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Ordinal Measures

Variables with attributes we can logically rank-order are ordinal measures. The different attributes of ordinal variables represent relatively more or less of the variable. Variables of this type are social class, conservatism, alienation, prejudice, intellectual sophistication, and the like. In addition to saying whether two people are the same or different in terms of an ordinal variable, you can also say one is " more" than the other—that is, more conservative, more religious, older, and so forth.

In the physical sciences, hardness is the most frequently cited example of an ordinal measure. We may say that one material (for example, diamond) is harder than another (say, glass) if the former can scratch the latter and not vice versa. By attempting to scratch various materials with other materials, we might eventually be able to arrange several materials in a row, ranging from the softest to the hardest. We could never say how hard a given material was in absolute terms; we could only say how hard in relative terms—which materials it is harder than and which softer than.

Let's pursue the earlier example of grouping the people at a social gathering. This time imagine that we ask all the people who have graduated from college to stand in one group, all those with only a high school diploma to stand in another group, and all those who have not graduated from high school to stand in a third group. This manner of grouping people satisfies the requirements for exhaustiveness and mutual exclusiveness discussed earlier. In addition, however, we might logically arrange the three groups in terms of the relative amount of formal education (the shared attribute) each had. We might arrange the three groups in a row, ranging from most to least formal education. This arrangement would provide a physical representation of an ordinal measure. If we knew which groups two individuals were in, we could determine that one had more, less, or the same formal education as the other.

Notice in this example that it is irrelevant how close or far apart the educational groups are from one another. The college and high school groups might be 5 feet apart, and the less-than-high-school group 500 feet farther down the line. These actual

distances don't have any meaning. The high school group, however, should be between the less-than-high-school group and the college group, or else the rank order will be incorrect.

Interval Measures

For the attributes composing some variables, the actual distance separating those attributes does have meaning. Such variables are interval measures. For these, the logical distance between attributes can be expressed in meaningful standard intervals.

For example, in the Fahrenheit temperature scale, the difference, or distance, between 80 degrees and 90 degrees is the same as that between 40 degrees and 50 degrees. However, 80 degrees Fahrenheit is not twice as hot as 40 degrees, because the zero point in the Fahrenheit scale is arbitrary; zero degrees does not really mean lack of heat. Similarly, minus 30 degrees on this scale doesn't represent 30 degrees less than no heat. (This is true for the Celsius scale as well. In contrast, the Kelvin scale is based on an absolute zero, which does mean a complete lack of heat.)

About the only interval measures commonly used in social scientific research are constructed measures such as standardized intelligence tests that have been more or less accepted. The interval separating IQ scores of 100 and 110 may be regarded as the same as the interval separating scores of 110 and 120 by virtue of the distribution of observed scores obtained by many thousands of people who have taken the tests over the years. But it would be incorrect to infer mat someone with an IQ of 150 is 50 percent more intelligent than someone with an IQ of 100. (A person who received a

ordinal measure A level of measurement describing a variable with attributes we can rank-order along some dimension. An example would be socioeconomic status as composed of the attributes high, medium, low.

interval measure A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes. The Fahrenheit temperature scale is an example of this, because the distance between 17 and 18 is the same as that between 89 and 90.

136. Chapter 5: Conceptualization, Operationalization, and Measurement

score of 0 on a standard IQ test could not be regarded, strictly speaking, as having no intelligence, although we might feel he or she was unsuited to be a college professor or even a college student. But perhaps a dean...?)

When comparing two people in terms of an interval variable, we can say they are different from one another (nominal), and that one is more than another (ordinal). In addition, we can say " how much" more.

Ratio Measures

Most of the social scientific variables meeting the minimum requirements for interval measures also meet the requirements for ratio measures. In ratio measures, the attributes composing a variable, besides having all the structural characteristics mentioned previously, are based on a true zero point. The Kelvin temperature scale is one such measure. Examples from social scientific research include age, length of residence in a given place, number of organizations belonged to, number of times attending church during a particular period of time, number of times married, and number of Arab friends. Returning to the illustration of methodological party games, we might ask a gathering of people to group themselves by age. All the one-year-olds would stand (or sit or lie) together, the two-year-olds together, the three-year-olds, and so forth. The fact that members of a single group share the same age and that each different group has a different shared age satisfies the minimum requirements for a nominal measure. Arranging the several groups in a line from youngest to oldest meets the additional requirements of an ordinal measure and lets us determine if one person is older than, younger than, or the same age as another. If we space the groups equally far apart, we satisfy the additional requirements of an interval measure and will be able to say how much older one person is than an-

ratio measure A level of measurement describing a variable with attributes that have all the qualities of nominal, ordinal, and interval measures and in addition are based on a " true zero" point. Age would be an example of a ratio measure.

other. Finally, because one of the attributes included in age represents a true zero (babies carried by women about to give birth), the phalanx of hapless party goers also meets the requirements of a ratio measure, permitting us to say that one person is twice as old as another. (Remember this in case you're asked about it in a workbook assignment.) Another example of a ratio measure is income, which extends from an absolute zero to approximately infinity, if you happen to be the founder of Microsoft.

Comparing two people in terms of a ratio variable, then, allows us to conclude (1) whether they are different (or the same), (2) whether one is more than the other, (3) how much they differ, and (4) what the ratio of one to another is. Figure 5-1 summarizes this discussion by presenting a graphic illustration of the four levels of measurement.

Implications of Levels of Measurement

Because it's unlikely that you'll undertake the physical grouping of people just described (try it once, and you won't be invited to many parties), I should draw your attention to some of the practical implications of the differences that have been distinguished. These implications appear primarily in the analysis of data (discussed in Part 4), but you need to anticipate such implications when you're structuring any research project.

Certain quantitative analysis techniques require variables that meet certain minimum levels of measurement. To the extent that the variables to be examined in a research project are limited to a particular level of measurement—say, ordinal—you should plan your analytical techniques accordingly. More precisely, you should anticipate drawing research conclusions appropriate to the levels of measurement used in your variables. For example, you might reasonably plan to determine and report the mean age of a population under study (add up all the individual ages and divide by the number of people), but you should not plan to report the mean religious affiliation, because that is a nominal variable, and the mean requires ratio-level data. (You could report the modal—the most common—religious affiliation.)

At the same time, you can treat some variables as representing different levels of measurement.

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