versus rote memorization.

We applaud the innovators who had the foresight and courage to make these important changes, and we have readily adopted their ideas. We will say little more about these important reforms, since we are in complete agreement with them. Below we highlight some of the areas where we feel we have gone beyond even the most recent reformers.

One serious limitation of traditional texts was their emphasis on formulas and calculations. The predictable result was that students found statistics courses irrelevant and boring. We have all heard the joke about students commenting that statistics was the worst course they took in college. In an era of hand calculations, this focus on formulas and "calculating the correct answer" was somewhat understandable. In an era of easy to use statistical software, and almost universal access to the Internet, this is simply not appropriate. The reformed texts on the market today have recognized this limitation, and switched the emphasis to understanding of important statistical concepts. This change in emphasis to conceptual understanding is right on the money in our opinion. Delving into core statistical concepts has been much more interesting to students than memorizing formulas. Relative to conceptual understanding, we would like to extend the concepts emphasized beyond the concepts of data analysis per se, such as random versus biased samples, controlled experiments versus observational data, and so on, to also included the fundamental concepts that precede and motivate collection and analysis of data.

These fundamental statistical thinking (versus statistics per se) concepts include:

• The need for improvement in business
• The importance of process thinking as a context for data and improvement
• The dynamic versus static nature of business processes
• The sequential nature of improvement and statistical applications
• The importance of integrating the individual tools into overall approaches to improvement (i.e., the overall process of scientific inquiry)

We have found that these concepts are fundamental to creating a mindset in students that promotes and motivates use of statistical tools. For example, without a "gut level" understanding that improvement is mandatory in today’s business environment, there is little motivation to change by learning new tools such as statistical methods. Once this and other fundamental concepts are understood, however, there is typically "suction" on the students’ part to utilize statistical methods. In this latter scenario, the statistical tools are seen as means to achieve a desired end (improvement). Without an understanding of these additional concepts, the tools are often perceived as ends in themselves. Students may be able to perform a t-test to compare the average height of females in their class to that of males, but they see no reason why they should want to. In other words, students may have gone from viewing statistics as boring to viewing it as intellectually stimulating, but we feel it is important to go beyond intellectual stimulation to viewing statistical thinking as useful and important in their careers.

The key differences between our approach and those of other recent reformers relate to the fundamental statistical thinking concepts listed above. After discussing our overall purpose and objectives for a course utilizing this text, we elaborate on each of these concepts below.

Overview

Table 1 contrasts the "reformed text", which aggregates the recent innovations, and the current text, which we submit as a "transformed text" because it is so radically different from the traditional text. For example, one area where we feel little progress has been made is in the clear definition of course objectives, and subsequent tailoring of the course to meet these objectives. Several authors have noted that the traditional course, and even some reformed courses, has been the result of numerous incremental changes to the previous version, without any overriding strategy or purpose in mind. We believe that if an objective observer read a traditional introductory statistics text, and then speculated on the likely purpose that was in the author’s mind, they would probably say exposure to as many individual techniques as possible. Some texts that do state a purpose often do so in such a vague way that it provides little direction to construct the text. For example, we have seen statements similar to the following: "Our purpose is to provide students with a clear, understandable text that will help them with their study of statistics." Such statements are hard to disagree with, of course, but on the other hand they do not specify what specific knowledge, skills, or attitude the students should have at the end of the course.

We believe that the overall purpose for an introductory course for business students should be to develop their capability to apply statistical thinking to improve business

processes. Therefore, our objectives include developing the students’ knowledge to be able to describe the role of statistical thinking and methods for problem solving and process improvement, including the need for understanding, quantifying, and reducing variation. In addition, we aim to develop skills to improve business performance by: identifying and understanding business processes; collecting appropriate data for a specified purpose, and recognizing limitations in existing data; graphically analyzing data using basic tools; deriving actionable conclusions from data analyses; and understanding the limitations of statistical analyses. Finally, it is also our objective that students will develop the attitude that statistical thinking and methods can help them do a better job in their chosen career. These objectives have led us to a course content emphasizing statistical thinking rather than statistical methods per se. In other words, a great deal of conceptual understanding is required to accomplish these goals, above and beyond ability to utilize a given tool.

Should Students View Statistics as Merely Interesting, or Also Useful?

The traditional text often created a perception in students’ minds that statistics is not relevant to their field, business in this case. This is because of an emphasis on formulas that were not motivated, and the use of unrealistic, hypothetical exercises to illustrate the calculations. Innovators identified these problems, and made many important improvements. Reformed texts today generally leave most calculations to the computer, and stress analysis of real data sets. Through discussion of real applications, such as the Salk Polio vaccine trials or US military draft lotteries, students can now see that statistical methods are relevant and do have application. An unfortunate result of emphasis on large, historical studies, however, is that the text may produce students who are consumers of statistics, rather than producers of statistics. In other words, they may now see that statistical methods can be applied, and may be able to properly interpret published studies, but they may also believe these methods are to be applied by others, typically large federal organizations such as NIST, FDA, the Census Bureau, and so on. It may not be clear to students that they can apply statistical methods to improve everyday situations they face, such as problems at work, home, or school. In summary, students may view statistics as a spectator sport!

