Description
Why Use Statistics?
As a researcher who uses statistics frequently, and as an avid listener of talk radio, I find myself yelling at my radio daily. Although I realize that my cries go unheard, I cannot help myself. As radio talk show hosts, politicians making political speeches, and the general public all know, there is nothing more powerful and persuasive than the personal story, or what statisticians call anecdotal evidence. My favorite example of this comes from an exchange I had with a staff member of my congressman some years ago. I called his office to complain about a pamphlet his office had sent to me decrying the pathetic state of public education. I spoke to his staff member in charge of education. I told her, using statistics reported in a variety of sources (e.g., Berliner and Biddle’s The Manufactured Crisis and the annual “Condition of Education” reports in the Phi Delta Kappan written by Gerald Bracey), that there are many signs that our system is doing quite well, including higher graduation rates, greater numbers of students in college, rising standardized test scores, and modest gains in SAT scores for all races of students. The staff member told me that despite these statistics, she knew our public schools were failing because she attended the same high school her father had, and he received a better education than she. I hung up and yelled at my phone.
Many people have a general distrust of statistics, believing that crafty statisticians can “make statistics say whatever they want” or “lie with statistics.” In fact, if a researcher calculates the statistics correctly, he or she cannot make them say anything other than what they say, and statistics never lie. Rather, crafty researchers can interpret what the statistics mean in a variety of ways, and those who do not understand statistics are forced to either accept the interpretations that statisticians and researchers offer or reject statistics completely. I believe a better option is to gain an understanding of how statistics work and then use mat understanding to interpret the statistics one sees and hears for oneself. The purpose of this book is to make it a little easier to understand statistics.
Uses of Statistics
One of the potential shortfalls of anecdotal data is that they are idiosyncratic. Just as the congressional staffer told me her father received a better education from the high school they both attended than she did, I could have easily received a higher quality education than my father did. Statistics allow researchers to collect information, or data, from a large number of people and then summarize their typical experience. Do most people receive a better or worse education than their parents? Statistics allow researchers to take a large batch of data and summarize it into a couple of numbers, such as an average. Of course, when many data are summarized into a single number, a lot of information is lost, including the fact that different people have very different experiences. So it is important to remember that, for the most part, statistics do not provide useful information about each individual’s experience. Rather, researchers generally use statistics to make general statements about a population. Although personal stories are often moving or interesting, it is often important to understand what the typical or average experience is. For this, we need statistics.
Statistics are also used to reach conclusions about general differences between groups. For example, suppose that in my family, there are four children, two men and two women. Suppose that the women in my family are taller than the men. This personal experience may lead me to the conclusion that women are generally taller than men. Of course, we know that, on average, men are taller than women. The reason we know this is because researchers have taken large, random samples of men and women and compared their average heights. Researchers are often interested in making such comparisons: Do cancer patients survive longer using one drug than another? Is one method of teaching children to read more effective than another? Do men and women differ in their enjoyment of a certain movie? To answer these questions, we need to collect data from randomly selected samples and compare these data using statistics. The results we get from such comparisons are often more trustworthy than the simple observations people make from nonrandom samples, such as the different heights of men and women in my family.
Statistics can also be used to see if scores on two variables are related and to make predictions. For example, statistics can be used to see whether smoking cigarettes is related to the likelihood of developing lung cancer. For years, tobacco companies argued that there was no relationship between smoking and cancer. Sure, some people who smoked developed cancer. But the tobacco companies argued that (a) many people who smoke never develop cancer, and (b) many people who smoke tend to do other things that may lead to cancer development, such as eating unhealthy foods and not exercising. With the help of statistics in a number of studies, researchers were finally able to produce a preponderance of evidence indicating that, in fact, there is a relationship between cigarette smoking and cancer. Because statistics tend to focus on overall patterns rather than individual cases, this research did not suggest that everyone who smokes will develop cancer. Rather, the research demonstrated that, on average, people have a greater chance of developing cancer if they smoke cigarettes than if they do not.
With a moment’s thought, you can imagine a large number of interesting and important questions that statistics about relationships can help you answer. Is there a relationship between selfesteem and academic achievement? Is there a relationship between the appearance of criminal defendants and their likelihood of being convicted? Is it possible to predict the violent crime rate of a state from the amount of money the state spends on drug treatment programs? If we know the father’s height, how accurately can we predict son’s height? These and thousands of other questions have been examined by researchers using statistics designed to determine the relationship between variables in a population.