SCST101 - Chapter 1 - Introduction to Statistics

Key Concept In this section we begin with a few very basic definitions, and then we consider an overview of the process involved in conducting a statistical study. This process consists of "prepare, analyze, and conclude." "Preparation" involves consideration of the context, the source of data, an...

Key Concept In this section we begin with a few very basic definitions, and then we consider an overview of the process involved in conducting a statistical study. This process consists of "prepare, analyze, and conclude." "Preparation" involves consideration of the context, the source of data, and sampling method. In future chapters we construct suitable graphs, explore the data, and execute computations required for the statistical method being used. In future chapters we also form conclusions by determining whether results have statistical significance and practical significance. Statistical thinking involves critical thinking and the ability to make sense of results. Statistical thinking demands so much more than the ability to execute complicated calculations. Through numerous examples, exercises, and discussions, this text will help you develop the statistical thinking skills that are so important in today's world. We now proceed to consider the process involved in a statistical study. See Figure 1-2 for a summary of this process and note that the focus is on critical thinking, not mathematical calculations. Thanks to wonderful developments in technology, we have powerful tools that effectively do the number crunching so that we can focus on understanding and interpreting results. Prepare Context Figure 1-2 suggests that we begin our preparation by considering the context of the data, so let’s start with context by considering the data in Table 1-1. Table 1-1 includes the numbers of registered pleasure boats in Florida (tens of thousands) and the numbers of manatee fatalities from encounters with boats in Florida for each of several recent years. The format of Table 1-1 suggests the following goal: Determine whether there is a relationship between numbers of boats and numbers of manatee deaths from boats. This goal suggests a reasonable hypothesis: As the numbers of boats increase, the numbers of manatee deaths increase. Source of the Data The second step in our preparation is to consider the source (as indicated in Figure 1-2). The data in Table 1-1 are from the Florida Department of Highway Safety and Motor Vehicles and the Florida Marine Research Institute. The sources certainly appear to be reputable. ✓ We should be very wary of such a survey in which the sponsor can somehow profit from the results. ✓ We should be skeptical of studies from sources that may be biased. In contrast, ▪ Kiwi Brands, a maker of shoe polish, commissioned a study that resulted in this statement, which was printed in some newspapers: “According to a nationwide survey of 250 hiring professionals, scuffed shoes was the most common reason for a male job seeker's failure to make a good first impression.” ▪ When physicians who conduct clinical experiments on the efficacy of drugs receive funding from drug companies they have an incentive to obtain favorable results. ▪ Some professional journals, such as the Journal of the American Medical Association, now require that physicians report such funding in journal articles. Sampling Method Figure 1-2 suggests that we conclude our preparation by considering the sampling method. The data in Table 1-1 were obtained from official government records known to be reliable. The sampling method appears to be sound. Sampling methods and the use of randomization will be discussed in Section 1-3, but for now, we stress that a sound sampling method is absolutely essential for good results in a statistical study. Analyze Figure 1-2 indicates that after completing our preparation by considering the context, source, and sampling method, we begin to analyze the data. Graph and Explore An analysis should begin with appropriate graphs and explorations of the data. Graphs are discussed in Chapter 2, and important statistics are discussed in Chapter 3. Apply Statistical Methods Later chapters describe important statistical methods, but application of these methods is often made easy with technology (Excel, calculators and statistical software packages). A good statistical analysis does not require strong computational skills. A good statistical analysis does require using common sense and paying careful attention to sound statistical methods. Conclude Figure 1-2 shows that the final step in our statistical process involves conclusions, and we should develop an ability to distinguish between statistical significance and practical significance. Key Concept A major use of statistics is to collect and use sample data to make conclusions about populations. We should know and understand the meanings of the terms statistic and parameter, Some data are numbers representing counts or measurements (such as an IQ score of 135), whereas others are attributes (such as eye color of green or brown) that are not counts or measurements. The terms quantitative data and categorical data distinguish between these types. Type of Data Quantitative (or numerical) Qualitative data: (or categorical or attribute) data: consist of numbers representing counts or measurements. consist of names or labels (not numbers that represent counts or measurements).  Type of Data Quantitative (or numerical) Qualitative data (or categorical or attribute) data Discrete data Continuous data Question 1: The numbers of cars serviced in McDonald’s drive-up window. This is an example of which type of data. a) Ordinal b) Continuous c) Qualitative d) Discrete Question 2: The length of time that students use their smartphones during the statistics class. This is an example of which type of data. a) Nominal b) Continuous c) Qualitative d) Discrete Levels of Measurement Another common way of classifying data is to use four levels of measurement: nominal, ordinal, interval, and ratio, all defined below. (Also see Table 1-2 for brief descriptions of the four levels of measurements.) When we are applying statistics to real problems, the level of measurement of the data helps us decide which procedure to use. There will be references to these levels of measurement in this book, but the important point here is based on common sense: Don’t do computations and don’t use statistical methods that are not appropriate for the data. For example, it would not make sense to compute an average (mean) of Social Security numbers, because those numbers are data that are used for identification, and they don’t represent measurements or counts of anything. Levels of Measurement Nominal Ordinal Interval Ratio Question: Which of the following represents an interval level of measurement a) Majors b) Salaries of five tops mangers in Jeddah c) Ranks of football teams d) Body temperatures (in degrees Fahrenheit) ❑ If sample data are not collected in an appropriate way, the data may be so utterly useless that no amount of statistical torturing can salvage them. The four basic methods of sampling: random, systematic, stratified, and cluster sampling. Other Sampling Methods Question 1: Every seventh customer entering a shopping mall is asked to select her/his favorite store. What type of sampling methods have been used. a) Simple random sample b) Systematic sample c) Stratified sample d) Cluster sample Question 2: A pollster uses a computer to generate 500 random numbers, then interviews the voter corresponding to those numbers. What type of sampling methods have been used. a) Cluster sample b) Systematic sample c) Stratified sample d) Simple random sample Basics of Design of Experiments Example 1 describes an experiment because subjects were given a treatment, but ethical, cost, time, and other considerations sometimes prohibit the use of an experiment. Basics of Design of Experiments Types of Observational Studies