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, students' scores on an exam 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, statistics 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 newly elected senators in a given election. By contrast, a continuous random variable is one that can take on any value within a range, such as a person's height (measured in the smallest possible fractions of an inch).
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.
A basic distinction in statistical analysis is between the DEPENDENT VARIABLE that the researcher is trying to explain and the INDEPENDENT VARIABLES that serve as predictors of the dependent variable. In REGRESSION, 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 statistical analysis is often looking at the distribution of the variables of interest, one at a time, including calculating appropriate univariate statistics. The changes in that variable over time can then be examined in TIME-SERIES ANALYSIS. Univariate analysis is usually just the jumping-off point for BIVARIATE or MULTIVARIATE ANALYSIS. For example, in ANALYSIS OF VARIANCE, the researcher examines the extent to which experimental conditions affect the variance in the dependent variable.