# Variables, Values, and Measurement in Sociological Research

## 1.2. Variables and Values

In research, we focus on **particular characteristics** of the **object of study**, which is the population under observation. These characteristics are called **variables**. *Research Methods and Techniques*

The **elements of a population** differ from one another and exist in different states, which can be configured within a variable. These different states are called **variable values**. Each element of the population will assume a value for a given variable.

*Example: A population (P) consisting of 12 elements (individuals) is divided by the variable “sex” into two groups: men (5 elements) and women (7 elements). According to the variable “marital status,” the population can be divided into: Single (2 elements), married (6 elements), divorced (4 elements), and widowed (0 elements).*

Given a set of units (a population), a **value** is something that can be predicated of a unit, and a **variable** is a set of values that form a classification. In the language of variables, “data are determined according to” the variables, units of analysis, and values of the variable. This is equivalent to “questions” and “answers” from “surveyed subjects” in the language of surveys.

### 1.5. Principles of Classification

**Rating:** An operation performed on a set of elements that generates a *fundamentum divisionis*, a principle or criterion for division. The *fundamentum divisionis* is what generates the different classes or categories of classification. All of these classes possess two properties: *completeness* and *mutual exclusivity* of categories.

A variable, involving the classification of the elements of a given population, must be exhaustive. That is, the potential values (categories and states) of these variables must cover all elements of a population. For this reason, we sometimes construct a residual category like “other” or “don’t know/no answer” in surveys.

The mutual exclusivity of the classification categories (values) of a variable must also be considered. The same case cannot be found in different categories. We can construct a variable from a series of questions. A variable must always respect the principle of mutual exclusivity of its categories, which is simply the effect of the unit classification criterion that defines a variable, its *fundamentum divisionis*.

**Uniqueness and completeness** are the two **basic principles** to consider when **building a variable**. We can summarize these two principles in the motto *“A category for each and every case in one category.”* Compliance with these principles is what makes measurement possible.

### 1.9. Independent Variable and Dependent Variable

A variable is dependent on another if the distribution of its values allows us to predict the distribution of values in the first (e.g., a higher level of education is correlated with a more favorable attitude toward an equitable distribution of tasks). The value that the dependent variable takes on in an analysis unit (or element) is determined by the value that the independent variable takes on in that unit.

Mathematically, the dependency is reversible, meaning that if one variable is dependent on another, the reverse is also true. Sociologically, however, the explanatory scheme (using the survey) allows us to distinguish **different types of variables**:

**Structural:**These variables place the individual in the social structure, such as gender, marital status, occupation, religion, age, and social class.**Attitudinal and Opinion:**These variables reflect beliefs and viewpoints, such as racism, egalitarianism, and conservatism.**Behavioral:**These variables capture actions and behaviors, such as voting, TV consumption, and trade union affiliation.

The first type explains the second, and the second and third explain each other. Within each type, we can also distinguish between variables that explain others. This typology is also known by other names. Structural variables are also called *identification* (or environmental) variables, attitudinal variables are called *positioning* variables (towards something: institution, object, event, etc.), and behavioral variables are called *response* (concrete) variables. In other words, we can distinguish between who you are, what you think (in general), and what you do (specifically).

However, **in a broader context** than sociological reflection, the **independent variable** would be the **cause** (antecedent in time) of the **dependent variable**. Sometimes the dependency relationship between two variables is affected by a third variable, which may be situated between the independent and dependent variables (*intervening variable*), or which may precede both and affect them simultaneously (*antecedent variable*). These are called **control variables**.

Some authors have criticized the *“scheme of sociological analysis that aims to reduce human social life to a number of variables and relations between them.”*

#### Rule of the Match:

If two or more cases of the phenomenon under investigation have only one circumstance in common, this circumstance is the cause (or effect) of the phenomenon.

#### Rule of the Difference:

If there is a case in which we observe the phenomenon under investigation and another case in which we do not, and all circumstances are common to both cases except for one, which only occurs in the first case, then this unique circumstance is the cause (or effect) of the phenomenon.

#### Concomitant Variation Method:

Any phenomenon that varies in some way whenever another phenomenon varies in a certain way is either a cause or an effect of it (or is otherwise related to it by some causal agent). This method is used when one can distinguish degrees and magnitudes of effects and causes (and not simply the presence or absence of effects and/or causes) and requires the use of measurement and statistical techniques.

Sociologists always work with concomitant variations between variables in their analyses.

## Nominal Scale

This is the simplest level of measurement. It only distinguishes elements from one another. For example, in the variable “marital status,” we can say that “single” is different from “married,” but we cannot say that “married” has more (or less) “marital status” than “single” – it is simply a different marital status. There is no order between the noun classes, or indeed any metric connection.

