a theory of juvenile delinquency, prejudice, or political revolution. Theories explain observations by means of concepts. Jonathan Turner (1989: 5) calls concepts the "basic building blocks of theory." Concepts are abstract elements representing classes of phenomena within the field of study. The concepts relevant to a theory of juvenile delinquency, for example, include "juvenile" and "delinquency," for starters. A "peer group"— the people you hang around with and identify with—is another relevant concept. "Social class" and "ethnicity" are undoubtedly relevant concepts in a theory of juvenile delinquency. "School performance" might also be relevant. A variable is a special kind of concept. Some of the concepts just mentioned refer to things, and others refer to sets of things. As we saw in Chapter 1, each variable comprises a set of attributes; thus, delinquency, in the simplest case, is made up of delinquent and not delinquent. A theory of delinquency would aim at explaining why some juveniles are delinquent and others are not. Axioms or postulates are fundamental assertions, taken to be true, on which a theory is grounded. In a theory of juvenile delinquency, we might begin with axioms such as "Everyone desires material comforts" and "The ability to obtain material comforts legally is greater for the wealthy than for the poor." From these we might proceed to propositions: specific conclusions, derived from the axiomatic groundwork, about the relationships among concepts. From our beginning axioms about juvenile delinquency, for example, we might reasonably formulate the proposition that poor youths are more likely to break the law to gain material comforts than are rich youths. This proposition, incidentally, accords with Robert Merton's classic attempt to account for deviance in society. Merton (1957: 139-57) spoke of the agreed-on means and ends of a society. In Merton's model, nondeviants are those who share the societal agreement as to desired ends (such as a new car) and the means prescribed for achieving them (such as to buy it). One type of deviant—Merton called this type the "innovator"—agrees on the desired end but does not have access to the prescribed means for achieving it. Innovators find another method, such as crime, of attaining the desired end. Two Logical Systems Revisited ■ 45 From propositions, in turn, we can derive hypotheses. A hypothesis is a specified testable expectation about empirical reality that follows from a more general proposition. Thus, a researcher might formulate the hypothesis, "Poor youths have higher delinquency rates than do rich youths." Research is designed to test hypotheses. In other words, research will support (or fail to support) a theory only indirectly—by testing specific hypotheses that are derived from theories and propositions. Let's look more clearly at how theory and research come together. Two Logical Systems Revisited The Traditional Model of Science Most of us have a somewhat idealized picture of "the scientific method." It is a view gained as a result of the physical-science education we've received ever since our elementary school days. Although this traditional model of science tells only a part of the story, it's helpful to understand its logic. There are three main elements in the traditional model of science: theory, operationaliza-tion, and observation. At this point we're already well acquainted with the idea of theory. Theory According to the traditional model of science, scientists begin with a thing, from which they derive testable hypotheses. For example, as social scientists we might have a theory about the causes of juvenile delinquency. Let's assume that we have arrived at the hypothesis that delinquency is inversely related to social class. That is, as social class goes up, delinquency goes down. Operationalization To test any hypothesis, we must specify the meanings of all the variables involved in it, in hypothesis A specified testable expectation about empirical reality that follows from a more general proposition; more generally, an expectation about the nature of things derived from a theory. It is a statement of something that ought to be observed in the real world if the theory is correct. 04945_ch02_ptg01.indd 45 8/21/14 11:24 AM 46 ■ Chapter 2: Paradigms,Theory, and Social Research observational terms. In the present case, the variables are social class and delinquency. To give these terms specific meaning, we might define delinquency as "being arrested for a crime," "being convicted of a crime," or some other plausible phrase, whereas social class might be specified in terms of family income, for the purposes of this particular study. Once we have defined our variables, we need to specify how we'll measure them. (Recall from Chapter 1 that science, in the classical ideal, depends on measurable observations.) Operationalization literally means specifying the exact operations involved in measuring a variable. There are many ways we can attempt to test our hypothesis, each of which allows for different ways of measuring our variables. For simplicity, let's assume we're planning to conduct a survey of high school students. We might operationalize delinquency in the form of the question "Have you ever stolen anything?" Those who answer "yes" will be classified as delinquents in our study; those who say "no" will be classified as nondelinquents. Similarly, we might operationalize social class by asking respondents, "What was your family's