Operational Definitions In our last class, we discussed (a) what it means to quantify psychological variables and (b) the different scales of measurement used for categorical and continuous variables. However, we deliberately side-stepped an important question: How do we determine “what matters” when we try to measure a variable?

Simple Example Let’s consider a relatively simple example: Let’s try to measure crying. Before we can do so, we need to decide “what counts” as crying behavior. What examples come to mind?

Definition of an Operational Definition It is critical that the set of rules, or operations, that we use to measure a behavior be as explicit and clear-cut as possible. These rules, or operations, constitute the operational definition of a variable.

Complex Example Now let’s consider a more complex variable: the experience of humor. Whether or not someone finds something funny is a much more challenging (i.e., less tangible) thing to measure than crying. In-Class Example: Two sets of operational definitions, and three students listening to jokes.

Important Distinction Latent vs. Observed variables –An observed variable, like crying, is directly observable and can be measured relatively easily once observers agree upon what counts as an instance of crying and what does not. –A latent variable or construct is not directly observable. Instead, it is inferred from variables that can be observed.

Measuring Latent Variables Latent variables can be measured, but their measurement is much more complicated than that of observed variables. The first thing we need to do is identify, usually on an intuitive or theoretical basis, the scale of the latent variable. Is it categorical or continuous? If continuous, should we scale it on an interval metric or a ratio metric? Next, we need to identify the indicators of the latent variable (i.e., the observable consequences or manifestations of the latent variable).

Measuring Latent Variables Let’s answer the following question: Someone who finds something funny should be likely to behave in the following ways: __________. These things (e.g., laughing)—which also need to be operationally defined—can be considered observable indicators of the unobserved state of “finding something humorous.”

Measuring Latent Variables So, to operationally define a latent variable, we need to –specify the scale of the variable, –identify the observable manifestations of that latent variable –operationally define those observable manifestations. Next, we need to know how the operational definitions of the observable variables map onto the latent variable.

Mapping Mapping—specifying the relationship between the latent and manifest variable— tends to be handled differently by different researchers. Two considerations: –How many indicators to use? –Can we assume a linear relationship between the measured variables and the latent variable?

> 1One Linear Nonlinear Multiple non- linear indicators (Very Complex) Single non- linear relationship (Complex) Multiple linear indicators (Simple) Equivalence relation (Simplest) How many indicators? Mathematical Mapping

Equivalence Relationship Simplest case: The equivalence relationship. In this case, we use one indicator and assume that the relation between the latent variable and the manifest variable is linear. The scale of the latent variable is identical to the scale chosen for the manifest variable. Example: We may operationally define laughing, and then measure humor as if it is equal to laughing.

Humor Laughing For each extra laugh, we assume the person thought the joke was one unit more funny Someone who laughs 8 times would get a humor score of 8.

Equivalence Relationship Advantages: –Explicit and straight-forward –Doesn’t require complicated mathematics –Other researchers can easily determine what you did Disadvantages: –Behaviors are influenced by many things. Thus, part of what you’re measuring may be unrelated to the latent variable of interest. –Latent variables manifest themselves in a variety of ways. By focusing on one variable, our measurements are not as rich or compelling.