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Part I
INTRODUCTION TO STATISTICAL ANALYSES
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Chapter 1
USING STATISTICS TO CONDUCT QUANTITATIVE RESEARCH
A World of Statistics
The Misleading Image of Statistics: A Bum Rap
Branches of Statistics: Descriptive and Inferential
Why Do Quantitative Research?
Typical Steps Involved in Quantitative Research
Isolating a Problem Question and Hypothesis
Selecting Measures
Sampling
Design
Selection of Statistics
Writing the Report
Sample Information
Measurement Adequacy Information
Manipulation Checks
Check Hypothesized Results
Report Unhypothesized Results
Interpret Results
Whether you are taking a class in empirical research methods, whether you are using this book to help prepare yourself to conduct research, or whether you just want help to understand some of the research you have read, this book is designed for you. The emphasis is on your practical use of statistical thinking to help make decisions. To this end, the first two chapters of this book will give you background and vocabulary to help you understand other sections of the book. In each subsequent section, you will find a brief introduction to the statistical tools of interest, including a description of ways computers have helped us make fast work of analyses (few people do major data analyses by hand anymore—why should you?). The descriptions here are short and sweet and designed to give you—not your instructors—immediate information to address issues of quantitative research methods. For further details on things suggested here, you may wish to refer to the Web site for this book or to examine an extensive reference book of statistical analysis of data.
A WORLD OF STATISTICS
Quantitative research uses statistical information to help make decisions to answer research questions. As innocent as it may sound, this statement often gets tied up with a lot of unpleasant associations that we probably should discard right away.
The Misleading Image of Statistics: A Bum Rap
Many people have some strange ideas about studying research statistics. Three of the major misperceptions are that the subject is boring, that you can prove anything with statistics, and that it is a subject for math majors. In each case, the charge is a bum rap.
A Technical, Unexciting Subject. Some people think that research statistics is a dry subject that involves deriving theorems and toiling over long columns of numbers. You may have chosen your major field of interest, in part, because you thought you were interested in content that had little to do with numerical information. But because so many interesting questions can be answered by looking at numbers, you may find yourself drawn to statistical analyses because there are topics that fascinate you. Actually, statistical analysis of data is just commonsense use of information to help explore meaningful research questions. As such, the statistical data analysis is as exciting and stimulating as the questions that it is being used to examine.
“You Can Prove Anything With Statistics.” Some people suspect that most statistics are used to mislead us. Way back in 1954, Darrell Huff wrote a lighthearted guide with the wry title How to Lie With Statistics, to help readers evaluate statistical reports. The book was intended to prevent mischief in the use of statistics, but the book’s title reinforced the image of statistics as a form of particularly untrustworthy information. But misleading statistics are no more prevalent than tricks used by deceitful people using any other sorts of information. In fact, statistics can only prove what data show. Most of the time, people cannot find statistics to prove their private views no matter how strangely they manipulate the numbers. Statistics are no more prone to deception than other forms of information. Indeed, one way to avoid being misled by deceptive use of statistics is to study a little about them. This guidebook may help you in this regard.
A Study for Mathematicians. The time is long past when methods of statistical analysis were the specialties only of mathematicians. But the stereotype remains. As this book will show you, statistical tools are available to anybody trying to answer research questions that invite quantitative methods. In reality, the statistical analysis is just a form of applied reasoning and logic. You do not need to have an extensive background in mathematics to understand the descriptions of tools in this book. Furthermore, computers have taken most burdens out of studying statistical reasoning. Hence, this guidebook reflects that convenience by showing you how to use and interpret these tools.
In reality, the study of statistics has at least as much of a link to politics, social relationships, and business as it does to mathematics. Early on, statistical analyses were completed for governments. In ancient Babylon before 3000 B.C.E., agricultural yields were regularly recorded on clay tablets. Before they began to build their pyramids, ancient Egyptians statistically analyzed their kingdom’s population and wealth in the 31st century before the Common Era. The Chinese kept extensive statistical records before 2000 B.C.E. Both the ancient Greeks and Romans used census data to aid in collecting taxes. The Romans were the first to hire permanent “statists” (“status takers”—a term from which the word “statistician” is derived) shortly before the beginning of the Common Era. But the serious modern study of statistics did not take off until the 17th century, when it was desired to keep track of “vital statistics” (birth and death rates) for use by governments and insurance underwriters.
