Variable concepts

A literature review should clarify the boundary of your topic and enable you to find the puzzles (or gaps) that lie within it. The review enables you to identify the various concepts that are relevant to the topic and describe those which are important. Depth and subtlety are normally a result of the relationships amongst concepts. The description must therefore explain those relationships where they are needed for your line of reasoning. Neuman (2011, p.65) explains it well.

Single versus Concept Clusters. We rarely use concepts in isolation from one another. Concepts form interconnected groups, or concept clusters. This is true for concepts in daily life as well as for those in social theory. Theories have collections of associated concepts that are consistent and mutually reinforcing. Together, the collections can form a broader web of meaning. For example, in a discussion of the urban decay, we may read about associated concepts such as urban expansion, economic growth, urbanization, suburbs, center city, revitalization, ghetto, mass transit, crime rate, unemployment, White flight, and racial minorities. Used together, these concepts form a mutually reinforcing collection of ideas that we use in theorizing and research studies.
We can simplify the concepts in daily life and social theory into two types. One type has a range of values, quantities, or amounts. Examples include amount of income, temperature, density of population, years of schooling, and degree of violence. These are variables, or variable concepts, that you will read about in Chapter 6. The other type expresses categories or non-variable phenomena (e.g., bureaucracy, family, college degree, homelessness, and cold).

Simple versus Complex Concepts. In addition to ranging from concrete to abstract and being a variable or non-variable type, concepts can be categorized as simple or complex. Simple concepts have only one dimension and vary along a single continuum. Complex concepts have multiple dimensions or many sub-parts. We can break: complex concepts down into several simple, or single-dimension, concepts. In general, the more complex concepts tend to be more abstract and simple ones more concrete, although this is not always true.

Neuman (p.218) also has helpful things to say about how to go about measuring a variable.

“The level of measurement is determined by how refined, exact, and precise a construct is in our assumptions about it. This means that how we conceptualize a construct carries serious implications.  It influences how we can measure the construct and restricts the range of statistical procedures that we can use after we have gathered data. Often we see a trade-off between the level of measurement and the ease of measuring. Measuring at a low level is simpler and easier than it is at a high level; however, a low level of measurement offers us the least refined information and allows the fewest statistical  procedures during data analysis. We can look at the issue in two ways: (1) continuous versus discrete variable, and (2) the four levels of measurement.

Continuous and Discrete Variables. Variables can be continuous or discrete. Continuous variables contain a large number of values or attributes that flow along a continuum. We can divide a continuous variable into many smaller increments; in mathematical theory, the number of increments  is infinite. Examples of continuous variables include temperature, age, income, crime rate, and amount of schooling. For example, we can measure the amount of your schooling as the years of schooling you completed. We can subdivide this into the total number of hours you have spent in classroom instruction and out-of-class assignments or preparation. We could further refine this into the number of minutes you devoted to acquiring and processing information and knowledge in school or due to school assignments. We could further refine this into all of the seconds that your brain was engaged in specific cognitive activities as you were acquiring and processing information.

Discrete variables have a relatively fixed set of separate values or variable attributes. Instead of a smooth continuum of numerous values, discrete variables contain a limited number of distinct categories. Examples of discrete variables include  gender (male or female), religion (Protestant,  Catholic, Jew, Muslim, atheist), marital status  (never married single, married, divorced or separated, widowed), or academic degrees (high school  diploma, or community college associate, four-year  college, master’s or doctoral degrees). Whether a variable is continuous or discrete affects its level of measurement.

Four Levels of Measurement. Levels of measurement build on the difference between continuous and discrete variables. Higher level measures are continuous and lower level ones are discrete.  The four levels of measurement categorize its precision.

Deciding on the appropriate level of measurement for a construct is not always easy. It depends on two things: how we understand a construct (its definition and assumptions), and the type of indicator or measurement procedure.

The way we conceptualize a construct can limit how precisely we can measure it. For example, we might reconceptualize some of the variables listed earlier as continuous to be discrete. We can think of temperature as a continuous variable with thousands of refined distinctions (e.g., degrees and fractions of degrees). Alternatively, we can think of it more crudely as five discrete categories (e.g., very hot, hot,  cool, cold, very cold). We can think of age as continuous (in years, months, days, hours, minutes, or seconds) or discrete categories (infancy, childhood, adolescence, young adulthood, middle age, old age).

While we can convert continuous variables into discrete ones, we cannot go the other way around, that is, convert discrete variables into continuous ones. For example, we cannot turn sex, religion, and marital status into continuous variables. We can, however, treat related constructs with slightly different definitions and assumptions as being continuous (e.g., amount of masculinity or femininity, degree of religiousness, commitment to a marital relationship). There is a practical reason to conceptualize and measure at higher levels of measurement: We can collapse higher levels of measurement to lower levels, but the reverse is not true.

Distinguishing among the Four Levels. The four levels from lowest to highest precision are nominal, ordinal, interval, and ratio. Each level provides a different type of information.

Nominal-level measurement indicates that a difference exists among categories (e.g., religion:
Protestant, Catholic, Jew, Muslim; racial heritage: African, Asian, Caucasian, Hispanic, other).

Ordinal-level measurement indicates a difference and allows us to rank order the categories (e.g., letter grades: A, B, C, D, F; opinion measures:  strongly agree, agree, disagree, strongly disagree).

Interval-level measurement does everything the first two do and allows us to specify the amount of distance between categories (e.g., Fahrenheit or celsius temperature: 5°, 45°, 90°; IQ scores:  95, 110, 125).

Ratio-level measurement does everything the other levels do, and it has a true zero.  This feature makes it possible to state relationships in terms of proportion or ratios (e.g., money in-  come: $10, $100, $500; years of formal schooling:  1, 10, 13).

In most practical situations, the distinction between interval and ratio levels makes little difference.”

NEUMAN, W. L. 2006. Social research methods : qualitative and quantitative approaches, Boston, Mass. ; London, Pearson, Allyn and Bacon.