Statistical Concepts - A First Course

Debbie L. Hahs-Vaughn

• Publisher: Routledge
• Year: 2020
• ISBN:
  9780429536854
• Edition: 1
• Topic: Psicologia
• Subtopic: Storia e teoria della psicologia

Statistical Concepts—A First Course presents the first 10 chapters from An Introduction to Statistical Concepts, Fourth Edition. Designed for first and lower-level statistics courses, this book communicates a conceptual, intuitive understanding of statistics that does not assume extensive or recent training in mathematics and only requires a rudimentary knowledge of algebra.

Covering the most basic statistical concepts, this book is designed to help readers really understand statistical concepts, in what situations they can be applied, and how to apply them to data. Specifically, the text covers basic descriptive statistics, including ways of representing data graphically, statistical measures that describe a set of data, the normal distribution and other types of standard scores, and an introduction to probability and sampling. The remainder of the text covers various inferential tests, including those involving tests of means (e.g., t tests), proportions, variances, and correlations.

Providing accessible and comprehensive coverage of topics suitable for an undergraduate or graduate course in statistics, this book is an invaluable resource for students undertaking an introductory course in statistics in any number of social science and behavioral science disciplines.

1
Introduction

Chapter Outline

1.1 What Is the Value of Statistics?

Cigarette Smoking Causes Cancer—Tobacco Industry Denies Charges

North Carolina Congressional Districts Gerrymandered—African Americans Slighted

Global Warming—Myth According to the President

1.2 Brief Introduction to the History of Statistics

1.3 General Statistical Definitions

1.3.1 Statistical Notation

1.4 Types of Variables

1.5 Scales of Measurement

1.5.1 Nominal Measurement Scale

1.5.2 Ordinal Measurement Scale

1.5.3 Interval Measurement Scale

1.5.4 Ratio Measurement Scale

1.5.5 Summary of Terms

1.6 Additional Resources

Key Concepts

1. General statistical concepts

• Population
• Parameter
• Sample
• Statistic
• Descriptive statistics
• Inferential statistics

2. Variable-related concepts

• Variable
• Constant
• Categorical variables
• Dichotomous variables
• Numerical variables
• Discrete variables
• Continuous variables

3. Measurement scale concepts

• Measurement
• Nominal scale
• Ordinal scale
• Interval scale
• Ratio scale

Welcome to the wonderful world of statistics! More than ever, statistics are everywhere. Listen to the weather report and you hear about the measurement of variables such as temperature, rainfall, barometric pressure, and humidity. Watch a sporting event and you hear about batting averages, percentage of free throws completed, and total rushing yardage. Read the financial page and you can track the Dow Jones average, the gross national product (GNP), and bank interest rates. Turn to the entertainment section to see movie ratings, movie revenue, or the top 10 best-selling novels. These are just a few examples of statistics that surround you in every aspect of your life. This is not to mention the way statistics have, probably unnoticeably, influenced our everyday lives—just consider the impact that statistics have had the next time you buckle your seatbelt or help a child into their booster seat.

Although you may be thinking that statistics is not the most enjoyable subject on the planet, by the end of this text you will (a) have a more positive attitude about statistics; (b) feel more comfortable using statistics, and thus be more likely to perform your own quantitative data analyses; and (c) certainly know much more about statistics than you do now. In other words, our goal is to equip you with the skills you need to be both a better consumer and producer of research. But be forewarned; the road to statistical independence is not easy. However, we will serve as your guides along the way. When the going gets tough, we will be there to provide you with advice and numerous examples and problems. Using the powers of logic, mathematical reasoning, and statistical concept knowledge, we will help you arrive at an appropriate solution to the statistical problem at hand.

Some students begin statistics courses with some anxiety, or even much anxiety. This could be the result of not having had a quantitative course for some time, apprehension built up by delaying taking statistics, a poor past instructor or course, or less than adequate past success, among other possible reasons. We hope this text will help alleviate any anxiety you may have. This is a good segue to discuss what this text is and what it is not. First, this is not a textbook on only one statistical procedure. This is a text on the application of many different types of statistics to a variety of disciplines. If you are looking for a text that goes very deep and into the weeds, so to speak, into just one area of statistics, then please review the Additional Resources sections at the conclusion of the respective chapters of interest. Although we feel we have provided a very comprehensive overview of and introduction into many types of statistics that are covered in the first few statistics courses, we do not pretend to suggest that everything you need to know about any one procedure will be covered in our book. Indeed, we do not know of any text that can make that claim! We do anticipate you will find the text is an excellent starting point, and should you desire to delve deeper, we have offered resources to assist in that endeavor.

Second, the philosophy of the text is on the understanding of concepts rather than on the derivation of statistical formulas. In other words, this is not a mathematical statistics textbook. We have written the book with the perspective that it is more important to understand concepts than to solve theorems and derive or memorize various and sundry formulas. If you understand the concepts, you can always look up the formulas if need be. If you do not understand the concepts, then knowing the formulas will only allow you to operate in a cookbook mode without really understanding what you are doing.

