MAIN POINTS

Measurement is closely related to the concept of operational definitions. Measurement is a procedure in which one assigns numerals-numbers or other symbols-to empirical properties (variables) according to a set of rules. Numerals are symbols, Roman or Arabic, that are given quantitative meaning and then become numbers that make possible the use of mathematical and statistical techniques for purposes of description, explanation, and prediction. Assignment refers to the mapping of symbols onto objects or events. Rules explicate the ways in which numerals or numbers are to be assigned to objects or events.

Rules are the most significant component of the measurement procedure because they determine the quality of measurement. Poor rules make measurement meaningless. Isomorphism means similarity or identity of structure. In measurement, the crucial question to be asked is whether the numerical system is isomorphic with the structure of the concepts being measured. Frequently, social scientists measure indicators of concepts, and often, multiple indicators must be developed to represent abstract concepts.

The requirement of isomorphism between numerical systems and empirical properties (or indicators) leads to a distinction among different ways of measuring-that is, to distinct levels of measurement.

The lowest level of measurement is the nominal level, where numbers or other symbols are used to classify objects or observations. A nominal level of measurement is attained when a set of objects can be classified into categories that are exhaustive and mutually exclusive.

Measurements at the ordinal level involve exhaustive and mutually exclusive categories, but the categories are also rank ordered from high to low. The assignment of symbols is arbitrary, but ordinal measurements are rank ordered.

The interval level of measurement involves difference, ranking, and equal intervals between categories; thus, the unit measurement is constant across the scale.

At the ratio level of measurement, the ratio of any two numbers is independent of the unit of measurement; this measure has all of the components of the interval level but involves natural zero points.

Variables that can be measured at a ratio level can also be measured at the interval, ordinal, and nominal levels. As a rule, properties that can be measured at a higher level can also be measured at lower levels, but not vice versa.

Differences in scores that are due to anything other than real differences in the aspects of the property being measured are termed measurement errors. Measurement errors result when the scores obtained are related to an associated attribute, or they may be due to differences in temporary conditions, in the setting, or in the administration of the measuring instrument. They may also result when different people interpret the instrument in different ways.

Systematic measurement errors are constant between cases and studies, whereas random errors affect the results differently each time the measuring instrument is used.

Validity is concerned with the question: "Is one measuring what one thinks one is measuring?" There are different types of validity.

Content validity means that the measurement instrument covers all the attributes of the concept you are trying to measure; that nothing relevant to the phenomenon under investigation is left out. There are two common varieties of content validity. Face validity rests on the investigators' subjective evaluation as to the validity of a measuring instrument. Sampling validity is concerned with whether the content of the instrument adequately represents the content population of the property being measured.

Empirical validity is concerned with the relations between a measuring instrument and the measurement of outcomes; if a measuring instrument is valid, then there should exist strong relations between the results produced by the instrument and other variables. Predictive validity is estimated by a prediction to an external measurement referred to as a criterion, and by checking a measuring instrument against some outcome.

Construct validity involves relating a measuring instrument to a general theoretical framework in order to determine whether the instrument is tied to the concepts and theoretical assumptions that are employed.

Reliability is a central concern to social scientists because it is rare when measuring instruments are completely valid. A frequently used method for evaluating an instrument is its degree of reliability. Reliability refers to the extent to which a measuring instrument contains variable errors. Each measure consists of two components: a true component and an error component. Reliability is defined as the ratio of the true score variance to the total variance in the scores as measured.

There are three common methods for estimating measurement reliability: the test retest method, the parallel forms technique, and the split half method.