Examples of nominal scale variables: sex, city of residence, voting, occupation, religion…

In the coding of these variables for subsequent computer processing, we assign numbers to the values of these variables [e.g., single (1), married (2), divorced (3), widowed (4)]. However, the numbers here are merely symbols that function only as names. Arithmetic or statistical calculations cannot be performed on them. The only statistical measure that can be used on nominal scales is to determine the largest class.

Nominal scales are also called *qualitative variables*.

## Ordinal Scale

This level of measurement is higher than the nominal scale. It allows us to order the categories or values of a variable. The variable is thus presented as a scale in which the values are sorted according to the degree to which they possess the property (or properties) defined by the variable. For example, we can measure the “attitude toward gender-equal division of household chores” on a scale of three values: “very favorable,” “somewhat favorable,” and “not favorable.”

These scales represent a certain linearity of categories: the establishment of a dimension. At this level, we can say that one class is larger (or smaller) than another. However, we do not know the exact distance separating one category from another. The distances between the categories may vary, and the subjective perception of the distances between two categories can be very different between different respondents. To know the exact distance that separates the categories, we have to move up the scale of measurement.

## Interval Scale

At this level, we know the exact distances that separate the categories or values of each variable. We are now dealing with a quantitative scale. At this level, we fix the distances between the classes using a unit of measurement. We know that one class (“v¹”) is “d” units away from another class (“v²”). If we add the same number to all classes, the relationship between them remains unchanged. At this level, we find a “true zero point.” The zero will be an **arbitrary zero**.

In most cases where we find an interval scale, we are also dealing with a ratio scale.

## Ratio Scale

We are dealing with a ratio scale when a value can be expressed as a ratio of another: v¹ = rx v² (where “r” is a rational number). It always involves an absolute zero.

Examples of such variables: age (in completed years), net monthly income (in euros), size of dwelling (in square meters), number of casualties in traffic accidents in Spain in the last ten years…

On this scale, we can say that someone earns twice as much as another, lives in a dwelling that is 0.66 times smaller, and so on. If all categories of the variable are multiplied by a certain number, the (numerical) relations between them remain intact.

Some authors consider these measurement scales to be strict because they allow for all sorts of algebra and statistical measures.

The **levels of measurement are cumulative**: higher levels contain the lower levels. As we move up the levels, the distinction between the values of a variable becomes more refined. Measurement in the strict sense of the word is only given above the ordinal level since it requires a unit of measurement and an origin (zero). Therefore, **measurement is only possible with ratio scales**.

In ratio scales, we can distinguish between:

**Key measures:**Scales obtained by simple application. For example, the number of unemployed/employed in a particular province.**Resulting measures:**Constructed by combining several key measures using a mathematical function. For example, the “unemployment rate” is the ratio of the number of unemployed to the number of employed.

According to **Lazarsfeld**, the phases of the process for characterizing an object of study, to identify variables capable of measuring complex (theoretical) objects, are:

- Literary representation of the concept.
- Specification of the dimensions.
- Choice of observable indicators.
- Summaries of indicators or indexing.

This is the **process of scaling techniques** as a measurement instrument that ensures the **operationalization of the concept**. The final meaning attached to a concept depends on the specific operations that allow its measurement. This is how we get different definitions of authoritarianism, religiosity, intelligence, racism…, as we operationalize these concepts with one set of indicators or another, also called *items*.

Often the objects of research, or the dimensions to be investigated, are clusters of variables or concepts. The researcher must find the most relevant variables, the most powerful indicators of the dimension we want to capture. Thus, sometimes intuitively, we establish the dimensions that affect the problem or research topic. The variables are evident, while the dimension is normally dormant.

## 3.2. Scaling Techniques

In sociological research, three types of mechanisms are typically used in surveys to create **derived measures (new indicators)** from the responses obtained in a series of questions. Characteristics such as age, sex, and family size are rarely measured from simple answers to direct questions.

**Established indicators:**Indicators (social, economic, demographic, health, etc.) that have gained the status of “measurement standards.”**Tests and psychometric scales:**Attitude scales, prestige scales, qualification scales, etc., usually standardized, and scaling techniques are applied to convert a series of qualitative facts (attributes) into a quantitative series (variable): ordering a series of manifest facts (indicators, items) along a continuum within an implicit dimension.

