Introductory Statistics

A Conceptual Approach Using R

William B. Ware, John M. Ferron, Barbara M. Miller

• Publisher: Routledge
• Year: 2013
• eBook ISBN: 9781136870101
• Topic: Education
• Subtopic: Education Theory & Practice

This comprehensive and uniquely organized text is aimed at undergraduate and graduate level statistics courses in education, psychology, and other social sciences. A conceptual approach, built around common issues and problems rather than statistical techniques, allows students to understand the conceptual nature of statistical procedures and to focus more on cases and examples of analysis. Wherever possible, presentations contain explanations of the underlying reasons behind a technique. Importantly, this is one of the first statistics texts in the social sciences using R as the principal statistical package. Key features include the following.

• Conceptual Focus – The focus throughout is more on conceptual understanding and attainment of statistical literacy and thinking than on learning a set of tools and procedures.
• Problems and Cases – Chapters and sections open with examples of situations related to the forthcoming issues, and major sections ends with a case study. For example, after the section on describing relationships between variables, there is a worked case that demonstrates the analyses, presents computer output, and leads the student through an interpretation of that output.
• Continuity of Examples – A master data set containing nearly all of the data used in the book's examples is introduced at the beginning of the text. This ensures continuity in the examples used across the text.
• Companion Website – A companion website contains instructions on how to use R, SAS, and SPSS to solve the end-of-chapter exercises and offers additional exercises.
• Field Tested – The manuscript has been field tested for three years at two leading institutions.

Part I

1

Introduction and Background

OVERVIEW

We recognize that the word “statistics” does not elicit the same response from everyone. In fact, the range of attitudes toward a statistics class may be quite extreme, perhaps even more so than other classes you've taken in your college career. If your reaction is somewhere toward the negative end of the emotional spectrum (Think: Ugh!), don't feel bad. That's a fairly common reaction for students beginning their first course in statistics.

We know that a few of you are starting this course because you have always enjoyed mathematics. Some of you are taking this course because you are curious. You've heard about statistics and want to see what it is all about. Many of you are taking this course because it is required; you've been told that you have to take it. You are not very happy about the prospect, but you know that you will survive. And then, there are a few of you who are taking the course against your will. You are afraid to the point that you are experiencing indigestion and sleep disorders. You are thinking about dropping out of school. How will you ever survive?

We have just described the typical composition of an introductory applied statistics course for the social sciences. For just a moment, consider the plight of the unfortunate person standing at the front the class—the instructor. He or she has the difficult task of presenting the content of this course to a very diverse group of students and doing so in such a way that will not result in getting destroyed on the student evaluations of teaching at the end of the course. This book has been written to help both students and instructors. As you will soon see, it is not a typical statistics text. Rather, it is written in a style that we hope will appeal to everyone. We provide conceptual overviews, detailed step-by-step instructions on how to calculate statistics, both by hand using a calculator and using the computer statistical package R; we also provide some support for SPSS and SAS on the book website. From time to time, we will provide mathematical derivations in technical notes that you are free to ignore. Now that we've been honest up front, let's get on with it!

WHY TAKE A COURSE IN STATISTICS?

There are many different positive reasons for taking a course (or more than one) in applied statistics. Some of you are practicing professionals who will never calculate another statistic after you complete this course. But even if you do not calculate a single statistic yourself, you will need to understand what the statistics you encounter everyday—from test grades to what you read in a newspaper or at work—are telling you. As technology continues to change the way we live, you will find that researchers are using increasingly more sophisticated statistical tools to analyze their data, and the reports that appear in professional journals are becoming more and more technical and very difficult to comprehend without some understanding of statistical concepts. Thus, as practicing professionals, you need some statistical background to enable you to read, understand, and evaluate research reports. Too many consumers of research simply read an abstract and then jump to the study's conclusions and implications section without reading about the study's methods and results.

Several of you will go on to careers in which you will be designing studies, writing grant applications, and such. Hopefully, you will be very successful, in which case you will be able to employ statisticians to carry out your analyses. Even though you may not conduct the analyses, you still need to know a lot about statistics. In designing the studies, you will need to know what statistical tools are available and which ones are appropriate for answering your research questions. If you are not aware of the variety of tools available, you will tend to design your studies in overly simplified ways. There is an old saying, “If the only tool you have is a hammer, everything looks like a nail.” For example, if the only statistical procedure you know is how to calculate percentages, then you may miss the opportunity to draw stronger conclusions from your research. Or, if the only statistical procedure that you know is a t-test, then you will tend to design all of your studies as consisting of two groups and analyze the data to compare the averages of the two groups. Furthermore, you will need to be able to communicate clearly with your hired statistician. Some of the most horrible mistakes are made when the principal investigator has a very limited understanding of statistics and the statistician similarly has a very limited understanding of the substantive research topic.

You should also be aware that what constitutes appropriate research methodology in the social sciences is not always a given. We have seen much controversy over the years between those who, on one extreme, believe that “if you can't measure it, it is not worth talking about” to those who, on the other extreme, believe that “the important aspects of human interaction cannot be measured.” At times each group has characterized the other group unkindly. Fortunately, we seem to be progressing beyond that point as more and more researchers are employing mixed methods in their research, or a combination of both quantitative and qualitative methods in their inquiry.

Without question, the focus of this book is on quantitative methods. However, we firmly believe that the results of statistical analyses cannot be interpreted without a context. In order to conduct useful statistical analyses, one must have information about the meaning of the numbers and the conditions in which they were generated.

