Interpreting and Using Statistics in Psychological Research. Andrew N. Christopher

clothes for some hint of what they are like. If someone is wearing a University of Florida T-shirt, you might ask them if they are from the state of Florida and perhaps mention you visited there (assuming that you did). You look for something, anything, to break the uneasiness of that situation. Even for the most socially outgoing among us, it is an awkward situation. So, you start looking to make connections with these people.

      Figure 1.2 Two Equally Likely Outcomes

      Our need to make connections is powerful. The world is much less stressful when it is predictable. Therefore, our minds seek to make connections between events in the world. We will highlight two of these tendencies now. The first tendency concerns perceiving connections that in fact do not exist. The second of these tendencies is a result of the first and concerns the misinterpretation of future events based on prior events.

      Illusory correlations

      To start a discussion of the first of these two tendencies, take a look at these two poker hands of cards in Figure 1.2. Which one is a player more likely to be dealt? A hand of 10 through ace, all of the same suit, feels highly unlikely. However, in reality, the odds of getting that hand are no lower than the odds of getting the other, seemingly random, hand of cards. We are wired as human beings to detect patterns in the world, and so it is here. We feel as though the 10 through ace is a more unusual hand than the other hand of cards. Statistically, however, the odds of getting either one are the same. This is an example of an illusory correlation. By “illusory,” we mean “not real” or an “illusion.” By correlation, we mean an “association” or “connection” between two behaviors or events. Much as an optical illusion is seeing something that is not present, an illusory correlation is perceiving a relationship when no relationship exists (Fiedler, 2000). We want the world to be a predictable, orderly place. So our minds impose order and logic even when order and logic do not exist.

      Illusory correlation: tendency to perceive a relationship when no relationship really exists.

      Let’s discuss some additional examples of illusory correlations. In college, I had a roommate, Alex, who was not only a nice guy, but smart, too. Alex worked hard and never took his natural intellectual ability for granted. He did well in all of his classes, and he went on to become an immigration lawyer in South Florida. We were roommates for our entire college careers, and he is still a good friend to this day. I am sure this information does not impress you. But here is what might impress you. Take a guess as to why Alex did so well in college and beyond. His intelligence? His hard work? Those would be reasonable guesses. Ask Alex, however, and he will tell you something different. Let me explain. In our first year of college, we had our first round of tests about five weeks into the semester. We both had two or three tests that week. Of course, as would become the norm, Alex did well on these assessments. About five weeks later, we had our second round of tests and papers coming due. Because Alex had done so well on tests and papers earlier in the semester, I asked him for some study tips. Here is what he told me: He told me that I could not wear his pair of “lucky socks.” They were his lucky socks, and no one else could wear them. He had worn them every day during the week of our first round of tests and papers, and because he did so well, he was going to wear them again when tests and papers came due. Of course, I thought he was joking, but no, it quickly became clear that in his mind, the reason he did well on tests was because of his lucky pair of socks. By believing, albeit erroneously, that his pair of socks aided his performance on his tests, Alex was able to feel as though he had gained some control over his environment. The next time he had a test, he just needed to wear that same pair of socks again, and he would do well.⁴

      Photo 1.9a and 1.9b Does a “lucky” charm really help us get good grades?

      If you have ever played a sport or been involved in the performing arts, did you ever have some sort of pre-performance routine that you felt you had to follow? Just like my college roommate and his belief that wearing a certain pair of socks contributed to his academic success, some highly accomplished professional athletes have pre-performance routines that they follow. For instance, three-time Ironman champion Chrissie Wellington wrote the Rudyard Kipling poem “If” on her water bottles before each event. Similarly, professional baseball player Justin Verlander reportedly used to eat Taco Bell® (Yum! Brands Inc., Louisville, KY) the night before the games in which he was the starting pitcher. Is there really a relationship between writing a poem on a water bottle and performance in an Ironman event? How about between eating Taco Bell and pitching a baseball? I doubt it; however, for these athletes, they have come to make these connections in their minds.

      Illusory correlations arise in part, as we said previously, from our need to detect order in the world. To satisfy this need, we tend to pay attention to instances that confirm this connection and disregard those instances that disconfirm that connection. Did my roommate ever do poorly on a test? Yes, actually, a few times he did. But in his mind, those exceptions had nothing to do with his socks. Did Chrissie Wellington win every race she competed in? No, but in her mind, she likely would have done even worse had she not written that poem on her water bottles. Indeed, once we establish relationships between events in our mind, they are difficult to dislodge.

      Gambler’s fallacy

      Our second obstacle in understanding connections between events is closely related to the illusory correlation. The gambler’s fallacy is a thinking tendency that involves making a connection between prior outcomes and future outcomes when those outcomes are independent of each other (Nickerson, 2002). Let’s discuss some examples of the gambler’s fallacy.

      Gambler’s fallacy: tendency to think that two mutually exclusive outcomes are somehow related.

      After graduating from high school in Texas, I went to college in a small town in Florida. At that time, Texas did not have a lottery, but Florida did have one. So, a few weeks after starting college, I decided to buy a lottery ticket for the weekly drawing on Saturday nights. I did so each week during my first year in college. By late April of that school year, I had won nothing. I figured I was overdue to win something, so instead of buying one ticket that week, I bought five tickets. After all, with such a long losing streak, I was bound to win something at some point, right? If you are shaking your head at my logic, good for you. My logic is an example of the gambler’s fallacy. That is, I thought that a previous outcome (not winning lottery money) was somehow connected to a future event (likelihood of winning lottery money) when in fact there was no connection between the prior outcome and the future outcome.

      To take another example of the gambler’s fallacy, consider the game of roulette. The dealer spins the wheel and a ball lands in one of the slots, each of which has a number and color associated with it. Players can bet on what color the ball lands on (red, black, or green), which specific number or set of numbers (e.g., evens or odds) the ball lands on, and so on. I have this game, and I decided to spin the wheel 50 times. Here are the outcomes of those spins. The color of the number represents whether it is a “red” or “black” number (or a “gray” number in a few outcomes). The first column is the first 10 spins, the second column is the second 10 spins, and so on.

      “Red number outcomes appear in blue font”

      Look at the first 10 spins. There were 8 black numbers that came up. So, on the 11th spin, it would just seem I was overdue for a red number. But of course, the 11th outcome had nothing to do with the first 10 outcomes, and indeed, the 11th outcome was another black number. The odds of the ball landing on a red number or a black number are the same for the 12th spin as they were for each of the first 11 spins.

      You might be thinking at this point that these examples of the gambler’s fallacy