income last year?" and providing them with a set of family income categories: under $10,000; $10,000-$24,999; $25,000-$49,999; $50,000-$99,999; $100,000 and above. At this point someone might object that delinquency can mean something more than or different from having stolen something at one time or another, or that social class isn't necessarily the same as family income. Some parents might think body piercing is a sign of delinquency even if their children don't steal, and to some, social class might include an element of prestige or community standing as well as how much money a family has. For the researcher testing a operationalization One step beyond conceptualization. Operationalization is the process of developing operational definitions, or specifying the exact operations involved in measuring a variable. operational definition The concrete and specific definition of something in terms of the operations by which observations are to be categorized. The operational definition of "earning an A in this course" might be "correctly answering at least 90 percent of the final exam questions." hypothesis, however, the meaning of variables is exactly and only what the operational definition specifies. In this respect, scientists are very much like Humpty Dumpty in Lewis Carroll's Through the Looking Glass [1895] 2009. "When / use a word," Humpty Dumpty tells Alice, "it means just what I choose it to mean—neither more nor less." "The question is," Alice replies, "whether you can make words mean so many different things." To which Humpty Dumpty responds, "The question is, which is to be master—that's all" ([1895] 2009: 190) Scientists have to be "masters" of their operational definitions for the sake of precision in observation, measurement, and communication. Otherwise, we would never know whether a study that contradicted ours did so only because it used a different set of procedures to measure one of the variables and thus changed the meaning of the hypothesis being tested. Of course, this also means that to evaluate a study's conclusions about juvenile delinquency and social class, or any other variables, we need to know how those variables were operationalized. The way we have operationalized the variables in our imaginary study could be open to other problems, however. Perhaps some respondents will lie about having stolen anything, in which cases we'll misclassify them as nondelinquent. Some respondents will not know their family incomes and will give mistaken answers; others may be embarrassed and lie. We'll consider issues like these in detail in Part 2. Our operationalized hypothesis now is that the highest incidence of delinquents will be found among respondents who select the lowest family income category (under $10,000); a lower percentage of delinquents will be found in the $10,000-$24,999 category; still fewer delinquents will be found in the $25,000-$49,999 and $50,000-$99,999 categories; and the lowest percentage of delinquents will be found in the $100,000 and above categoriey. Now we're ready for the final step in the traditional model of science—observation. Having developed theoretical clarity and specific expectations, and having created a strategy for looking, all that remains is to look at the way things actually are. 04945_ch02_ptg01.indd 46 8/21/14 11:24 AM Observation The final step in the traditional model of science involves actual observation, looking at the world and making measurements of what is seen. Let's suppose our survey produced the following data: Percent Delinquent Under $10,000 20 $10,000-$24,999 15 $25,000-$49,999 10 $50,000-$99,999 5 $100,000 and above 2 Observations producing such data would confirm our hypothesis. But suppose our findings were as follows: Percent Delinquent Under $10,000 15 $10,000-$24,999 15 $25,000-$49,999 15 $50,000-$99,999 15 $100,000 and above 15 These findings would disconfirm our hypothesis regarding family income and delinquency. Disconfirmability, or the possibility of falsification, is an essential quality in any hypothesis. In other words, if there is no chance that our hypothesis will be disconfirmed, it hasn't said anything meaningful. You cannot test whether a hypothesis is true unless your test contains the possibility of deciding it is false. For example, the hypothesis that juvenile delinquents commit more crimes than do nondelin-quents cannot possibly be disconfirmed, because criminal behavior is intrinsic to the idea of delinquency. Even if we recognize that some young people commit crimes without being caught and labeled as delinquents, they couldn't threaten our hypothesis, because our actual observations would lead us to conclude they were law-abiding nondelinquents. Figure 2-2 provides a schematic diagram of the traditional model of scientific inquiry. In it we see the researcher beginning with an interest in Two Logical Systems Revisited ■ 47 THEORETICAL UNDERSTANDING X causes Y HYPOTHESIS Y =f(X) Theoretical expectation Operationalization y = f(x) Testable hypothesis L • y = f (x) Observation (hypothesis testing) FIGURE 2-2 The Traditional Image of Science. The deductive model of scientific inquiry begins with a sometimes vague or general question, which is subjected to a process of specification, resulting in hypotheses that can be tested through empirical observations. © 2016 Cengage Learning® a phenomenon (such as juvenile delinquency). Next comes the development of a theoretical understanding, in this case that a single concept (such as