Interpreting and Using Statistics in Psychological Research. Andrew N. Christopher
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wheel). And indeed, you are correct. As we said at the outset of this section of the chapter, these issues in statistical thinking are closely related. With the gambler’s fallacy, it is more likely to manifest itself in our thinking when we have only a limited number of observations available. Take a look back at the outcomes of my 50 spins of the roulette wheel. If you take only my first 10 spins, it looks like the wheel is somehow “fixed” because so many black numbers emerged. But then consider the middle 10 spins; here, we have disproportionately more red numbers emerge. However, on average across the 50 spins, the emergence of red and black numbers is close to 50% each (24 black numbers and 23 red numbers).
Photo 1.10 A roulette table and a roulette wheel.
Source: ©iStockphoto.com/macrovector
Let’s consider a nongambling example of the gambler’s fallacy. In well-known research, Thomas Gilovich and his colleagues (Gilovich, Vallone, & Tversky, 1985) examined the belief that basketball players have “hot streaks” when shooting the ball. That is, if basketball players have made a few shots consecutively, are they more likely to make their next shot than if they had missed their previous shot? In other words, is there a connection between the prior outcome (i.e., making a previous shot) and a future outcome (i.e., making one’s next shot)? Gilovich and his colleagues examined shooting statistics for the Philadelphia 76ers and the Boston Celtics for the 1980–1981 season. For the 76ers, it was found that players were slightly less likely to make a shot after making their previous shot (51%) than after missing their previous shot (54%). Furthermore, the odds of making a shot after making the previous three or four shots (50%) were slightly lower than the odds of making a shot after missing the previous three or four shots (57%). For the Celtics, it was found that players are no more likely to make a second free throw attempt after making the previous free throw attempt or missing that first attempt. In fact, the team as a whole made 75% of its second free throw attempts after making the first free throw, and it made 75% of its second free throws after missing the first one. Taken together, these data strongly suggest that there is no “hot hand” in shooting a basketball even though it may feel that way when playing or watching a game.
Learning Check
1 In college, it sometimes seemed as though the harder I studied for a test, the worse I did on it. Explain how my thinking could be an example of an illusory correlation.A: If I study hard, I should do well on tests. If I don’t study hard, I should do poorly on tests. Those are normal states of affairs. What I recall, though, are the “weird” instances in which I studied hard but did poorly on a test. Because such instances are rare, they stand out and are easier to recall. Thus, I’ve made a false (illusory) connection between my study habits and test scores.
2 If a couple has had three children who were all girls, they might assume their fourth child is likely to be a boy. Explain why the couple might think their fourth child is likely to be a boy.A: There should be an “evening out” that occurs eventually (or so it feels to this couple). Of course, the sex of their fourth child has nothing to do with the sex of their first three children. This is an example of the gambler’s fallacy.
3 Explain why some people have a “lucky charm” that they like to carry with them wherever they go.A: People have established a connection in their mind between an object and desirable outcomes that resulted from that object. That’s how it became a “lucky charm” to them. For instance, some students have a “lucky pen” that they like to write with. For whatever reason, they have developed an illusory correlation that the pen is associated with good things, so they keep it with them. Likewise, some people may have a “lucky coin” that they keep in their possession at all times, figuring it will bring them good luck (or at least avoid bad luck). Indeed, illusory correlations are pervasive!
Goals of Research
As we have discussed, we as humans tend to have “efficient flaws” in our thinking. They are efficient because they allow us to navigate the world quickly and prevent us from exhausting our cognitive capacities. They are flaws, though, because they allow for mistakes in how we think about the world. When conducting scientific research, we want to do what we can to minimize mistakes. This is where statistics can help. I find it helps students to approach classes in statistics with the mind-set that statistics are tools we need to understand research. Just as we need a screwdriver to tighten a loose screw or scissors to cut paper, we need statistics to understand scientific research. The goal of a research study will guide the type of statistic (or tool) that the researcher needs to use. We now examine four goals of scientific research.
Scientific research in psychology has four overriding goals: (1) to describe, (2) to predict, (3) to explain, and (4) to apply behavioral and cognitive phenomena. The first three goals have different statistical tools associated with them, which we will discuss as we present each goal in turn now.
Goal: To Describe
Descriptive research aims to communicate variables as they exist in the world. To conduct descriptive research, we need to make observations and measurements of the phenomena we want to study. If you want to know the temperature outside, a thermometer located outside can provide this information. The temperature is descriptive information. If we want to describe the health-related behaviors of college students, we can take measurements of how much sleep they get each night, how many times per week they exercise, and their daily fruit and vegetable consumption. We could then describe the health-related behaviors of college students along these dimensions.
How might we go about collecting data to describe the health behaviors of college students? First, we can conduct observational studies. By using naturalistic observation, we could sit in the student cafeteria and record what students eat. Likewise, we can go to the student recreational facility and see how many students work out there, including the types of exercises that they perform. Naturalistic observation will be more difficult to use to record sleep habits; however, we might use laboratory observations, in which we observe behavior in a more controlled setting, such as a research laboratory. In this case, we could have a bed available and record how long students sleep.
In addition to observational research, we can use case studies to describe behavior. A case study involves studying one or more people in great depth. We could examine the health behaviors of a small number, perhaps three or four, college students. An advantage of using the case study method over observational studies is that we can go into great detail on the behaviors of this small sample. In addition, case studies are particularly useful when studying rare phenomena, such as certain diseases that occur in only a few people. The disadvantage, though, is that it is extremely time-consuming to conduct a large number of case studies, especially if we want the research to be representative of the college student population.
Finally, surveys can be used to describe behavior. In our case, we would ask questions of college students about their health-related behaviors. Surveys can be administered through questionnaires via campus mail, over the Internet, or in a research lab setting. Likewise, surveys can be administered as interviews either in person or over the phone. Questionnaires are advantageous because the researcher asks respondents to provide the same information. Interviews are advantageous because the researchers can ask follow-up questions depending on a respondent’s answers. Surveys are particularly helpful because it is easier to collect more data than with case studies or most observational research. However, researchers must pay close attention to the wording of the questions to make sure respondents are interpreting them correctly. We must also be sure that the sample of survey respondents is representative of the population we want to study. In this case, it might only be the more health-conscious students who complete a survey. If that happens, our sample data will not reflect the population of college students.
Descriptive research: depicts variables as they exist in the world.
Observational studies: consist of watching