NOMI NAL VARIAB LES

Nominal variables, the most basic kinds o f variables, are defined by the absence of both ordering and metric. Their values are merely distinct from each other, and hence unordered. The mathematics for nominal variables is set theory, a calculus concerned with unordered entities. The adjective nominal suggests the " by name only" nature of these variables. Calling nominal variables "nominal scales"

is a misnomer, because a "scale" conjures images of a linear ordering of values, which is precisely what the values of nominal variables do not possess. They may be arranged in any way conceivable without making a difference. Data recorded in nominal categories are also called qualitative because the difference between any two values of a nominal variable is the same for all possible pairs of values.

The nine standards for rejecting Freud's dream theory listed above constitute one nominal variable. Other examples are alphabetical characters, speech acts, forms of government, ethnic identities, and social security numbers. Analysts must take care not to be misled by the use of numbers as names for nominal cat­

egories. Numerical listings of bank customers' PINs or of the numbers on the j er­

seys of athletes have no operational significance. A more technical way of stating this property is to say that the distinctions within a nominal variable are pre­

served under all permutations of its values.

All variables reduce to nominal variables when their orderings and their metrics are removed from them. In the following sections, I discuss what distin­

guishes other variables from nominal variables. Table 8 . 1 shows, orderings by metrics, the types of variables to be discussed and useful in content analysis.

Table 8.1 Types of Variables by Orderings and Metrics

Order: None Chains Recursions Cubes

Metric

None Nominal variable

Trees

Ordinal G rouping Ord i na l scale Loop Cross-tab of Typology

ord. variables

I nterval N etwork of I nterval scale Circ l e 1t Geometric I nterval tree

distances space

Ratio Ratio scale Vector space Ratio tree

O RD E R I N G S

For a variable to make sense, any ordering o f its values must somehow be appro­

priate to the phenomena the variable is to record. Something that varies along one dimension, such as length, audience size, or positive or negative evaluation, is very different from daily time, which repeats over and over again and is circu­

lar, or individual names, which are either this or that but nothing in between.

Networks of concepts extracted from a writer's work (Baldwin, 1 942), the semantic connections within a text as stored in a computer (Klir & Valach, 1 965), and the hierarchy of organizing a piece of writing (from the work as a whole to its chapters, down to individual sentences)-these exhibit other order­

ings. Below, I discuss four common orderings of values: chains, recursions, cubes, and trees. These are not intended to constitute an exhaustive classifica­

tion; I have chosen them merely to expand the conventional limitation to linear scales of measurement, so-called measuring scales, which are favored by statisti­

cians but rarely capture the meanings of text.

Chains

Chains are linearly ordered sets of values, as in scales of measurement. The values of a chain are transitive in the sense that a--'7b and b--'7c implies a--'7C for any three values of a chain. In speaking of body temperature, for instance, we have a conception of what is normal and we conceive of temperature as going up or down in degrees. Temperature is a unidimensional variable. It can move through all of its values between extremely high and extremely low, never moving sidewise, never bypassing or jumping over any one temperature. The actual unit of measurement (degrees Fahrenheit, degrees Celsius, or degrees Kelvin) is secondary to the conception that it moves to one or the other of two neighbors. When we talk of more or less, before or after, or changes, we tend to imply chains, even when we use relative terms such as wealthy, intelligent, successful, or progressive. Chains may be open-ended or bounded. Polar adjective scales, introduced in Chapter 7 and mentioned above, have defined beginnings and ends. Chains may also be con­

ceived of as emanating from one outstanding value in one direction, as in the size, readership, or frequency of a newspaper or Zillmann's ( 1 964) semantic aspect scale, or in two directions, as in the positive or negative bias of reporting. Figure 8.2 adds a train schedule and a ladder conception to the examples of chains.

The familiar ordinal scales, interval scales, and ratio scales are all chains to begin with; the difference between these scales and chains is one of metrics. As noted above, the term nominal scale is a misnomer, as nominal variables exhibit no ordering at all.

