Topic Page: Variable
A variable is a logical expression which receives no fixed value, but can be used to range over all entities of the appropriate sort within the model in question. Firstorder variables, usually denoted by lowercase letters from the end of the alphabet (x, y, z ...) range over objects, while higherorder variables range over concepts, relations, or functions. (Concept and relation variables usually take the form of uppercase letters, while function variables are often lowercase f, g, or h.)
See also: Bound Variable, Existential Variable, Individual, Universal Variable, Variable Assignment
A variable is something that varies in value, as opposed to a constant (such as the number 2), which always has the same value. These are observable features of something that can take on several different values or can be put into several discrete categories. For example, respondents’ scores on an index are variables because they have different values, and religion can be considered a variable because there are multiple categories. Scientists are sometimes interested in determining the values of constants, such as π, the ratio of the area of a circle to its squared radius. However, survey research involves the study of variables rather than constants.
A quantity X is a random variable if, for every number a, there is a probability p that X is less than or equal to a. A discrete random variable is one that attains only certain values, such as the number of children one has. By contrast, a continuous random variable is one that can take on any value within a range, such as a person’s income (measured in the smallest possible fractions of a dollar).
Data analysis often involves hypotheses regarding the relationships between variables, such as “If X increases in value, then Y tends to increase (or decrease) in value.” Such hypotheses involve relationships between latent variables, which are abstract concepts. These concepts have to be operationalized into manifest variables that can be measured in actual research. In surveys, this operationalization involves either using one question to tap the concept or combining several questions into an index that measures the concept.
A basic distinction in statistical analysis is between the dependent variable that the researcher is trying to explain and the independent variable that serves as a predictor of the dependent variable. In regression analysis, for example, the dependent variable is the Y variable on the lefthand side of the regression equation Y = a + bX, whereas X is an independent variable on the righthand side of the equation.
The starting point in survey analysis is often looking at the distribution of the variables of interest, one at a time, including calculating appropriate univariate statistics such as percentage distributions. The changes in that variable over time can then be examined in a timeseries analysis. Univariate analysis is usually just the jumpingoff point for bivariate or multivariate analysis. For example, in survey experiments, the researcher examines the extent to which experimental manipulations in the survey (such as alternative wordings of a question) affect the variance in the variable of interest.

See also
Dependent Variable; Experimental Design; Independent Variable; Null Hypothesis; Regression Analysis
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