Data and conclusions based on data appear regularly in a variety of settings: newspapers, television and radio advertisements, magazines, and professional publications. In business, industry, and government, informed decisions are often data driven. Statistical methods, used appropriately, allow us to draw reliable conclusions based on data. Once data have been collected or once an appropriate data source has been identified, the next step in the data analysis process usually involves organizing and summarizing the information. Tables, graphs, and numerical summaries allow increased understanding and provide an effective way to present data. Methods for organizing and summarizing data make up the branch of statistics called descriptive statistics. After the data have been summarized, we often wish to draw conclusions or make decisions based on the data. This usually involves generalizing from a small group of individuals or objects that we have studied to a much larger group. For example, the admissions director at a large university might be interested in learning why some applicants who were accepted for the fall 2006 term failed to enrollat the university. The population of interest to the director consists of all accepted applicants who did not enroll in the fall 2006 term. Because this population is large and it may be difficult to contact all the individuals, the director might decide to collect data from only 300 selected students. These 300 students constitute a sample. The second major branch of statistics, inferential statistics, involves generalizing from a sample to the population from which it was selected. When we generalize in this way, we run the risk of an incorrect conclusion, because a conclusion about the population is based on incomplete information. An important aspect in the development of inferential techniques involves quantifying the chance of an incorrect conclusion. ■ The Data Analysis Process ................................................................................ Statistics involves the collection and analysis of data. Both tasks are critical. Raw data without analysis are of little value, and even a sophisticated analysis cannot extract meaningful information from data that were not collected in a sensible way. ■ Planning and Conducting a Statistical Study Scientific studies are undertaken to answer questions about our world. Is a new flu vaccine effective in preventing illness? Is the use of bicycle helmets on the rise? Are injuries that result from bicycle accidents less severe for riders who wear helmets than for those who do not? How many credit cards do college students have? Do engineering students pay more for textbooks than do psychology students? Data collection and analysis allow researchers to answer such questions. The data analysis process can be viewed as a sequence of steps that lead from planning to data collection to informed conclusions based on the resulting data. The process can be organized into the following six steps: 1. Understanding the nature of the problem. Effective data analysis requires an understanding of the research problem. We must know the goal of the research and what questions we hope to answer. It is important to have a clear direction before gathering data to lessen the chance of being unable to answer the questions of interest using the data collected. 2. Deciding what to measure and how to measure it. The next step in the process is deciding what information is needed to answer the questions of interest. In somecases, the choice is obvious (e.g., in a study of the relationship between the weight of a Division I football player and position played, you would need to collect data on player weight and position), but in other cases the choice of information is not as straightforward (e.g., in a study of the relationship between preferred learning style and intelligence, how would you define learning style and measure it and what measure of intelligence would you use?). It is important to carefully define the variables to be studied and to develop appropriate methods for determining their values. 3. Data collection. The data collection step is crucial. The researcher must first decide whether an existing data source is adequate or whether new data must be collected. Even if a decision is made to use existing data, it is important to understand how the data were collected and for what purpose, so that any resulting limitations are also fully understood and judged to be acceptable. If new data are to be collected, a careful plan must be developed, because the type of analysis that is appropriate and the subsequent conclusions that can be drawn depend on how the data are collected. 4. Data summarization and preliminary analysis. After the data are collected, the next step usually involves a preliminary analysis that includes summarizing the data graphically and numerically. This initial analysis provides insight into important characteristics of the data and can provide guidance in selecting appropriate methods for further analysis. 5. Formal data analysis. The data analysis step requires the researcher to select and apply the appropriate inferential statistical methods. Much of this textbook is devoted to methods that can be used to carry out this step. 6. Interpretation of results. Several questions should be addressed in this final step—for example, What conclusions can be drawn from the analysis? How do the results of the analysis inform us about the stated research problem or question? and How can our results guide future research? The interpretation step often leads to the formulation of new research questions, which, in turn, leads back to the first step. In this way, good data analysis is often an iterative process.
