# Section 3.2: Variables

Variables may be attributes that are different for different people, such as weight, gender, religious affiliation, political affiliation, and so forth.  Variables can also be conditions in the environment that can affect the results of a study, such as the time of day when an experiment takes place.

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Key Term
A variable is a characteristic, attribute, or condition that has different values for different individuals.

When variables are measured, researchers often identify the variables by a letter, such as X.  If two variables are used, then the researcher may denote the first variable as X and the second as Y.  This shorthand is useful in describing the relationships between variables.

A value that does not change from person to person is called a constant.  The idea of constancy is closely related to the scientific concept of control, which we will discuss in more detail in a later section.

Key Term
A constant is an attribute of a person or a condition that does not change from person to person but stays the same for every individual.

## Independent and Dependent Variables

An attribute is a specific value of a variable.  For example, the variable gender has two attributes: male and female.  Attributes are commonly referred to as a level of the variable or simply the category.  Take care not to confuse a variable with its categories.  Male, for example, is not a variable. It is a category of the variable gender, along with the category female.  Ideally, researchers define variables in such a way that each category is mutually exclusive.  That is, all observations will fall into one and only one category.  It is also desirable that the categories be exhaustive.  This means that every observation has a category to which it can be assigned.

Special names are used for the two variables that a researcher is studying in an experiment.  The variable that is manipulated by the researcher—the one thought to cause a change in the other—is called the independent variable (IV).  The variable that is observed to see if it was changed by the independent variable is called the dependent variable (DV).  It is called dependent because its value depends on the independent variable.  Recall that a basic purpose of experiments is to determine the extent to which a change in the independent variable causes changes in the dependent variable.

In an experiment, the independent variable often reflects that the researcher administered some type of treatment—something we do to the participants.  In other words, the researcher must manipulate the level of the independent variable to have a true experiment.  In its simplest form, an experiment involves two groups. The first is the group that got the treatment—the experimental group.  A second group does not get the treatment.  Individuals in this group are said to be in the control group.

In correlation and regression-based research where the researcher is using one or more variables to predict values of another variable, the independent variable (IV) is often called the predictor variable because it is used to predict the dependent variable.  The dependent variable (the outcome) is called the criterion variable in these cases.

## Discrete and Continuous Variables

The variables in a study can also be described in terms of the types of values that can be assigned to them.  A discrete variable consists of separate categories that cannot be divided.  Take the variable gender for example.  Generally, you are either male or female—the categories are indivisible.  Discrete variables usually define categories, or are restricted to whole, countable numbers.  The variable felony convictions is an example.  Either you have been convicted of no felonies, or you have been convicted of a whole number of felonies.  You cannot have been convicted of 2.78 felonies.

A continuous variable, on the other hand, can be subdivided into an infinite (or practically infinite) number of fractional parts.  Annual household income (measured in dollars and cents) is a good example of a continuous variable.  Variables that are continuous can be imagined to be along a line (like the number line) with no obvious points of separation.  Note that it will be rare for any two subjects to have the same exact score on a continuous variable.

Understanding the nature of variables as either discrete or continuous is a fundamental aspect of research design in social sciences and other disciplines. Discrete variables, characterized by distinct and indivisible categories, help researchers capture phenomena that are qualitative or categorical in nature. For example, variables like gender, felony convictions, or the type of education received are discrete.

These variables usually exist in defined states, and their discrete nature simplifies the data collection and analysis processes. By focusing on whole numbers or distinct categories, discrete variables make it easier to classify subjects, generate frequency distributions, and conduct comparative analyses. In essence, discrete variables offer a straightforward and structured way to organize data, allowing researchers to focus on identifying patterns, differences, or other relationships among groups.

On the other hand, continuous variables add nuance and depth to research by allowing for a practically infinite range of values. These variables, like annual household income, temperature, or age when measured to the decimal, offer a more expansive and detailed view of phenomena under study. The infinite divisibility of continuous variables enables more precise measurements and richer statistical analyses, such as correlation coefficients or regression models, which can capture subtleties in relationships among variables.

