give the impression that most millennials do not prefer YouTube as a learning tool. But wait! Look carefully at Figure 1-1 and see that the vertical axis has a scale that ranges from 52% to 60%. The graph in Figure 1-1 is misleading because it uses the scale of 52% to 60% instead of a scale that begins with 0%. As a result, the difference between the two bars is visually exaggerated in Figure 1-1. In Figure 1-2, the same data are shown in the graph, but we use a scale that begins with 0%. Figure 1-2 shows that the Gen-Z prefers YouTube as a learning tool only slightly more than millennials (actually 4% more to be exact). Figure 1-1 is misleading, whereas Figure 1-2 depicts the data fairly. We might now consider how these survey data can be used to improve the learning experience for Elementary Statistics! Figure 1-2 shows that the majority of both Gen-Z and millennials prefer YouTube as a learning tool and this percentage has increased from one generation to the next. Knowing that YouTube and other videos are increasingly preferred learning tools, the author has created a YouTube channel with custom instructional videos to support this textbook (visit www.TriolaStats.com for the link). In addition, MyLab includes additional instructional videos and interactive content to support students. The flaw shown in Figure 1-1 is among the most commonly used tactics to present misleading arguments, so it is especially important to recognize. Here are brief descriptions of common flaws: Flaw 1: Misleading Graphs The bar chart in Figure 1-1 is very deceptive. By using a vertical scale that does not start at zero, the difference between the two percentages is grossly exaggerated. Deceptive graphs are discussed in more detail in Section 2-3. Flaw 2: Bad Sampling Method Figure 1-1 and Figure 1-2 are based on data from the Pearson survey cited earlier. This study included 2587 respondents from a nationally representative sample, and the sampling method appears to be sound based on the description provided in the report. However, many other surveys obtain participants by using methods that are inappropriate and may lead to biased results, such as these: • Voluntary response sample: Participants decide themselves whether to participate. Example: A survey question is posted on a website, and then Internet users decide whether to respond. With a voluntary response sample, it often happens that those with a strong interest in the topic are more likely to participate, so the results are very questionable. • Convenience sample: Participants are selected because they are easy to reach and are readily available. Example: A student conducts a survey of fellow students relaxing in the cafeteria. When using sample data to learn something about a population, it is extremely important to obtain sample data that are representative of the population from which the data are drawn. As we proceed through this chapter and discuss types of data and sampling methods, we should focus on these key concepts: • Sample data must be collected in an appropriate way, such as through a process of random selection. • If sample data are not collected in an appropriate way, the data may be so completely useless that no amount of statistical torturing can salvage them. It is all too easy to analyze sample data without thinking critically about how the data were collected. We could then develop conclusions that are fundamentally wrong and misleading. Instead, we should develop skills in statistical thinking and critical thinking so that we can distinguish between collections of sample data that are good and those that are seriously flawed. FIGURE 1-1 YouTube as a Preferred Learning Tool FIGURE 1-2 Same as Figure 1-1 but with scale beginning with 0% 2 CHAPTER 1 Introduction to Statistics
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