Interpreting and Using Statistics in Psychological Research. Andrew N. Christopher
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necessary a qualification for efficient citizenship as the ability to read and write.”
—H. G. Wells
When I was in high school and college, I took a math-based class (e.g., algebra, geometry, statistics, and calculus) every semester. I did fairly well in these classes because I worked hard and usually earned decent grades, never spectacular but not bad either. Playing around with numbers was a fun intellectual exercise for me back then. During that same time, I took writing-based classes (e.g., composition, creative writing, business communications, and literature). At the risk of being arrogant, I usually earned solid “A”s in those classes (and even some “A+”s because we could get those at my high school). Candidly, I did not work nearly as hard in my writing classes as I did in my math classes. I was by no means a gifted writer, but thanks in large part to my parents, I always understood the importance of writing and communication abilities even when I was in middle school. Indeed, how can good writing and other communication skills do anything but help a person in a job or many other life situations, such as developing personal relationships? I took more writing classes than my high school and college required just because they were so much fun and easy for me. Math classes? Not so much. Until I was in graduate school, I never saw the relevance of math classes outside of the classroom. Then, in my third graduate-level statistics class (yes, you read that correctly, my third graduate-level statistics class), something clicked. Even now, 19 years later, I don’t know what it was that clicked. But something clicked, and I began understanding the relevance of the numbers I was using. When I began to see the logic of each statistic that I was calculating, all I wanted to do was learn more about statistics. And as I did so, I understood the logic of statistics, even fairly high-level statistics, more quickly and became much better able to use such logic not only in research but in “real-life” situations as well.
Photo 1.1 Statistical information is everywhere. Understanding it is essential for success not just in school, but also in life more generally.
Source: ©Bradford Veley/CartoonStock
Maybe I was not very smart in high school or college, but I look back at that time and cannot understand what took me so long to see the logic behind statistics. When I started teaching statistics more than 15 years ago, I swore that my students would leave the class understanding the logic of statistics. Some have gone on and used statistics in research careers; most have not. Those who are not using technical statistics in their work are still dealing with situations that require the same logical thinking that statistics requires. If you are interested in doing research or are already enthusiastic about dealing with quantitative information, you probably don’t need to be sold on the idea that statistics will be important to you. However, before we dive into specific statistical information, I want to take some time to discuss the general importance of statistics, both to researchers and to alike. For those of you taking this class solely because you have to take it, I hope it will give you some idea of why you are here and the benefits you should expect to gain while you are here. It is my hope that by the time you complete this class, you will understand the importance of statistics in making sense of research, in addition to using the logic of statistical thinking in more everyday situations.
In the first part of this chapter, we will discuss why a lot of people are not good at using statistical logic in their daily lives. I do not want you to be like a lot of people in this regard as it can be costly in many ways. We will highlight the reasons most people are not good at dealing with statistical information in daily life and, in doing so, detail some of these everyday situations, describing how statistical logic is (or should be) used in each one. The second section will discuss some basic goals of research and the role that statistics play in achieving each of these goals. Finally, we will introduce some basic statistical information we will see throughout this course and, in doing so, highlight how such information can improve our ability to think about the world.
Statistical Thinking and Everyday Life
We easily can get our hands on information via the Internet for any situation we may be in. However, we need to know how to interpret and make use of such information, especially as not all of it is objective or even correct. The world is full of statistical information, much of it we hardly ever notice or pay much attention to (until now). In addition to potential value in the workplace, learning about statistics and the logic behind them will help you navigate everyday situations you will encounter, some of which we’ll discuss in this section.
Before we begin this section in detail, let me say that, in general, the human mind works magnificently well. We rarely notice how well it works until something goes wrong. I say this because as you read this section of the chapter, you might think people are generally stupid, but that is just not the case. But here, I want to draw your attention to some flaws in our ability to process information as they relate to statistical thinking. By learning about statistics in subsequent chapters, I hope that you will be able to spot these shortcomings in your thinking and in the thinking of other people.
“What has been very successful for me through my whole life is to not be arrogant about knowing, but to embrace the fact that I have weaknesses, that I don’t know a lot about this, that and the other thing. The more you learn, the more you realize you don’t know.”
—Ray Dalio, Founder and Co–Chief Investment Officer, Bridgewater Associates, the world’s largest hedge fund
I have classified these flaws in human thinking loosely into two categories: failing to use information about probability and misunderstanding connections between events. However, in practice, they are more interrelated than I will present them here.
Failing to Use Information About Probability
Last night, I put my life in great jeopardy. I did so voluntarily. What did I do, you ask? I carried dirty clothes downstairs and did laundry.
If you are wondering what the risk was, more than 8 million visits to the emergency room each year are due to falls at home, and more than 17,000 people in the United States die each year from such falls and resulting complications (National Safety Council, 2015). Now, I said I put my life in “great jeopardy.” Almost anything we do (e.g., walking, exercising, or eating) carries some risk. While walking, we could trip and fall. While exercising, we could dislocate a joint. While eating, we could choke or ingest something poisonous. So, I need to clarify what I meant by “great jeopardy.” I am guessing the risks associated with these everyday behaviors have not crossed your mind unless, of course, they have happened to you. However, other risks may well have crossed your mind. Terrorism is in the news a lot. There is a chance you could be a victim of terrorism. However, how great is that risk? The U.S. Department of State (2014) reported that worldwide, 16 Americans died from terrorist-related activity worldwide in 2013. Another 12 Americans were kidnapped and another 7 were injured from terrorism. Compare that total (35 Americans) with the 17,000 Americans who die from falling each year. I have a 485 times greater chance of dying trying to do my laundry than I do of dying in a terrorist attack. Based on these statistics, should we be more concerned about falling at home or about terrorism?
Even with this statistical information, you may not be convinced that terrorism is less of a threat than is falling at home, and that is understandable. We tend to ignore probabilities for a very good reason. We need to make a lot of decisions in our lives. We make decisions all of the time. What class to study for first? Go running or go to yoga (or, in my case, what TV show to watch)? What to eat for a snack? What to wear today? We make many of our decisions using heuristics, which are mental shortcuts, based on prior experience, that allow us to make decisions quickly. Let’s take a simple example. Suppose you are at the grocery store needing to buy toothpaste; you probably would not look in the fresh produce section. Likewise, if you want to buy fresh strawberries, you probably would not look on the baking supplies isle. Did you ever notice those signs above the various isles in the grocery store (and many other types of stores)? Those signs are heuristics in that they give shoppers a general idea of the products contained