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Measurement theory is a sub-field of methodology that deals with the relationship between theoretical constructs and their measurement in the research process.
Generally 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.
In measurement, there are three central concepts: numerals, assignment, and rules (e.g. Wimmer & Dominick 2014). Numerals are symbols such as S, 5, 10, or 100, and have no explicit quantitative meaning. Assignment is the designation of numerals or numbers to certain objects or events. For example, we assign numbers to classify people by how they get their news. 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 can be obvious (i.e., measuring reading speed with a stopwatch) or not so obvious (i.e., measuring ‘enjoyment of televised sports’).
In addition, measurement systems also strive to be isomorphic to reality. Basically, isomorphism means identity or similarity of form or structure. To strive for isomorphism, researchers must define the sets of objects being measured and the numerical sets from which they 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 social sciences, researchers must ask the question, “Do the measurement procedures being used have some rational and empirical correspondence with ‘reality’?” (Kerlinger & Lee 1999). The ultimate question that must be asked is ‘Is the measurement procedure isomorphic to reality?’
In 1946, Stevens suggested four levels, or types, of measurement. Nominal measurement is the weakest form of measurement and identifies variables whose values have no mathematical interpretation. In addition, they must be mutually exclusive and exhaustive. Examples are gender, ethnicity, occupation, religious affiliation, and social security number. 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. Examples are a student’s academic level and socio-economic status.
The interval scale of measurement is characterized by two features: it has (1) equal units of measurement; and (2) an arbitrarily established zero point. It includes the characteristics of the nominal and ordinal scales, plus the numbers indicating the values of a variable represent fixed measurement units, and there is no absolute or fixed zero point. The most familiar examples of interval-level measurement are in both the Fahrenheit (F) and Celsius (C) scales as well as rating scales employed to assess opinions on any objects.
The highest level of measurement is the ratio scale. It possesses the characteristics of the nominal, ordinal, and interval scales, plus it has an absolute or natural zero point that has empirical meaning. If a measurement is zero on a ratio scale, then the object in question has none of the property being measured. 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. Examples include a person’s age or time spent on the Internet.
One can determine one’s level of measurement by applying it to the following test: If one can say that one object is different from another, one has a nominal scale; one object is bigger or better or more of anything than another, one has an ordinal scale; one object is so many units (degrees, inches) more than another, one has an interval scale; one object is so many times as big or bright or tall or heavy as another, one has a ratio scale.
- Babbie, E. (2013). The practice of social research, 13th edn. Belmont, CA: Wadsworth Cengage Learning.
- 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. & Lee, H. B. (1999). Foundations of behavioral research, 4th edn. Boston: Wadsworth.
- Leedy, P. D. & Ormrod, J. E. (2014). Practical research: Planning and design, 10th edn. Harlow: Pearson
- Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680.
- Wimmer, R. D. & Dominick, J. R. (2014). Mass media research: An introduction, 10th edn. Boston: Wadsworth Cengage Learning.