Variable

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 left-hand side of the regression equation Y = a + bX, whereas X is an independent variable on the right-hand 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 time-series analysis. Univariate analysis is usually just the jumping-off 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.