Unconcerned with politics, many people examined principles of probability to prosper in gambling. Soon the basic notions were applied to setting annuity prices for life insurance policies. Scientists explored such things as the notion of “least squares” and various distributions to help advance the study of astronomy. By the 20th century, social science work led large numbers of students to study statistics to keep up with the experimental and survey work being done in their fields. The communication field often is classified as a social science because so many scholars approach the discipline with empirical research interests.
Branches of Statistics: Descriptive and Inferential
Quantitative analyses of data involve two kinds of statistical tools. Descriptive statistics are “numbers that are designed to characterize some information in a data set” (Reinard, 2001, p. 434). In essence, these numbers are designed to help summarize some collection of information. These sorts of statistics are contrasted with inferential statistics, which, as the term suggests, are tools to help researchers use sample data to draw conclusions about populations. This process usually involves assessing the probability that samples were part of populations with particular characteristics. The term population refers to a universe of events (e.g., people, types of statements, numbers of newspaper articles, or the like) from which a sample is drawn. These populations are universes to which a researcher is interested in generalizing, but a population does not have to be enormous. A communication studies department chair may be interested in knowing what proportion of undergraduate majors tend to apply to graduate school. The population of interest would not include all college students in the world, but only those at one location. This population could be small because the department might have a modest number of students. The point is that populations are defined by the researcher. In statistics, a number that is “a characteristic of a population” (Vogt, 2005, p. 227) or computed from a population is called a parameter. Though in everyday conversation people sometimes use “parameter” as a synonym for “perimeter” or boundary, this meaning is not preferred, and you probably should avoid using it. Most parameters of interest to researchers have nothing to do with boundaries or limits. Many pieces of data are from samples or selections from a larger collection of events. Naturally, nearly all published research in communication and the social sciences involves sample data. When a number is derived or computed from a sample, it is called a statistic. Of course, if one had more than one sample statistic, they would be called “statistics.” Thus, the word “statistics” carries a double meaning. Statistics (a singular noun) is a subject that deals with analysis of quantitative information. Statistics (a plural noun) are numbers computed from samples of data. To help keep things straight, different symbols are used. When referring to population data (by observation or inference), Greek letters are used. When referring to sample data, the Roman alphabet letters that we use every day are employed.
WHY DO QUANTITATIVE RESEARCH?
The quantitative methods studied here are tools in which descriptions of observations are expressed in predominantly numerical terms. A reasonable person might wonder why it is necessary—or even desirable—to complete quantitative research. In part, the answer to this question stems from the fact that the tradition of quantitative research comes from efforts to apply the scientific method to explore vital research questions. Yet, this statement does not mean that something is scientific just because it uses numbers. The scientific method is described in many ways, but one widely accepted view is that, at the very least, it involves gathering data and advancing “a functional relationship among these data” (Bachrach, 1981, p. 4).
Not all research questions require quantitative research methods. For instance, some research questions may be answered by applying critical standards to speeches. Other research questions may be answered by looking at the development of ideas through the contributions of scholars over the years. These sorts of matters may be explored by use of qualitative research methods, which involve examination of predominantly nonquantitative data. In general, qualitative methods are used most often when researchers wish to describe, interpret, or criticize phenomena that typically are not summarized numerically.
Research questions invite use of quantitative analysis of data if they involve
Issues of the current status of things that can meaningfully be summarized numerically,
Prediction of values of variables from the occurrence of other variables, and
Development of research measures.
Such research questions involve phenomena that can be identified and measured. These methods allow us to describe and predict phenomena rather than gathering evidence to help make philosophic or individualistic judgments about communication.1 The benefits of using quantitative tools include the following:
- Emphasizing work where replication of results is possible;
- Using measurement that usually is strong;
- Permitting researchers to examine complex phenomena (both the nature of simple effects of variables and complex interactions may be explored directly) (first three benefits loosely adapted from the classic treatment by Dahle and Monroe, 1961, pp. 176–178); and
- Efficiently examining data when large numbers of events are involved (though such things as single subject experiments exist [Barlow & Hersen, 1984] and one may find quant...
