Level of measurement or scale of measure is a classification that describes the nature of information within the numbers assigned to variables. Psychologist Stanley Smith Stevens developed the best known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. Other classifications include those by Chrisman and by Mosteller and Tukey.This framework of distinguishing levels of measurement originated in psychology and is widely criticized by scholars in other disciplines.

Overview

Stevens proposed his typology in a 1946 Science article titled “On the theory of scales of measurement”. In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called “nominal,” “ordinal,” “interval,” and “ratio,” unifying both “qualitative” (which are described by his “nominal” type) and “quantitative” (to a different degree, all the rest of his scales). S. S. Stevens (1946, 1951, 1975) claimed that what counted was having an interval or ratio scale. Subsequent research has given meaning to this assertion, but given his attempts to invoke scale type ideas it is doubtful if he understood it himself … no measurement theorist I know accepts Stevens’s broad definition of measurement … in our view, the only sensible meaning for ‘rule’ is empirically testable laws about the attribute.

Nominal level

The nominal type differentiates between items or subjects based only on their names or (meta-)categories and other qualitative classifications they belong to; thus dichotomous data involves the construction of classifications as well as the classification of items. Discovery of an exception to a classification can be viewed as progress. Numbers may be used to represent the variables but the numbers do not have numerical value or relationship: For example, a Globally unique identifier.

Examples of these classifications include gender, nationality, ethnicity, language, genre, style, biological species, and form. In a university one could also use hall of affiliation as an example. Other concrete examples are

• in grammar, the parts of speech: noun, verb, preposition, article, pronoun, etc.
• in politics, power projection: hard power, soft power, etc.
• in biology, the taxonomic ranks below domains: Archaea, Bacteria, and Eukarya
• in software engineering, type of faults: specification faults, design faults, and code faults

Nominal scales were often called qualitative scales, and measurements made on qualitative scales were called qualitative data. However, the rise of qualitative research has made this usage confusing. The numbers in nominal measurement are assigned as labels and have no specific numerical value or meaning. No form of mathematical computation (+,- x etc.) may be performed on Nominal measures. Nominal level is the lowest measurement level used from a statistical point of view.

Ordinal scale

The ordinal type allows for rank order (1st, 2nd, 3rd, etc.) by which data can be sorted, but still does not allow for relativedegree of difference between them. Examples include, on one hand, dichotomous data with dichotomous (or dichotomized) values such as ‘sick’ vs. ‘healthy’ when measuring health, ‘guilty’ vs. ‘innocent’ when making judgments in courts, ‘wrong/false’ vs. ‘right/true’ when measuring truth value, and, on the other hand, non-dichotomous data consisting of a spectrum of values, such as ‘completely agree’, ‘mostly agree’, ‘mostly disagree’, ‘completely disagree’ when measuring opinion.

Interval scale

The interval type allows for the degree of difference between items, but not the ratio between them. Examples includetemperature with the Celsius scale, which has two defined points (the freezing and boiling point of water at specific conditions) and then separated into 100 intervals, date when measured from an arbitrary epoch (such as AD), percentagesuch as a percentage return on a stock, location in Cartesian coordinates, and direction measured in degrees from true or magnetic north. Ratios are not meaningful since 20 °C cannot be said to be “twice as hot” as 10 °C, nor can multiplication/division be carried out between any two dates directly. However, ratios of differences can be expressed; for example, one difference can be twice another. Interval type variables are sometimes also called “scaled variables”, but the formal mathematical term is an affine space (in this case an affine line).

Ratio scale

The ratio type takes its name from the fact that measurement is the estimation of the ratio between a magnitude of a continuous quantity and a unit magnitude of the same kind (Michell, 1997, 1999). A ratio scale possesses a meaningful (unique and non-arbitrary) zero value. Most measurement in the physical sciences and engineering is done on ratio scales. Examples include mass, length, duration, plane angle, energy and electric charge. In contrast to interval scales, ratios are now meaningful because having a non-arbitrary zero point makes it meaningful to say, for example, that one object has “twice the length” of another (= is “twice as long”). Very informally, many ratio scales can be described as specifying “how much” of something (i.e. an amount or magnitude) or “how many” (a count). The Kelvin temperature scale is a ratio scale because it has a unique, non-arbitrary zero point called absolute zero.

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