fatal beatings; comparatively mundane cases of neglect are far more common. But defining child abuse through examples of fatal beatings can shape how we think about the problem, and child-protection policies designed to prevent fatalities may not be the best way to protect children from neglect. Whenever examples substitute for definitions, there is a risk that our understanding of the problem will be distorted.
Of course, not all definitions of social problems depend on dramatic examples. People promoting social problems sometimes do offer definitions. When they do so, they tend to prefer general, broad, inclusive definitions. Broad definitions encompass more cases—and more kinds of cases. Suppose we want to define sexual violence. Certainly our definition should include rapes. But what about attempted rapes—should they be included? Does being groped or fondled count? What about seeing a stranger briefly expose himself? A narrow definition—say, “sexual violence is forcible sexual contact involving penetration”—will include far fewer cases than a broad definition—for example, “sexual violence is any uninvited sexual action.”16 This has obvious implications for social statistics because broad definitions support much larger estimates of a problem’s size.*
No definition of a social problem is perfect, but there are two principal ways such definitions can be flawed. On the one hand, we may worry that a definition is too broad, that it encompasses more than it ought to include. That is, broad definitions identify some cases as part of the problem that we might think ought not to be included; statisticians call such cases false positives (that is, they mistakenly identify cases as part of the problem). On the other hand, a definition that is too narrow excludes cases that we might think ought to be included; these are false negatives (incorrectly identified as not being part of the problem).17
In general, activists trying to create a new social problem view false negatives as more troubling than false positives. Remember that activists often feel frustrated because they want to get people concerned about some social condition that has been ignored. The general failure to recognize and acknowledge that something is wrong is part of what the activists want to correct; therefore, they may be especially careful not to make things worse themselves by defining the problem too narrowly. A definition that is too narrow fails to recognize the problem’s full extent; in doing so, it continues ignoring at least a part of the harm and suffering that ought to be recognized. Thus, activists might point to an example of a woman traumatized by a flasher exposing himself, and then argue that the definition of sexual violence needs to be broad enough to acknowledge the harm suffered by that woman. Activists sometimes favor definitions broad enough to encompass every case that ought to be included; that is, they promote broad definitions in hopes of eliminating all false negatives. Remember, too, that broad definitions make it easier to justify the big numbers advocates prefer.
However, broad definitions invite criticism. Not everyone finds it helpful to lump rape and flashing into a single category of sexual violence. Such broad definitions obscure important differences within the category: rape and flashing both may be unwanted, but classifying them together may imply they are equally serious. Worse, broad definitions encompass cases that not everyone considers instances of social problems; that is, while they minimize false negatives, they do so at the cost of maximizing cases that critics may see as false positives. Consider the long-running debate over the definition of pornography.18 What ought to be considered pornographic? Presumably hard-core videos of people having sex are included in virtually all definitions. But is Playboy pornographic? What about nude sculptures, or the annual Sports Illustrated swimsuit issue? Some antipornography activists may favor a very broad, inclusive definition, while their critics may argue that such definitions are too broad (“That’s not pornography!”).
Clearly, the definition of a social problem will affect statistics about that problem. The broader the definition, the easier it is to justify large estimates for a problem’s extent. When someone announces that millions of Americans are illiterate, it is important to ask how that announcement defines illiteracy.19 Some might assume that illiteracy means that a person cannot read or write at all, but the speaker may be referring to “functional illiteracy” (that is, the inability to read a newspaper or a map or to fill out a job application or an income tax form). Does illiterate mean not reading at all? Not reading at the third-grade level? Not reading at the sixth-grade level? Defining illiteracy narrowly (as being unable to read at all) will include far fewer people and therefore produce far lower statistical estimates than a broad definition (being unable to read at the sixth-grade level).
Often, definitions include multiple elements, each of which can serve to make the definition broader or narrower. Consider homelessness again. What should a definition of homelessness encompass? Should it include the cause of homelessness? If a tornado destroys a neighborhood and the residents have to be housed in temporary emergency shelters, are they homeless, or should we count only people whose poverty makes them homeless? What about the length of time spent homeless? Does someone who spends a single night on the streets count, or should the label “homeless” be restricted to those who spend several (and if so, how many?) nights on the streets? Each element in the definition makes a difference. If we’re counting homeless persons, and we count only those whose poverty made them homeless, we’ll find fewer than if we include disaster victims. If we count those who were without a home for thirty days in the last year, we will find fewer homeless people than if our standard is only ten days, and using ten as a standard will produce a lower number than if we agree that even a single night on the streets qualifies someone to be considered homeless.
In fact, some advocates for the homeless argue that definitions based on these elements are far too narrow, and they offer even broader definitions.20 They suggest that people who stay in the homes of friends or relatives—but who have no homes of their own—ought to be counted as homeless. Under this definition, an impoverished mother and child who never spend a night on the streets or in a shelter but who “double up” and live with relatives or another poor family ought to be counted as homeless. Obviously, using this broader standard to count cases will produce higher numbers than definitions that restrict homelessness to those living on the streets. Still other advocates argue that people whose housing is inadequate or insufficient also ought to be counted as homeless. This still broader definition will lead to even larger numbers. Calculating the number of homeless people (or illiterate people or acts of sexual violence) inevitably reflects our definitions.
In other words, statistics about social problems always depend on how we define the problem. The broader the definition, the bigger the statistic. And, because people promoting social problems favor big numbers (because they make the problem seem bigger and more important), we can expect that they will favor broad definitions. Often, advocates justify broad definitions by emphasizing the importance of being inclusive. People who spend a single night on the streets (or who have to stay with friends, or who live in substandard housing) also suffer. Who are we to decide that their suffering shouldn’t count? Clearly, advocates argue, these people deserve to be included when we speak of “homelessness.”
There are, then, two questions about definitions that ought to be asked whenever we encounter statistics about social problems. First, how is the problem defined? It is all too easy to gloss over definitions, to assume that everybody knows what it means to be homeless or illiterate or whatever. But the specifics of definitions make a difference, and we need to know what they are. Second, is the definition reasonable? No definition is perfect. Definitions that are too narrow exclude false negatives (cases that ought to be included), while definitions that are too broad include false positives (cases that ought to be excluded). It is difficult to have a sensible discussion about a social problem if we can’t define the problem in a way that we can agree is reasonable. But even if we cannot agree, we can at least recognize the differences in—and the limitations of—our definitions.
MEASURING
Any statistic based on more than a guess requires some sort of counting. Definitions specify what will be counted. Measuring involves deciding how to go about counting. We cannot begin counting until we decide how we will identify and count instances of a social problem.*