Continuous and discrete variables

Variables can also be viewed as continuous or discrete. Continuous variables are measured in terms of smaller and smaller amounts. Age is an example of a continuous variable. We start by measuring age in hours, then days, followed by months, and finally in terms of years. But, if you wanted to be absolutely precise you could measure age in terms of seconds or tenths or even small factions of a second. We think you get the point of continuous variation. In contrast, a discrete variable changes from one category or level to another without any in-between steps or increments. Your class level at the university is an example of a discrete variable. You go from being a first year to a second year student in one jump: university officials, for example, do not recognize a first year and one-half.

As you will see in Part 4, different analysis techniques are used for continuous versus discrete data.

For an additional view of measuring social characteristics, visit: Measurement, this site discusses the fundamental ideas involved with measurement in social research

In developing measures for indicators, you also have to be concerned about their validity and reliability.

Validity

Validity is the extent to which an indicator or set of indicators actually measure the concept it represents. When students argue with their professor whether an exam really measured their knowledge of a subject, they are questioning the validity of the questions making up the exam. Did the questions provide a valid measure of the students' knowledge of the course content? This is the idea behind validity of indicators. For social scientists, an indicator is valid to the extent that it measures the intended concept or one of its dimensions and not something else. Schooling, for example, could be a valid indicator of several concepts, such as social status or achievement, but it probably would not be a valid indicator of happiness. Different indicators would be needed for measures of happiness.

Validity is never absolutely established. The best researchers can do is to offer evidence for the validity of measurements they use. Three ways are frequently used to test the validity of indicators.

Content validity

In making the case for content validity, the investigator shows that the wording of the items used to measure a concept are clearly related to that concept or one of its dimensions. To illustrate, in the next chapter we list seven items used to measure attitudes toward wives working outside the home. (See Box 7.3). One of these items is: "A woman's place is in the home." Another item is: "Children can be assured of love and guidance even if the mother is employed." One could reasonably argue that these items can be considered measures of attitudes toward wives working outside the home.

Some researchers draw a distinction between content and f ace validity. In practice, however, it is hard to distinguish between the two and the terms are often used interchangeably. Like content validity, face validity is based on the "face value" of the items or measures. This assertion, however, is considered weak because it is based only on the judgment of the researcher. To strengthen claims for content or face validity, other knowledgeable persons can be asked to judge whether the items represent the concept being measured. Strong agreement among the ratings of qualified judges can increase validity claims, but stronger evidence for the validity of a measuring instrument is usually expected.

For many variables, face or content validity is assumed. There is little doubt that most simple questions, like asking for the gender of persons, their ages, their occupations, and many other commonly known facts about persons, are valid ways of getting the needed data. Requirements for establishing validity apply mainly to development of measures of less easily established variables. These include attitudes, perceptions, beliefs, and many other things researchers measure.

In presenting data for validity you should, as a minimum, establish the basis for asserting the content validity of any indicator you use. If a measuring instrument lacks obvious validity, based on the content of the indicators used, there is no point in proceeding to stronger bases for establishing the validity of the instrument. Careful researchers, however, do not stop with just claims for content validity. They seek more convincing evidence for the validity of any measure they use.