Thinking about measurement brings to mind an old adage, “If it exists, it is measurable.” However, in research, we tend to go beyond that adage, saying “If it exists, it must be measurable” (Leedy 1997). Most researchers will likely agree that measurement is a pillar of social and behavioral sciences research (Guilford 1954).

## What Is Measurement?

Given this, what exactly is measurement? The things that come to mind when we think of measurement are rulers, yardsticks, and scales, to name a few, but in research, measurement takes on a whole new meaning. Leedy (1997, 26) defines measurement as “limiting the data of any phenomenon – substantial or insubstantial – so that those data may be examined mathematically and according to an acceptable qualitative and quantitative standard.” Similarly, Babbie (2001, 199) views measurement as “careful, deliberate observations of the real world for the purpose of describing objects and events in terms of the attributes composing a variable.”

In other words, scientists make a deliberate decision to observe, are equally deliberate about what they will observe, take precautions against erroneous observations, and record their observations carefully as measurements. Ultimately, measurement is the process whereby a thing, concept, or object measured is compared against a point of limitation. For example, in the social and behavioral sciences, we frequently compare the results of research against statistical norms such as the normal curve, point of central tendency, and degree of dispersion for quantitative data, and across data sources, methods, and time for qualitative data (Leedy 1997). Measurement, therefore, is a tool by which data is inspected, analyzed, and interpreted so that the researcher may probe to discover or attribute meaning.

The fundamentals of measurement are quite simple: A researcher assigns numerals to objects, events, or properties according to systematic rules (Kerlinger 1986; Wimmer & Dominick 2003). Examples of measurement are everywhere: we turn on the television and see an advertisement for toothpaste with the slogan “9 out of 10 dentists recommend . . .” Sometimes measurements are numerical or quantitative, such as “students purchased sandwiches from the Sub Shop 2.4 times more than the previous month.” Other times they are qualitative, such as “the motorist expressed annoyance on being told the emergency road service closed at 5 p.m.” (Wimmer & Dominick 2003).

## Concepts Of Measurement

In measurement, there are three central concepts: numerals, assignment, and rules (Katzer et al. 1998; Kerlinger 1986; Wimmer & Dominick 2003). Numerals are symbols such as S, 5, 10, or 100, and have no explicit quantitative meaning. When a numeral has been given quantitative meaning, it becomes a number and can be used in mathematical and statistical computations. Assignment is the designation of numerals or numbers to certain objects or events. An example of a simple measurement system would be to assign the numeral 1 to the people who obtain most of their news from television, the numeral 2 to those who get most of their news from a newspaper, and the numeral 3 to those who receive most of their news from the Internet. Rules specify the way that numerals or numbers are to be assigned. Rules are the foundation of any measurement system, so if the rules are faulty the measurement system will be faulty too. For some research studies, the rules often seem to be obvious (i.e., a stopwatch and standardized message may be sufficient to measure reading speed). In other research studies the rules may not be apparent. For example, before a researcher can measure “enjoyment of televised sports” or “attitude toward violence,” he or she must articulate thoughtful measurement techniques.

## Measurement And “Reality” Isomorphism

In addition, measurement systems also strive to be isomorphic to reality. Basically, isomorphism means identity or similarity of form or structure (Kerlinger 1986; Wimmer & Dominick 2003). To strive for isomorphism, researchers must define the sets of objects being measured and the numerical sets from which we assign numerals to those objects, and check that the rules of assignment or correspondence are tied to “reality.” To assess isomorphism to reality, researchers ask the question “Is this set of objects isomorphic to that set of objects?” In the physical sciences, for example, isomorphism is not a problem, because there is usually a direct relationship between the objects being measured and the numbers assigned to them: if an electric current travels through a substance with less resistance than it does through a different substance, it can be concluded that the first substance is a better conductor than the second. Additionally, testing more substances can lead to a ranking of conductors, where the numbers assigned indicate the degrees of conductivity. In this example, the measurement system is isomorphic to reality (Wimmer & Dominick 2003).

In the social sciences, this assessment is not as clear cut or obvious. For example, researchers must ask the question “Do the measurement procedures being used have some rational and empirical correspondence with ‘reality’?” (Kerlinger 1986). The ultimate question that must be asked is “Is the measurement procedure isomorphic to reality?” The only problem is that we rarely discover easily the degree of correspondence to reality of our measurements. Unfortunately, many researchers often do not know whether they are measuring what they are trying to measure. Even so, researchers must find a way to test the isomorphism with reality of the measurement numbers game they play.