social class) might explain others. The theoretical considerations result in an expectation about what should be observed if the theory is correct. The notation Y = f(X) is a conventional way of saying that Y (for example, delinquency) is a function of (depends on) X (for example, social class). At that level, however, Zand Ystill have rather general meanings that could give rise to quite different observations and measurements. Operationalization specifies the procedures that will be used to measure the variables. The lowercase y in Figure 2-2, for example, is a precisely measurable indicator of capital Y. This operationalization process results in the formation of a testable hypothesis: For example, self-reported theft is a function of family income. Observations aimed at finding out whether this statement accurately describes reality are part of what is typically called hypothesis testing. (See the Tips and Tools box, "Hints for Stating Hypotheses," for more on the process of formulating hypotheses.) 04945_ch02_ptg01.indd 47 8/21/14 11:24 AM 48 ■ Chapter 2: Paradigms,Theory, and Social Research Tips and Tools Hints for Stating Hypotheses Riley E. Dunlap Department of Sociology, Oklahoma State University A hypothesis is the basic statement that is tested in research. Typically a hypothesis states a relationship between two variables. (Although it is possible to use more than two variables, you should stick to two for now.) Because a hypothesis makes a prediction about the relationship between the two variables, it must be testable so you can determine if the prediction is right or wrong when you examine the results obtained in your study. A hypothesis must be stated in an unambiguous manner to be clearly testable. What follows are suggestions for developing testable hypotheses. Assume you have an interest in trying to predict some phenomenon such as"attitudes toward women's liberation "and that you can measure such attitudes on a continuum ranging from "opposed to women's liberation" to "neutral" to "supportive of women's liberation." Also assume that, lacking a theory, you'll rely on"hunches"to come up with variables that might be related to attitudes toward women's liberation. In a sense, you can think of hypothesis construction as a case of filling in the blank:"__is related to attitudes toward women's liberation." Your job is to think of a variable that might plausibly be related to such attitudes, and then to word a hypothesis that states a relationship between the two variables (the one that fills in the "blank" and"attitudes toward women's liberation"). You need to do so in a precise manner so that you can determine clearly whether the hypothesis is supported or not when you examine the results (in this case, most likely the results of a survey). The key is to word the hypothesis carefully so that the prediction it makes is quite clear to you as well as others. If you use age, note that saying "Age is related to attitudes toward women's liberation"does not say precisely how you think the two are related (in fact, the only way this hypothesis could be falsified is if you fail to find a statistically significant relationship of any type between age and attitudes toward women's liberation). In this case a couple of steps are necessary. You have two options: 1. "Age is related to attitudes toward women's liberation, with younger adults being more supportive than older adults." (Or, you could state the opposite, if you believed older people are likely to be more supportive.) 2. "Age is negatively related to support for women's liberation." Note here that I specify "support"for women's liberation (SWL) and then predict a negative relationship—that is, as age goes up, I predict that SWL will go down. In this hypothesis, note that both of the variables [age, the independent variable or likely"cause,"and SWL, the dependent variable or likely"effect") range from low to high. This feature of the two variables is what allows you to use"negatively" (or"positively") to describe the relationship. Notice what happens if you hypothesize a relationship between gender and SWL. Because gender is a nominal variable (as you'll learn in Chapter 5), it does not range from low to high—people are either male or female (the two attributes of the variable gender). Consequently, you must be careful in stating the hypothesis unambiguously: 1. "Sex is positively (or negatively) related to SWL" is not an adequate hypothesis, because it doesn't specify how you expect sex to be related to SWL—that is, whether you think men or women will be more supportive of women's liberation. 2. It's tempting to say something like"Women are positively related to SWL,"but this really doesn't work, because female is only an attribute, not a full variable [sex is the variable). 3. "Sex is related to SWL, with women being more supportive than men"would be my recommendation. Or, you could say,"with men being less supportive than women,"which makes the identical prediction. (Of course, you could also make the opposite prediction, that men are more supportive than women are, if you wished.) 