Additionally, continuous variables are generally subject to a wider array of statistical methods, offering researchers greater flexibility in their analyses. Given that continuous variables do not have obvious points of separation, they allow researchers to investigate variations on a much finer scale. This enables more nuanced interpretations and often results in richer, more insightful conclusions. Therefore, understanding whether a variable is discrete or continuous helps researchers select appropriate methods for data collection, analysis, and interpretation, thereby contributing to more rigorous and meaningful scientific inquiry.

## Latent v. Observable Variables

There is a big difference between variables that we can directly observe and the more abstract variables that cannot be observed that we refer to as constructs.  One way to look at constructs is as nonobservables.  This is related to what are called latent variables.  Latent variables are unobserved “things” that a researcher presumes to underlie an observable variable.  Intelligence is a common example of a latent variable.  We cannot directly measure intelligence, but we can observe things that we think are related to it, such as verbal ability and mathematical ability (operationalized as scores on a standardized test).

Most of the problems that social scientists are interested in are latent variables.  We as social scientists are not interested in specific children hitting each other on the playground; our real concern is understanding the latent variable aggression.  We are not interested in a child’s ability to select correct responses on a test; we are interested in the latent variable intelligence.  Generally, we cannot measure these variables we are interested in.  Thus, we are forced to measure behaviors that we think indicate the presence of the latent (unobservable) variable that we are interested in.

Understanding latent variables is crucial for social scientists as they often aim to study underlying, abstract phenomena that aren’t directly observable. Latent variables like aggression, intelligence, or social inequality are constructs that capture complex, multifaceted realities. For example, while one may not be specifically focused on instances of children fighting in a playground, these observable behaviors serve as indicators of the underlying latent variable of aggression. Similarly, a child’s performance on a standardized test is not the ultimate goal of study; it is merely a measurable representation of the latent variable, which in this case would be intelligence. Because latent variables cannot be directly measured, social scientists use observable variables as proxies to gauge these hidden constructs.

The concept of latent variables underscores the methodological complexities in social science research. The need to accurately identify observable indicators of latent variables imposes a significant challenge, as poor indicators can lead to misleading conclusions. To capture the essence of the latent variable, researchers often have to use multiple indicators and rely on complex statistical methods, such as factor analysis or structural equation modeling, to validate their constructs. Moreover, understanding that the focus is on latent variables helps to frame the research questions, guide the methodology, and interpret the findings in a broader context. Rather than simply describing observable behaviors, social scientists are able to dig deeper, aiming to explain the ‘why’ and ‘how’ behind these behaviors by focusing on the unobservable latent variables. This nuanced approach enhances the depth and explanatory power of social scientific research.

## Summary

The text provides a comprehensive overview of various types of variables and their significance in research. Variables, described as attributes or conditions with different values for different individuals, are foundational in scientific inquiry. The text outlines different classifications of variables: independent and dependent variables, discrete and continuous variables, and latent versus observable variables.

Independent variables are manipulated to observe their effect on dependent variables. This concept is central to experimental design, which often includes control and experimental groups. In correlational and regression-based research, these are termed predictor and criterion variables, respectively. Discrete and continuous variables differ in the nature of their values; the former comprises indivisible categories (e.g., gender, felony convictions), while the latter involves infinitely divisible values (e.g., annual income). Discrete variables are advantageous for their ease in classification and analysis, while continuous variables offer greater depth and flexibility in statistical analysis.

Latent variables represent unobservable constructs like intelligence or aggression that are inferred from observable behaviors. These latent constructs pose methodological challenges, requiring rigorous design and statistical models to validate their relationship with observable indicators. Recognizing the type and nature of variables is crucial for researchers as it influences the choice of research methods, data analysis, and the validity of findings. The text illustrates how understanding these variable types can guide researchers in framing their questions, choosing appropriate methodologies, and interpreting data in a context that is both nuanced and scientifically rigorous.

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