Since our stated purpose is that students will apply statistical thinking themselves, we have emphasized the need for students to apply the concepts and tools themselves to make real improvements to processes that affect them. This is one of the reasons for including a real course project, and also why we have included a mix of case studies, some which are expensive studies done by large organizations, such as the Busch advertising case, and others which are zero-budget applications by motivated individuals, such as Ian Hau’s applications with high school soccer teams. We believe it is important for students to come out of the course being producers of statistical applications, as well as informed consumers. They should be active participants in statistical applications, rather than just spectators. They should view statistics as being useful, in addition to being interesting.

We have emphasized usefulness by devoting a full chapter (Chapter 1) to the need for improvement in business. In our experience, lack of an improvement mindset leaves students with the impression that statistics could be applied, but not necessarily that it should be. For example, historical case studies investigating the efficacy of a new drug demonstrate applicability, but a skeptical student may point out that the drug had already been developed and its efficacy determined, prior to the application of statistics. They may suggest that statistics didn’t really help do the most critical work of discovering and developing the drug. Such perceptions are typical of "test" oriented texts, i.e., those that portray statistics as a means of proving something that we already know. We believe that drug and other testing does perform a valuable service for society, but also feel that statistical thinking is much more valuable when applied in a proactive mode to improve something. Of course, the truth is that most drug and other research is significantly enhanced through proper application of statistical techniques in developing the drug in the first place. Unfortunately this point is often not clear to students unless the use of statistical methods to make real improvements is explicitly taught and demonstrated.

Are Static Populations or Dynamic Processes More Common in Applications?

It appears generally accepted today that most real business processes are not static, but rather dynamic. Unfortunately, most formal statistical methods assume a static population, i.e., that there is a "true" average and variance. Applying formal statistical methods that assume a static population to an unstable business process can produce misleading and inaccurate results. This issue has several practical implications. First of all, students obviously need a tool to help them differentiate between stable and unstable processes. We have incorporated run and control charts for this purpose. Secondly, they need to know how to approach improvement of an unstable process, as well as how to approach improvement of a stable one. Formal statistical methods are readily applicable to stable processes, but most aren’t applicable to unstable processes. This is one reason that two different approaches are needed. We have therefore included one overall model, or roadmap, for improving stable processes, and another for improving unstable processes. Run and control charts are key tools to determine which approach is likely to be most successful for a given problem.

There are additional benefits to developing a process mindset in students. Our experience is that the process provides the context for improvement, as well as for the data that is analyzed during the improvement efforts. As noted by Box, Hunter, and Hunter (1978), "Data have no meaning in themselves; they are meaningful only in relation to a conceptual model of the phenomenon studied." We refer to "a conceptual model of the phenomenon being studied" as the "process". In many cases, understanding of the process that produced the data provides the subject matter knowledge needed to properly interpret the data. Traditional texts, and unfortunately even most reformed texts, generally discuss interpretation of data in a vacuum. In other words, students may be taught to focus solely on the actual data in hand, and restrict their conclusions to hypotheses that can be proven by this data. In real business applications, however, we always have some degree of subject matter knowledge, based on our current understanding of the process. The data should always be interpreted in light of this knowledge. This is the key point from the Box, Hunter, and Hunter quote above. Sometimes data will confirm our hypotheses, sometimes they will disprove them, and in other cases new theories will be suggested. These new theories will generally require additional data to verify. Proper integration of subject matter knowledge with data is a recurring theme throughout the current text, and is illustrated with several sequential case studies, discussed below.

Another important benefit of a process view is that students now have the theoretical understanding needed to transfer applications of statistical techniques to new environments. For example, suppose they have seen an example of regression applied to marketing research. Without a process view, they might struggle to subsequently apply regression to an inventory control problem, since they have never seen regression applied to this area. However, with a process view they will understand that regression predicts or explains the variation in an output variable as a function of input and process variables. Their process mindset allows them to use their subject matter knowledge to identify the key input, process, and output variables in the inventory control process. It will now be clear how to apply regression to this problem. Of course, a process mindset only makes the application possible, not necessarily easy! We have emphasized the need for a process viewpoint by devoting an entire chapter (Chapter 3) to process understanding and analysis. By design, this chapter precedes any chapters on data analysis tools.

Are Business Applications Typically One Shot Studies or Sequential Investigations?