4. Equally legitimate would be"Women are more likely to support women's liberation than are men." (Note the need for the second "are,"or you could be construed as hypothesizing that women support women's liberation more than they support men—not quite the same idea.) The previous examples hypothesized relationships between a "characteristic" (age or sex) and an"orientation" (attitudes toward women's liberation). Because the causal order is pretty clear (obviously age and sex come before attitudes, and are less alterable), we could state the hypotheses as I've done, and everyone would assume that we were stating causal hypotheses. Finally, you may run across references to the null hypothesis, especially in statistics. Such a hypothesis predicts no relationship (technically, no statistically significant relationship) between the two variables, and it is always implicit in testing hypotheses. Basically, if you have hypothesized a positive (or negative) relationship, you are hoping that the results will allow you to reject the null hypothesis and verify your hypothesized relationship. 04945_ch02_ptg01.indd 48 8/21/14 11:24 AM Deductive and Inductive Reasoning: A Case Illustration In Chapter 1,1 introduced deductive and inductive reasoning, with a promise that we would return to them later. It's later. As you probably recognized, the traditional model of science just described is a nice example of deductive reasoning: From a general theoretical understanding, the researcher derives (deduces) an expectation and finally a testable hypothesis. This picture is tidy, but in reality, science uses inductive reasoning as well. Let's consider a real research example as a vehicle for comparing the deductive and inductive linkages between theory and research. Years ago, Charles Glock, Benjamin Ringer, and I (1967) set out to discover what caused differing levels of church involvement among U.S. Episcopalians. Several theoretical or quasi-theoretical positions suggested possible answers. I'll focus on only one here: what we came to call the "Comfort Hypothesis." In part, we took our lead from the Christian injunction to care for "the halt, the lame, and the blind" and those who are "weary and heavy laden." At the same time, ironically, we noted the Marxist assertion that religion is an "opiate for the masses." Given both, it made sense to expect the following, which was our hypothesis: "Parishioners whose life situations most deprive them of satisfaction and fulfillment in the secular society turn to the church for comfort and substitute rewards" (Glock, Ringer, and Babbie 1967: 107-8). Having framed this general hypothesis, we set about testing it. Were those deprived of satisfaction in the secular society in fact more religious than those who received more satisfaction from the secular society? To answer this, we needed to distinguish who was deprived. The questionnaire, which was constructed for the purpose of testing the Comfort Hypothesis, included items that seemed to offer indicators of whether parishioners were relatively deprived or gratified in secular society. To start, we reasoned that men enjoy more status than women do in our generally male-dominated society. Though hardly novel, this conclusion laid the groundwork for testing the Comfort Hypothesis. If we were correct in our Two Logical Systems Revisited ■ 49 hypothesis, women should appear more religious than men. Once the survey data had been collected and analyzed, our expectation about gender and religion was clearly confirmed. On three separate measures of religious involvement— ritual (such as church attendance), organizational (such as belonging to church organizations), and intellectual (such as reading church publications)—women were more religious than men. On our overall measure, women scored 50 percent higher than men. In another test of the Comfort Hypothesis, we reasoned that in a youth-oriented society, old people would be more deprived of secular gratification than the young would. Once again, the data confirmed our expectation. The oldest parishioners were more religious than the middle-aged, who were more religious than young adults. Social class—measured by education and income—afforded another test of the Comfort Hypothesis. Once again, the test succeeded. Those with low social status were more involved in the church than those with high social status were. The hypothesis was even confirmed in a test that went against everyone's commonsense expectations. Despite church posters showing worshipful young families and bearing the slogan "The Family That Prays Together Stays Together," the Comfort Hypothesis suggested that parishioners who were married and had children—the clear American ideal at that time—would enjoy secular gratification in that regard. As a consequence, they should be less religious than those who lacked one or both family components. Thus, we hypothesized that parishioners who were both single and childless should be the most religious; those with either spouse or child should be somewhat less religious; and those married with children— representing the ideal pictured on all those posters—should be the least religious of all. That's exactly what we found. null hypothesis In connection with hypothesis testing and tests of statistical significance, that hypothesis that suggests there is no relationship among the variables under study. You may conclude that the variables are related after having statistically rejected the null hypothesis. 