#### Variables

Behavioral scientists are always concerned with variables. Each variable takes on values in a set, which might be numerical, as in real numbers, or symbolic, as in colors, labels, or names. From their perspective, the three most important classes of variables are:

• Dependent: These are the main objects of interest for the hypothesis.
• Independent: These have values that are directly changed or manipulated by the scientist.
• Nuisance: As these vary, their values might affect the values of the dependent variable, but the scientist has less control over them and they are not the objects of interest.
The high-level task is to formulate a hypothesis that can be evaluated in terms of the relationship between independent and dependent variables, and then design an experiment that can keep the nuisance variables under control and can be conducted within the budget of time, resources, and access to subjects.

The underlying mathematics for formulating models of how the variables behave and predicting their behavior is probability theory, which was introduced in Section 6.4. Unfortunately, we are faced with an inverse problem, as was noted in Figure 12.3. Most of the behavior is not directly observable, which means that we must gather data and make inferences about the underlying models and try to obtain as much confidence as possible. Thus, resolving the hypothesis is a problem in applied statistics, which is the natural complement or inverse of probability theory.

Steven M LaValle 2020-01-06