Interpreting and Using Statistics in Psychological Research. Andrew N. ChristopherЧитать онлайн книгу.
nutritional labels for each type of Ruffles, indeed, the Baked Ruffles have more than 50% less fat than Original Ruffles. However, the Original Ruffles have more potassium than do Baked Ruffles. Examining the protein, vitamin, and mineral contents of each bag, they are both low on all dimensions. When we look at the data regarding nutritional content of both types of Ruffles, we see that in terms of vitamins and minerals, there is no big health advantage to Baked Ruffles (maybe less of a “health disadvantage”), no matter how healthy an image such a label may create in our minds. If I want to eat something healthy, data suggest eating snacks such as peppers, bananas, and apples.
Photo 1.6a and 1.6b Are baked chips really better for you?
Representativeness heuristic
The availability heuristic is one barrier to using statistical information. There is another heuristic we use that also makes it difficult to use statistical information. To start this discussion, let me to tell you about my cousin Adam. When he was a toddler, he lived in a house with two dogs. So when Adam saw any four-legged, furry creature, he called it “doggie.” One day when we were at a petting zoo, he saw what I, as a teenager, knew was a horse. But to him, it was a “big doggie.” And indeed, dogs and horses do share some outward similarities (e.g., four legs, fur, and a tail). One difference between dogs and horses is that whereas dogs bark, horses neigh.
So when this “big doggie” neighed, Adam looked most perplexed. That sound did not fit in his mental notion of “dog.” He was forced to change his mental picture of what a dog was, and in addition, he needed to create a new, distinct mental category for this creature he had encountered called a “horse.” In this example, Adam was using the representativeness heuristic (Gilovich & Savitsky, 2002). That is, he had created a mental category of “dog” that included all animals with four legs, fur, and a tail.
Representativeness heuristic: judging how likely something or someone is to the typical instance of a mental category that we hold; can lead us to ignore other relevant information.
So what’s the problem that representativeness plays in our thinking? Those mental categories had to come from somewhere, and indeed, they are often correct or else we would stop using them. In Adam’s situation, the sound that the horse made forced him to redefine his mental category of “dog.” This may not be too difficult to do at least in theory. But remember, I want you to be aware of when our thinking goes awry and how such missteps are rooted in statistical thinking.
Photo 1.7 They look similar, don’t they?
Source: ©iStockphoto.com/GlobalP; ©iStockphoto.com/fotojagodka
There are two potentially problematic results of using representativeness that we will discuss. First, the base-rate fallacy is the tendency to ignore information that describes (i.e., represents) most people or situations. Rather, we rely on information that fits a mental category we have formed (Bar-Hillel, 1980). To take a simple example, approximately 90% of the students at my college are from Michigan, Indiana, and Ohio. At first-year orientation this fall, I talked with a tall, athletic-looking, suntanned student who had long blond hair and was wearing a Ron Jon Surf Shop® (Cocoa Beach, FL) T-shirt. Where was he from? California? Florida? Perhaps. But without knowing any additional information, you have a 90% chance of being correct (assuming you say “Michigan,” “Indiana,” or “Ohio”). Even though the description seems to fit someone from California or Florida, those states are sparsely represented in our student body. Thus, there was minimal chance he was from one of those places despite fitting our mental category of “Californian” or “Floridian.” Let’s explore the base-rate fallacy in a little more detail.
Base-rate fallacy: tendency to prefer information derived from one’s experience and ignore information that is representative of most people or situations.
When we started this chapter, I lamented that we as humans often have difficulty thinking statistically. Again, 90% of the student population at my college is from three states. Therefore, the probability of a student being from any of the other 47 states or another country is low. That probability is even lower for any one specific state of those 47. However, in this instance, the only thing I “saw” was that one student I talked with at orientation. He was a sample of the entire student body at my college. The entire study body at my college consists of people primarily from three states. Therefore, even though he fit my mental representation of “Californian” or “Floridian,” the odds are that he was from Michigan, Indiana, or Ohio.
One danger, in terms of statistical thinking, of our everyday experiences is that rarely, if ever, do we have all of the information about a given situation (we are egocentric, remember). Much as we can rarely, if ever, be familiar with everyone in a large group of people, we rely on our personal experiences to draw conclusions about the world. An extension of the base-rate fallacy is the law of small numbers, which is the second potential problem with using representativeness. The law of small numbers holds that results based on a small number of observations are less likely to be accurate than are results based on a larger number of observations (Asparouhova, Hertzel, & Lemmon, 2009; Taleb, 2004). We assume that our experiences are representative of the larger world around us when, in fact, that is not always the case. For instance, when you toss a coin, there is a 50% chance the coin will land on heads and a 50% chance it will lands on tails. If you flip that coin four times, you would expect it to land on heads twice and on tails twice. That would be 50/50, just the way coin tosses should turn out. However, with only four flips of the coin, weird things might happen. You might flip three tails but only one heads. Or maybe all four flips will be heads. Does this mean the coin is “fixed”? No. Rather, with such a small number of flips (i.e., a small sample), you might get outcomes that are markedly different than what you would expect to find (i.e., all coin flips in history). Flip a coin 20 times. I bet you will not get exactly 10 heads and 10 tails, but overall, it should be closer to 50/50 than 75/25. Now flip the coin 40 times, and again, you are likely to be closer to 50/50 than you were with 20 flips.2
Law of small numbers: results based on small amounts of data are likely to be a fluke and not representative of the true state of affairs in the world.
Let’s take another, more mundane example of the law of small numbers. You are thinking about where to go for dinner tonight. Your roommate said a friend of hers really liked the local pizza place. Based on this information, you decide to have dinner at the local pizza place. How is this instance an example of the law of small numbers? Let me ask you, how much information did you gather to make your decision? You have a suggestion from one friend of your roommate; that is all. So, with one piece of data, you drew your conclusion of where to eat dinner. Let’s hope your food preferences are similar to those of your roommate’s friend. Had you read reviews of this restaurant, you would have had more data on which to base your decision of where to eat.
As one real-world example of the law of small numbers, many people are afraid to invest their money in stocks because they think bonds are a safer investment. However, a great deal of research (e.g., Index Fund Advisors, 2014) has demonstrated that over the long term, investing in stocks is the best way to grow one’s money. Since 1928, the U.S. stock market’s average annual return has been about 9.6%. During that same time span, U.S. government long-term bonds have grown on average by only about 5.4% each year. So, when deciding where to invest our money, clearly it should go into the stock market, right? Maybe. Keep in mind that 1928 was a long, long time ago. Over a long period of time, then yes, the stock market has indeed been the best investment available. However, you know enough about history to know what happened in October 1929, again in October 1987, and in the fall of 2008. There are comparatively small pockets of time during which stocks do poorly, sometimes disastrously so. These time periods are the exceptions, but if it is your money being lost when stocks decline in value, you probably