Statistics for the Social Sciences Section 1.4: Variables This Revision: 02/21/2019 Prepared by Adam J. McKee

What are Variables? Science attempts to discover patterns in a reality that often seems chaotic. Ancient peoples noted the changes of the season, changes in the phase of the moon, changes in the tide. They also noted that these things (and many others) changed in a regular pattern. In the sciences, things that change and have different values from time to time or from person to person are called variables.

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

Many Things Vary 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.

Naming Conventions 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.

Back to Spreadsheet Lingo A variable is sometimes referred to as a column of data because of the convention of placing information for each person in rows, which makes each column form a single variable. All the variables taken together form the data that we analyze in a research project.

Constants 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.

Attributes 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. It is important to note the difference between the variable and its value for a particular individual. For example, the variable gender can take on two different levels: Male and female.

Independent Variables (IV) Special names are used for the two variables that are being studied by a researcher 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.

Dependent Variable The variable that is observed to see if it was changed by the independent variable is called the dependent variable. It is called dependent because its value depends on the independent variable.

Groups In an experiment, the independent variable often reflects that the researcher administered some type of treatment—something we do to the participants. 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.

Discrete 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 as Categories 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. Another common way to look at discrete variables is as counts of things.

Continuous Variables A continuous variable 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.