Measurement, Levels

In its basic form, research is about the relationships between concepts measured as variables. Researchers make inferences, draw conclusions, and form new hypotheses based on the patterns they detect in these relationships. It is important, therefore, for researchers to be as precise in their measurement of concepts as possible. The statistical techniques that can be applied to a set of variables are contingent on the level of precision at which the variables are measured. The more precise a measure, the more sophisticated statistical techniques can be employed in the analysis, and the stronger the conclusions that can be drawn. In this entry, the major levels of measurement, the appropriate statistical procedures based on them, and a few concrete examples are discussed.

Measurement is usually discussed in terms of four levels, as stated by S. S. Stevens (1946). Moving from least precise to most precise, they are nominal, ordinal, interval, and ratio. Nominal measures simply classify members based on particular attributes. These must be mutually exclusive and exhaustive. For example, gender is a nominal variable. It is made up of the mutually exclusive and exhaustive categories of (a) male and (b) female or (a) female and (b) male (neglecting other possible distinctions). It makes no difference how numbers are assigned to the categories because there is no judgment made as to how much of a variable is possessed by an attribute. That is, male is not higher than female, or vice versa. It is simply a way to categorize a sample or population, and neither male nor female possess more of the quality of gender than the other.

For instance, suppose we have a population in which everyone belongs to one of four religions: Catholicism, Judaism, Islam, or Protestantism. Then, religion is a variable—that is, it is mutually exclusive and exhaustive (at least with reference to our example population). Everyone is classified into one of the four categories. However, none is higher on the scale. Protestant is not more or less religious than any of the others, nor is Catholic, Jewish, or Muslim. The only quantitative techniques we can use with nominal variables are those based on the categories—that is, frequency distributions and the mode. We cannot perform statistical procedures—for instance, take a mean or find a standard deviation—using this variable. We cannot add or subtract them. Statistical procedures must turn these variables into binary (“dummy”) variables to be able to use them; this is discussed below. Many examples of nominal variables exist in social science, such as race, ethnicity, region, marital status, and occupation.

The next level of measurement is the ordinal level. Ordinal variables, like nominal variables, allow the researcher to classify attributes into mutually exclusive and exhaustive categories, but, unlike nominal variables, the attributes categorized in ordinal variables can be ordered so that they run from less of an attribute to more of that attribute. Big, bigger, biggest is an example of a logical order. Ordinal variables are quite common [Page 1526]in social sciences. Agree/disagree questions measure on an ordinal scale. For example, “The world is flat. Do you (a) strongly disagree, (b) disagree, (c) neutral, (d) agree, or (e) strongly agree?” This answering scheme produces an ordinal measure because there is a logical ordering from strongly agree (with the statement) to strongly disagree. A “feeling thermometer” is an ordinal variable. For example, on a scale of 0 to 100, with 0 being very cold and 100 being very warm, one can ask, “How do you feel about Barack Obama? John McCain?” Statistical measures that one can use when the variables are measured at the ordinal level are the median, percentiles, Spearman's rho, and gamma. Other examples of ordinal variables used in social science are variables with answer patterns running from like to dislike and variables measuring attitudes.

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