## Levels Of Measurement

In 1946, Stevens suggested a hierarchy of levels for the measurement of data that has become a classic of categorization for statisticians and researchers. Stevens suggested four levels, or types, of measurement, which he called (1) nominal, (2) ordinal, (3) interval, and (4) ratio.

The word nominal comes from the Latin nomen meaning “a name.” Thus, we can measure data by assigning names to them. In other words, by assigning a specific name to a concept or object, we have restricted that thing to the meaning of its name (Leedy 1997). Nominal measurement is the weakest form of measurement and identifies variables whose values have no mathematical interpretation. Examples of nominal-level measurement are gender, ethnicity, occupation, religious affiliation, social security number, license plates, and so on. They must be mutually exclusive (only check one) and exhaustive (everyone can be classified into a category).

In the ordinal scale of measurement, we think in terms of the symbols > (greater than) or < (less than). The ordinal scale implies that the entity being measured is quantified in terms of being of a higher or lower or a greater or lesser order than a comparative entity. In measuring on the ordinal scale, the relationship is always asymmetrical. For example, something is always greater than, less than, older than, younger than, more intelligent than, more desirable than, more tactful than, etc. (Babbie 2001; Leedy 1997; Wimmer & Dominick 2003). In other words, the numbers assigned to cases specify only the order of the cases, allowing for greater than/less than distinctions. Examples of ordinal-level measurement are a student’s academic level, and socio-economic status.

The interval scale of measurement is characterized by two features: (1) it has equal units of measurement, and (2) its zero point has been established arbitrarily (Leedy 1997). Thus, it includes the characteristics of the nominal and ordinal scales, and in addition the numbers indicating the values of a variable represent fixed measurement units. In the interval-level measurement there is no absolute or fixed zero point. The most familiar example of interval-level measurement is temperature: in both the Fahrenheit (F) and Celsius (C) scales, each degree is equal to the others and the zero point has been established arbitrarily. For instance, it takes the same amount of heat to warm an object from 30° to 40° as from 50° to 60°. Also, since heat does not begin at 0° on the Fahrenheit scale, 60° is not twice as hot as 30°. A common use of interval measurement is in the rating scales employed by many businesses, survey groups, and professional organizations.

The highest level of measurement is the ratio scale. Ratio measurement is also the measurement ideal of the research scientist. It possesses the characteristics of the nominal, ordinal, and interval scales, and in addition it has an absolute or natural zero point that has empirical meaning (Leedy 1997). If a measurement is zero on a ratio scale, then we can say that the object in question has none of the property being measured. Since there is an absolute or natural zero point, all arithmetic operations are possible, such as multiplication and division, and the numbers on the scale indicate the actual amounts of the property being measured. For example, if a ratio scale of achievement existed, then we could say that a student with a score of 8 had an achievement level twice as great as a student with a score of 4. Other examples of ratio level measurement include driving speed, weight, hours of coursework completed, age, and the balance in your checking account.

Interestingly, Senders (1958, 51) has summarized the four levels of measurement in the following test for various kinds of data measurement. If you can say that: one object is different from another, you have a nominal scale; one object is bigger or better or more of anything than another, you have an ordinal scale; one object is so many units (degrees, inches) more than another, you have an interval scale; one object is so many times as big or bright or tall or heavy as another, you have a ratio scale.

Taken together, we see that measurement is crucial to any research project. Without good measurement, we have faulty research. Measurement involves the assignment of numerals to objects and concepts according to rules. Then researchers decide the appropriate level of measurement and also assess whether the measurement procedure is isomorphic to reality. To be useful, a measurement must be both valid and reliable. Measurements begin with observations, but these raw materials must often be refined and clarified.

**References:**

- Babbie, E. (2001). The practice of social research, 9th edn. Belmont, CA: Wadsworth and Thomson Learning.
- Guilford, J. P. (1954). Psychometric methods. New York: McGraw-Hill.
- Katzer, J., Cook, K. H., & Crouch, W. W. (1998). Evaluating information: A guide for users of social science research, 4th edn. Boston, MA: McGraw-Hill.
- Kerlinger, F. N. (1986). Foundations of behavioral research, 3rd edn. New York: CBS College Publishing.
- Leedy, P. D. (1997). Practical research: Planning and design, 6th edn. Upper Saddle River, NJ: Prentice Hall.
- Senders, V. L. (1958). Measurement and statistics: A basic text emphasizing behavioral science. New York: Oxford University Press.
- Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677– 680.
- Wimmer, R. D., & Dominick, J. R. (2003). Mass media research: An introduction, 7th edn. Belmont, CA: Wadsworth and Thomson Learning.