Another area where we feel the reformed texts have not gone far enough is the need to portray the sequential, iterative nature of statistical applications. The "test" orientation of many texts portrays statistical methods as something done in a discrete fashion, i.e., through "one-shot" studies. Since there are so many statistical tools available, students are often confused as to which individual tool to use when confronted with a complex real problem, such as declining sales in a business. Of course, in reality there is likely no single tool that will completely solve their problem. The student may search in vain, however, for the "silver bullet" for this problem, i.e., the one "correct" tool to apply. Successful applications in the business world are almost always sequential efforts involving integration of several different tools in an iterative fashion. Since this is a subtle concept, students will not learn this by being told; they will need to see and experience it. This is why we have included several sequential case studies that illustrate the natural linkages between various tools, which are not used in isolation, but rather used in conjunction to make sequential improvements. There is a brief sequential case study in Chapter 1, two detailed sequential cases in Chapter 2, two more in Chapter 4, a sequential regression application in Chapter 6, a sequential DOE case in Chapter 7, a sequential transformation application in Chapter 9, and then two more sequential cases in Chapter 10. These sequential case studies enable students to see the proper integration of the tools, and working on a sequential project will enable them to experience it personally.

An important implication of the true nature of business applications is that if improvement efforts tend to be sequential, applying several different tools in conjunction, then students will need to be taught how to properly integrate them. In other words, they will have to be taught the overall process of improvement, or the "overall process of scientific inquiry" as it is sometimes called. Of course, each application is different, so there is no single "correct" cookbook for integrating the tools. We can’t prescribe exactly which tools to use in a predefined sequence. However, there are general models for sequencing the tools that are widely applicable. Recall that all models are wrong, but some are useful. In this case, we believe it is critically important to teach overall models, or roadmaps, that provide useful guidance for integrating the tools. Once students understand and apply these roadmaps, they will be able to adapt or modify them appropriately to address new problems, especially if they have a process orientation. We first provide an overall conceptual model for the improvement process, which we call the statistical thinking model. Chapter 2 is devoted to developing conceptual understanding of this overall model. The statistical thinking model is then reinforced with more detailed versions designed for specific types of problems, which suggest which sets of tools are likely to be used at each stage of the improvement process. These more detailed models are the focus of Chapter 4. After completing this chapter, students will understand the big picture of when and why to apply individual tools, hence detailed instruction in the tools follows in subsequent chapters. This sequence of teaching is explained below.

Do Students Need to See the Big Picture?

We noted above that it is important to provide students with overall models for how to properly integrate and sequence the individual tools. This provides students with an overall approach that can be used to attack unstructured problems. There has been little emphasis, even in reformed texts, on overall approaches to integrate the tools. Where these have been provided, they are generally at the end of the text, where there is an attempt to finally tie all the individual pieces together. Unfortunately, our experience is that by this time many students have either been lost due to confusion over when to apply all the individual tools, or have already forgotten the details of the tools they previously learned. Educational and behavioral research, not to mention our own experience, suggests that this traditional approach is not the best sequence to help students learn easily. Research suggests that the big picture, i.e., overall models, should be taught first, and illustrated via sequential case studies, prior to getting into the details of individual tools. This research suggests that students learn best when instruction flows from the "big picture" to the details, rather than the other way around. In business and industrial training circles, this is called "top-down" instruction.

The top-down approach is becoming the norm in the private sector, and has been used in the US military for some time. As another example, many progressive high schools in the US now begin their history sequence with a World History course, which briefly reviews the major themes and cultural interrelationships in human history, from the dawn of recorded time to the present. After students see this big picture, they are then prepared to put subsequent detailed study of US (or European, Asian, African, etc.) history in proper perspective. For example, the slave trade in the "New World" during the 16^th to 19^th centuries involved various cultures in North America, South America, Europe, and Africa. Therefore, this important historical subject is virtually impossible to properly understand by studying the history of only a single country, or even a single continent. We believe many subjects, including statistical thinking, are similar in that one cannot come to a proper understanding by studying the pieces in isolation. Students must see and experience the big picture. This is referred to as a "holistic" approach.

We have found the theory behind the top-down approach to be valid, and have experienced "suction" from students anxious to learn the individual tools once they see how they fit into the bigger picture. We have therefore organized the text in a top-down fashion, specifically in a "why-what-how" sequence. We begin by explaining why statistical thinking is needed in business. Next, we show students the "big picture" (i.e., the "what") by reviewing sequential case studies that integrate several tools and iterate between subject matter knowledge with data. We then provide both high-level and detailed models of overall approaches to improvement, which are based on the case studies. Only after these models have been illustrated and taught do we go into detailed instruction in the tools themselves (i.e., the "how"). Each tool is introduced by referring back to its role in the bigger picture, hence there is no confusion over when and why a tool is needed. While this approach has been much more intuitive for students we have taught, it does result in a text that is in nearly the exact reverse order from traditional and even reformed texts. Note also that each chapter is organized in the same "why-what-how" sequence.

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