04945_ch02_ptg01.indd 49 8/21/14 11:24 AM 50 ■ Chapter 2: Paradigms,Theory, and Social Research Finally, the Comfort Hypothesis suggested that the various kinds of secular deprivation should be cumulative: Those with all the characteristics associated with deprivation should be the most religious; those with none should be the least. When we combined the four individual measures of deprivation into a composite measure, the theoretical expectation was exactly confirmed. Comparing the two extremes, we found that single, childless, elderly, lower-class female parishioners scored more than three times as high on the measure of church involvement than did young, married, upper-class fathers. Thus was the Comfort Hypothesis confirmed. I like this research example because it so clearly illustrates the logic of the deductive model. Beginning with general, theoretical expectations about the impact of social deprivation on church involvement, one could derive concrete hypotheses linking specific measurable variables, such as age and church attendance. The actual empirical data could then be analyzed to determine whether empirical reality supported the deductive expectations. I say this example shows how it was possible to address the issue of religiosity deductively, but, alas, I've been fibbing. To tell the truth, although we began with an interest in discovering what caused variations in church involvement among Episcopalians, we didn't actually begin with a Comfort Hypothesis, or any other hypothesis for that matter. The study is actually an example of the inductive model. (In the interest of further honesty, Glock and Ringer initiated the study, and I joined it years after the data had been collected.) A questionnaire was designed to collect information that might shed a bit of light on why some parishioners participated in the church more than others, but it was not guided by any precise, deductive theory. Once the data were collected, the task of explaining differences in religiosity began with an analysis of variables that have a wide impact on people's lives, including gender, age, social class, and family status. Each of these four variables was found to relate strongly to church involvement, in the ways already described. Indeed, they had a cumulative effect, also already described. Rather than being good news, however, this presented a dilemma. Glock recalls discussing his findings with colleagues over lunch at the Columbia faculty club. Once he had displayed the tables illustrating the impact of each individual variable as well as their powerful composite effect, a colleague asked, "What does it all mean, Charlie?" Glock was at a loss. Why were those variables so strongly related to church involvement? That question launched a process of reasoning about what the several variables had in common, aside from their impact on religiosity. Eventually we saw that each of the four variables also reflected differential status in the secular society. He then had the thought that perhaps the issue of comfort was involved. Thus, the inductive process had moved from concrete observations to a general theoretical explanation. It seems easier to lay out the steps involved in deductive than inductive research. Deductive research begins with a theory, from which we may derive hypotheses—which are then tested through observations. Inductive research begins with observations and proceeds with a search for patterns in what we have observed. In a quantitative study, we can search for correlations or relationships between variables (discussed further in Chapter 16). Thus, once a relationship has been discovered between gender and religiosity, our attention turns to figuring out logical reasons why that is so. Most qualitative research is oriented toward the inductive rather than the deductive approach. However, qualitative research does not, by definition, allow us to use statistical tools to find correlations that point toward patterns in need of explanation (see Chapter 14). Although there are computer programs designed for recording and analyzing qualitative data, the qualitative inductive analyst needs a strong reserve of insight and reflection to tease important patterns out of a body of observations. A Graphic Contrast As the preceding case illustration shows, theory and research can usefully be done both inductively and deductively. Figure 2-3 shows a graphic comparison of the two approaches as applied to an inquiry into study habits and performance on exams. In both cases, we are interested in the relationship between the number of hours 04945_ch02_ptg01.indd 50 8/21/14 11:24 AM spent studying for an exam and the grade earned on that exam. Using the deductive method, we would begin by examining the matter logically. Doing well on an exam reflects a student's ability to recall and manipulate information. Both of these abilities should be increased by exposure to the information before the exam. In this fashion, we would arrive at a hypothesis suggesting a positive relationship between the number of hours spent studying and the grade earned on the exam. We say "positive" because we expect grades to increase as the hours of studying Two Logical Systems Revisited ■ 51 increase. If increased hours produced decreased grades, that would be called a "negative," or "inverse," relationship. The hypothesis is represented by the graph line in part 1 (a), representing the deductive model in Figure 2-3. In part (a) we see the expectation of a simple, positive, linear relationship between the two variables. Part (b) represents what we observe when we study the two variables. Finally, part (c) is the need to decide whether the observations are close enough to what was expected to justify accepting the hypothesis. 1. Deductive Method 2. Inductive Method a. Hypothesis 100 T3 CO o 10 20 30 Hours studying 40 b. Observations 100 in