One technique of particular interest is the **attitude scale**. An attitude scale is a “coherent set of items that are considered indicators of a more general concept of an underlying attitude.” An *item* on an attitude scale is a “statement” about something that appears in a questionnaire, asking the interviewee to express their agreement or disagreement with it, or the extent to which they agree or disagree. Each scale is composed of cases or claims that are only a sample of the possible universe of cases or claims. All scales should contain no less than 16 to 20 claims. The essence of scaling is to bring together several qualitative characteristics into a single quantitative variable.

### 3.3. Validity and Reliability

**Validity** and **reliability** are two critical aspects that determine the accuracy of the information provided by scales and measurement techniques.

**Reliability** refers to the consistency of a scale. A scale is reliable if it produces the same results when applied at different times to the same sample or population. We can measure the reliability of a scale in different ways. We can apply the same scale on two separate occasions to the same population and compare the results. However, this implies a risk that the memory of the first interview will alter the second. The reliability of a scale is related to its internal consistency, with the high correlation among its items. However, a consistent measurement may not be a valid measurement (e.g., a rigid yardstick may be poorly calibrated and provide an incorrect measurement).

**Validity** refers to the accuracy of a scale. A scale is valid if it measures what it claims to measure. However, no measuring instrument, no scale, is perfectly valid. There are always measurement errors. The validity of an instrument can be measured by:

**Pragmatic validation:**The focus is on the usefulness of the scale as an indicator or predictor of a specific behavior of the person being measured.**Theoretical or construct validation:**The focus is on knowing the extent to which an individual possesses a certain characteristic that cannot be identified with any particular behavior, a theoretical construct.

### 3.4. Measurement Errors

Systematic errors can occur, which are constant, and random errors, which depend on aspects of the measurement situation.

**Constant errors:**Social desirability (a tendency to agree with statements that are presumed to be socially correct) and acquiescence in responses (a tendency to agree or disagree with statements regardless of their content).**Systematic errors:**These are controllable to some extent.**Random errors:**These reveal a lack of consistency in the measurements if they are assumed to be of the same individuals.

No research is perfectly valid and reliable, nor is it free from measurement errors. The researcher has to assume this, but they must develop sufficiently valid and reliable scales and try to minimize measurement errors.

### 3.5. Attitude Scales

**Attitude** denotes the total sum of inclinations, feelings, prejudices, preconceived notions, ideas, fears, threats, and convictions of an individual towards any particular issue. An **opinion** is a verbal expression of attitude. In attitude scales, the underlying dimension is the attitude, and opinions are the manifest indicators (collected items). Opinions are “means of measuring attitudes.”

#### Thurstone Scales (Differential Scales)

Initially called *“apparently equal interval scales,”* the **method of production** (of establishing the order of categories) was **decisive** because it determined whether these attitude scales could be treated as interval scales. In this type of scale, before constructing the questionnaire, a number of people were chosen to act as judges. They were given a large number of statements (collected each as a tab) and asked to order them into 11 groups representing eleven points on the scale. Each item was given the *average* score obtained from all judges. A series of items were then selected that spanned the continuum of the scale significantly, meeting the completeness criteria that any classification must meet, and avoiding items that were too ambiguous. Finally, the items were presented in the questionnaire in random order. Respondents were asked to select from a series of items and express their *agreement* or *disagreement* with each statement. An individual’s score on the scale was the mean (or median) of the scalar values of the different items with which they disagreed.

#### Likert Scales (Additive Scales)

These scales add a measure of the degree of intensity of agreement with the statements raised in the items. They are the most commonly used scales. The selection of items in these scales is not based on the prior criteria of judges but on the subsequent analysis of the internal consistency of the items. Here, respondents also indicate their agreement or disagreement with a series of statements, indicating the **degree or intensity of agreement or disagreement** with each statement. Each item on the scale is itself scaled, forming a scale. These scales are assumed to be **interval scales**. Generally, the possible positions of each item are coded in ascending or descending order. *(Example: 1) Strongly disagree, 2) Somewhat disagree, 3) Neither agree nor disagree, 4) Somewhat agree, 5) Strongly agree).* The scale score is obtained by adding the scores on all items. Only the most significant items (those most consistent with each other) of the total proposed in the questionnaire are counted, thus ensuring the unidimensionality of the scale. These scales are not only used to measure attitudes but are also applicable to other types of attributes (individual or collective).

#### Guttman Scales (Cumulative Scales)

The items are structured in stages, and the response to each one predetermines the following response. The possible responses are binary (yes/no, agree/disagree). In these scales, unidimensionality is clearly evident.

### 3.6. Multidimensional Scales or Indices

With the development of multivariate analysis techniques, it is now possible to determine the underlying dimensions to which a series of observations (given by questionnaire responses) belong, allowing us to work with multidimensional data.