OUR THOUGHTS ON THE NATURE OF REALITY

We hold the belief that there is order in the universe, and that there is an external reality that exists independent of our perceptions. We believe that, in that external reality, there are cause-and-effect relationships. However, these relationships are probabilistic rather than deterministic. That is, the effect does not follow the cause every time the cause is present. We acknowledge that our ability to perceive the external world is far from perfect. Furthermore, different people can experience the same object or event and construct different perceptions. For example, many years ago, researchers looked at children's perceptions of the common silver quarter. The results indicated that children from low-income backgrounds drew quarters that were consistently larger than those drawn by children from high-income backgrounds. Other researchers have staged events such as an automobile accident at an intersection. After the accident, interviews of witnesses showed that, although the witnesses all experienced the same event, reports of what happened differed considerably from one person to another. Just as people construct their own meanings of their experiences, we offer a quote defining statistics as “a place where knowledge is neither certain nor random” (Keller, 2006, p. ix). Simply stated, there may be multiple beliefs about reality, but that does not imply that there are multiple realities.

We believe that we can build a common knowledge base. By pooling our information over time, over replications, and with input from others, we firmly believe that we can build a useful understanding of the world around us. We believe that our position is consistent with that of postpositivism as described by Phillips and Burbules (2000). “In short, the postpositivist sees knowledge as conjectural. These conjectures are supported by the strongest (if possibly imperfect) warrants we can muster at the time and are always subject to reconsideration” (Phillips & Burbules, 2000, pp. 29–30). Similarly, “It is a confusion—and a pernicious one—to say that because a person believes X, and another doesn't, that X is both true and not true, or, relatedly, to say that there are ‘multiple (incompatible) realities’” (Phillips & Burbules, 2000, p. 36). We urge you to give this well-written book a quick read. For a more extreme position on philosophy and science, we refer you to Bunge (1996). We should also note that the field of statistics predates postpositivism and that statistical arguments have been, and continue to be, used by researchers who identify with a wide variety of philosophical positions. We felt it relevant, however, to share our position in that it may help to shed light on the examples chosen and the arguments made. The remainder of this book is devoted to presenting a description of statistical methods and showing how they can be used to assist us in building an understanding of the world around us.

SCIENCE AND RESEARCH IN THE SOCIAL SCIENCES

What is Science?

The word “science” is derived from the Latin word scientia, meaning “knowledge.” Bodies of knowledge consist of general truths and laws obtained by applying the scientific method, or agreed-upon principles and procedures for the systematic generation of knowledge. Generally, the process begins with the recognition or formulation of a problem. Based on previous knowledge, observations, and experience, we develop a hypothesis, or tentative explanation. Subsequently, we collect data through observation and/or experimentation, under conditions which, as much as possible, control or rule out other explanations. Finally, the validity of the hypothesis is assessed in light of the data. When the hypothesis is in conflict with the data, the hypothesis is regarded as incorrect. However, when the hypothesis and the data are in agreement, we can say that the hypothesis is supported, although not proven. This point is somewhat subtle and often misunderstood.

Scientific research is systematic. Scientists have agreed upon what constitute legitimate ways to pursue knowledge. Scientists conduct their work in public, and their work is open to correction. Perhaps most important, scientific hypotheses are both rational and testable. That is, they make sense and they are capable of being disproved.

What is Research?

We think of research as the process of building a science. There are many ways to characterize approaches to research. Some researchers employ methods that are described as qualitative, such as observation, interviews, and focus groups. Other researchers use methods that may be described as quantitative, such as experiments, quasi-experiments, and statistics. Both approaches require creativity and rigor. Qualitative researchers collect large amounts of data; their hard work begins when they begin to analyze the data. Quantitative researchers put a lot of hard work into the development of their measures and the design of their studies; data analysis is pretty easy, relatively speaking. That said, we think that the differences between qualitative and quantitative methods have been greatly exaggerated. Indeed, one of the authors learned about experiments, observations, and interviews in a research methods course in the middle of the last century, before the term “qualitative methods” had been coined. As you might expect, however, our focus is on quantitative research. There are three main types of quantitative research: experiments, quasi-experiments, and observational studies.

Experiments

Experiments are studies in which the researcher has quite of bit of control. There is some sort of experimental treatment or intervention that is administered to a group of participants. There is also a placebo or control condition experienced by the control group. Furthermore, the researcher has the ability to determine which participants are assigned to which condition, and that assignment is made with randomization. Often, the study is completed in an isolated context, permitting the elimination of extraneous events that might influence the data.

Quasi-experiments

Quasi-experiments have many of the features of experiments, with one important difference. In typical quasi-experiments, the researcher does not have the ability to assign participants to conditions at random. Thus, quasi-experiments do not permit conclusions that are as strong as those from experiments. There are many threats, or rival explanations, that may account for the results, rather than the treatment/intervention. Much has been written about quasi-experiments, stemming from the work of Donald Campbell. The seminal work was Campbell and Stanley (1963), which was followed by an expanded coverage in Cook and Campbell (1979). Th...

Table of contents

• Front Cover
• Half Title
• Title Page
• Copyright
• Dedications
• Contents
• List of Illustrations
• Preface
• PART I
• PART II DESCRIPTIVE STATISTICS
• PART III THE FUNDAMENTALS OF STATISTICAL INFERENCE
• PART IV STATISTICAL INFERENCE
• PART V k-SAMPLE TESTS
• Appendix A—Statistical Tables
• Appendix B—An Introduction to R
• Subject Index
• Author Index