Variables, Values, and Observations
Variables
When discussing data, social scientists often speak in terms of variables, values, and observations. For the type of research discussed here, a variable refers to some specific participant characteristic that can assume different values (i.e., the values vary). For the participants in the study just described, Amount of Insurance Sold is an example of a variable: some participants had sold a lot of insurance whereas others had sold less. A second variable was Goal Difficulty: some participants set more difficult goals while others set less difficult goals. Participant Age and Sex (male or female) were other variables, though not considered in our initial hypothesis.
Values
A value is a specific quantity or category of a variable. For example, Amount of Insurance Sold is a variable that can assume a range of values. One agent might sell $2,000,000 worth of insurance in one year, one might sell $100,000, whereas another may sell nothing (i.e., $0). Age is another variable that can assume a variety of values. In our example, these values range from a low of 22 years (the youngest agent) to a high of 64 years (the oldest agent). In other words, age is a variable that is comprised of a wide array of specific values.
Quantitative Variables versus Classification Variables
For both types of these variables, a given value is the specific score that indicates participants’ standing with respect to variable of interest. Amount of Insurance Sold and Age are quantitative variables since numbers serve as values. The word “score” is an appropriate substitute for the word value in these cases.
A different type of variable is a classification variable or, alternatively, qualitative variable or categorical variable. With classification variables, different values represent different groups to which participants can belong. Sex is a good example of a classification variable as it (generally) assumes only one of two values (i.e., participants are classified as either male or female). Race is an example of a classification variable that can assume a larger number of values: participants can be classified as Caucasian; African American; Asian American; or as belonging to a large number of other groups. Notice why these variables are classification variables and not quantitative variables. The values represent only group membership; they do not represent a characteristic that some participants possess in greater quantity than others.
Observational Units
In discussing data, researchers often make reference to observational units that can be defined as individual participants (or objects) that serve as the source of the data. (Observational units are also referred to as units of analysis.) Within the social sciences, a person usually serves as the observational unit under study (although it is also possible to use some other entity such as an individual school or organization as the observational unit). In this text, the person is used as the observational unit in all examples. Researchers often refer to the number of observations (or cases) included in their datasets. This simply refers to the number of participants studied.
For a more concrete illustration of the concepts discussed so far, consider the following dataset:
| Observation | Name | Sex | Age | Scores | Goal Difficulty Rank | Sales |
|---|---|---|---|---|---|---|
| 1 | Bob | M | 34 | 97 | 2 | $598,243 |
| 2 | Pietro | M | 56 | 80 | 1 | $367,342 |
| 3 | LeMont | M | 36 | 67 | 4 | $254,998 |
| 4 | Susan | F | 24 | 40 | 3 | $80,344 |
| 5 | Saleem | M | 22 | 37 | 5 | $40,172 |
| 6 | Mack | M | 44 | 24 | 6 | $0 |
The preceding table reports information about six research participants: Bob; Pietro; LeMont; Susan; Saleem; and Mack. Therefore, the dataset includes six observations. Information about a given observation (participant) appears as a row running left to right across the table. The first column of the dataset (running vertically) indicates the observation number, and the second column reports the name of the participant. The remaining five columns report information on the five research variables under study. The “Sex” column reports participant sex, which can assume one of two values: “M” for male and “F” for female. The “Age” column reports participants’ age in years. The “Goal Difficulty Scores” column reports participants’ scores on a fictitious goal difficulty scale. (Assume that each participant completed a 20-item questionnaire that assessed the difficulty of his or her work goals.)
Depending on their responses, participants receive a score that can range from a low of 0 (meaning that work goals are quite easy) to a high of 100 (meaning that they are quite difficult). The “Rank” column shows how participants were ranked by their supervisor according to their overall effectiveness as agents when compared to one another. A rank of 1 represents the most effective agent whereas a rank of 6 represents the least effective. Finally, the “Sales” column indicates the amount of insurance sold by each agent (in dollars) during the past year.
This example illustrates a very small dataset with six observations and five research variables (i.e., Sex, Age, Goal Difficulty, Rank and Sales). One variable is a classification variable (Sex), while the remainder are quantitative variables. The numbers or letters that appear within a column represent some of the values that can be assumed by that variable.