1 11 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1

Figure 8.2 Cha i n s

DATA LAN G UAG ES

1 63 Recursions

Recursions are circular connections between values. Recursions can be conceived of as chains whose ends are seamlessly joined. Each value has exactly two immediate neighbors; there is no end and no outstanding value. Moving from any given value in one direction eventually brings one back to where one began-which was arbitrary to begin with. Transitivity applies locally but not to all values. Figure 8.3 shows this graphically. Examples of recursively ordered phenomena include seasonal fluctuations, ecological cycles, and human­

computer interactions. Namenwirth and Weber ( 1987) demonstrated cyclicity in the use of political values and adopted a recursive notion of time (see Figure 10.5). Biologists describe biological phenomena in terms of life cycles, and cyber­

neticians have identified the stabilizing efforts of complex systems in terms of circular causal feedback loops. In accounts of how social prejudices take hold in a population, how political candidates get elected, and how the "spiral of silence" affects public opinion, recursive variables are indispensable.

The practice of cutting recursions into more easily analyzable linear continua usually destroys their circular essence. For example, some social psychology researchers have cut speech acts out of the ongoing circularity of human interactions that realize their meanings, and this may account for the rather artificial causal con­

ceptions that dominate social psychological explanations of language use. In the same way, when one describes a computer interface in terms of the graphics involved, one hides the dynamic nature of the interface. Many so-called inconsistent preferences, such as a � b, b � c, and c � a, in fact define recursions. These are far from irrational or abnormal; rather, they belong to a nonlinear ordering.

12

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^TExr

< �

2.1 2.3 ^{9 3}

t o t

₀

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^{TExr04 TExr3 6}

3.2^-- 3.3

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6 TExr42

Figure 8.3 Loops and C i rc l es

Cubes

Cubes depict variations multidimensionally. The values in cubes are ordered so that neighboring values differ in only one of a cube's dimensions. Cubes often arise by default. Consider Lasswell and Kaplan's ( 1 950) eight value categories:

Power Rectitude Respect Affection Wealth Well-being Enlightenment Skill

Superficially, these eight values have no apparent order and so resemble a nom­

inal variable. However, Lasswell and Kaplan allowed their recording units­

persons, symbols, and statements-to score high on more than one of these values. If the eight kinds of values are taken as a nominal variable, the permis­

sion to record combinations of such values would violate the mutual exclusivity requirement of variables and render the data so recorded no longer analyzable as a nominal variable. In fact, any instruction to coders to "check as many as applicable" signals a data structure other than a scale. When any of the eight val­

ues could be present or absent independent of all of the others, the values define an eight-dimensional cube consisting of eight binary variables. Figure

8.4

shows cubes of increasing dimensionality created by the presence or absence of independent qualities.

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Figure 8.4

1'10- DI._IIIML

CUM Cubes

Trees

PCILIIt>

� ega

Trees have one origin and two kinds of values, terminal and branching. All of them are available for coding. Trees show no recursions, as Figure

8.5

illustrates.

DATA LAN G UAG ES

1 65

Each value in a tree can be reached from its one origin by a separate path that passes through a number of branching values. Trees are basic to the recording of linguistic representations and conform to one of the earliest theories of meaning.

Aristotle's notion of a definition, for example, requires naming the genus (the general class) to which the definiens (the word to be defined) belongs and distin­

guishing the latter from all other species of that genus. Moving from genus to genus describes moving through the branching points of a tree. The system of categories in the Linnean classification in biology-not the organisms it classi­

fies--constitutes a tree. Closer to content analysis, a reference to Europe is implicitly a reference to France, Italy, Germany, and so on. A reference to France is implicitly a reference to the regions of that country. The relation connecting

"Europe, " "France," and "Provence" is one of inclusion and defines a path or chain through a tree. France and England are on different paths, as neither includes the other.

Figure 8.5 Trees

Vice President I 1

I

President I

Dep. Head A Dep. Head B Dep. Head C

Vice President 2 I

Dep. Head D

I

I

I

I

� �

I

I

I

Sup.i Sup.ii Sup.iii Sup.iv Sup.v Sup.vi Sup. vii Sup. viii Sup.ix Sup.x

Most content analyses fix the level of abstraction on which countries, popu­

lations, products, or mass-media programs are coded. Trees offer a richer alter­

native. Other examples include family trees, decision trees, telephone trees, the trees that the rules of a transformational grammar generate, and social hierar­

chies in business organizations, in the military, and in government. (I discuss the possible confusion of trees with groupings below, in section 8.6. 1 . Note here only that each branching point can be occupied by a value.)