Third, the calculator and computer are your friends. These devices are tools that allow you to complete the necessary computations and obtain the results of interest. There is no need to compute equations by hand (another reason why we concentrate on the concepts rather than formulas). If you are performing computations by hand, find a calculator that you are comfortable with; it need not have 800 functions, as the four basic operations, sum, and square root functions are sufficient (one of our personal calculators is one of those little credit card calculators, although we often use the calculator on our computers). If you are using a statistical software program, find one that you are comfortable with (most instructors will have you use a program such as R, SPSS, or SAS). In this text, we do walk through basic formulas by hand so that you become acquainted with how the statistical program works and the numbers that are used in it. However, we don’t anticipate (nor do we encourage) that you make a practice of working statistics by hand. Throughout the text, we use SPSS and R to illustrate statistical applications. Although this book is not a guide on all things SPSS and R, we do try to provide the tools you need to compute the various statistics. We hope that you will supplement what we provide with your own motivation to learn more about software that can assist you in computing statistics.

Finally, this text will take you from raw data to results using realistic examples. The examples may not always be from a discipline that is like the one you are in, but we hope that you are able to transfer or generalize the illustration to an area in which you more comfortable. These examples can then be followed up using the problems at the end of each chapter. Thus, you will not be on your own, but will have the text, a computer/calculator, as well as your course and instructor, to help guide you.

The intent and philosophy of this text is to be conceptual and intuitive in nature. We have written the text so that students who have completed basic mathematical requirements in high school can be comfortable reading the text. Thus, the text does not require a high level of mathematics, but rather emphasizes the important concepts in statistics. Most statistical concepts really are fairly easy to learn because (a) concepts can be simply stated, (b) concepts can be related to real-life examples, (c) many of the same concepts run through much of statistics, and therefore (d) many concepts can be related.

In this introductory chapter, we describe the most basic statistical concepts. We begin with the question, “What is the value of statistics?” We then look at a brief history of statistics by mentioning a few of the more important and interesting statisticians. Then we consider the concepts of population, parameter, sample, statistic, descriptive and inferential statistics, types of variables, and scales of measurement. Our objectives are that by the end of this chapter you will (a) have a better sense of why statistics are necessary, (b) see that statisticians are an interesting group of people, and (c) have an understanding of several basic statistical concepts.

1.1 What Is the Value of Statistics?

Let us start off with a reasonable rhetorical question: “Why do we need statistics?” In other words, what is the value of statistics, either in your research or in your everyday life? As a way of thinking about these questions, consider the following headlines, which have probably appeared in your local newspaper.

Cigarette Smoking Causes Cancer—Tobacco Industry Denies Charges

A study conducted at Ivy-Covered University Medical School recently published in the New England Journal of Medicine has definitively shown that cigarette smoking causes cancer. In interviews with 100 randomly selected smokers and nonsmokers over 50 years of age, 30% of the smokers have developed some form of cancer, while only 10% of the non-smokers have cancer. “The higher percentage of smokers with cancer in our study clearly indicates that cigarettes cause cancer,” said Dr. Jason P. Smythe. On the contrary, “this study doesn’t even suggest that cigarettes cause cancer,” said tobacco lobbyist Cecil B. Hacker. “Who knows how these folks got cancer; maybe it is caused by the aging process or by the method in which individuals were selected for the interviews,” Mr. Hacker went on to say.

North Carolina Congressional Districts Gerrymandered—African Americans Slighted

A study conducted at the National Center for Legal Research indicates that congressional districts in the state of North Carolina have been gerrymandered to minimize the impact of the African American vote. “From our research, it is clear that the districts are apportioned in a racially biased fashion. Otherwise, how could there be no single district in the entire state which has a majority of African American citizens when over 50% of the state’s population is African American? The districting system absolutely has to be changed,” said Dr. I. M. Researcher. A spokesman for the American Bar Association countered with the statement, “according to a decision rendered by the U.S. Supreme Court in 1999 (No. 98–85), intent or motive must be shown for racial bias to be shown in the creation of congressional districts. The decision states a ‘facially neutral law … warrants strict scrutiny only if it can be proved that the law was motivated by a racial purpose or object.’ The data in this study do not show intent or motive. To imply that these data indicate racial bias is preposterous.”

Global Warming—Myth According to the President

Research conducted at the National Center for Global Warming (NCGW) has shown the negative consequences of global warming on the planet Earth. As summarized by Dr. Noble Pryze, “our studies at NCGW clearly demonstrate that if global warming is not halted in the next 20 years, the effects on all aspects of our environment and climatology will be catastrophic.” A different view is held by U.S. President Harold W. Tree. He stated in a recent address that “the scientific community has not convinced him that global warming even exists. Why should our administration spend millions of dollars on an issue that has not been shown to be a real concern?”

How is one to make sense of the studies described by these headlines? How is one to decide which side of the issue these data support, so as to take an intellectual stand? In other words, do the interview data clearly indicate that cigarette smoking causes cancer?...

Table of contents

• Cover
• Half Title
• Title
• Copyright
• Dedication
• Contents
• Preface
• Acknowledgments
• 1. Introduction
• 2. Data Representation
• 3. Univariate Population Parameters and Sample Statistics
• 4. The Normal Distribution and Standard Scores
• 5. Introduction to Probability and Sample Statistics
• 6. Introduction to Hypothesis Testing: Inferences About a Single Mean
• 7. Inferences About the Difference Between Two Means
• 8. Inferences About Proportions
• 9. Inferences About Variances
• 10. Bivariate Measures of Association
• Appendix
• References
• Name Index
• Subject Index