Levels of Measurement

Also known as scales of measurement, levels of measurement describe how data variables, numbers, and associated attributes are defined and categorized. Mathematical operations and statistical techniques have requirements that must be met in order for meaningful data analysis and interpretation to be undertaken. An assessment of the data measurement level facilitates determining the appropriate statistical analysis to use based on the data parameters. Listed in order of increasing variable complexity, four major levels of measurement are commonly identified: nominal, ordinal, interval, and ratio. This entry describes each of these levels.

Nominal level is the lowest or simplest measurement level. Information is assigned to categories that are mutually exclusive (a single group) and all-inclusive (contain all cases). The categories do not have any meaningful ordering and only denote whether the information should be assigned to a particular group. For instance, nominal-level data may include information on eye color (e.g., brown, blue, and green), religious affiliation (e.g., Christian, Muslim, and Buddhism), and political orientation (e.g., democrat, republican, and libertarian), among others. As per these examples, the data provide qualitative or named information, although nominal-level data can have quantitative values. Arbitrary number codes may be assigned to groups, such as coding gender as 1 = female and 2 = male; however, the values do not denote magnitude or ordering and no mathematical operations are possible. Nominal data are often displayed in pie, bar, or line charts showing the number or percentage of cases assigned to a particular group.

Ordinal level implies an ordering or ranking relationship among the measurements. In contrast to the nominal scale, more quantitative measures can be made. Ordinal-level variables are either strongly ordered or weakly ordered. Strongly ordered data assigns a ranking to each individual value or data unit in an ordered sequence. Consumer Reports ranks products according to several criteria and assigns each product a number indicating those that are the best and worst performers. Each product holds a particular position in the sequence, but the ranking does not indicate how much better (or worse) the products are compared to one another.

For a weakly ordered variable, data are placed in groups and the groups themselves are ranked; thus, each group consists of frequency counts rather than individual rankings. Agreement-response surveys (e.g., Likert-scale assessments) are a good example of weakly ordered data, where responses are grouped according to relative agreement with a statement (e.g., strongly agrees, agrees, undecided, disagrees, or strongly disagrees). Regardless of whether the variable is strongly or weakly ordered, the differences and ratios between rankings are not meaningful, only the relative order.

Interval level specifies quantitative information on the exact differences or intervals between successive values on a continuous number line. Unlike ordinal-level data, the difference between values is meaningful and indicates a magnitude change. However, the magnitude of this difference is not comparable across scales with different measurement units.

Interval scales are also characterized by an arbitrary (nontrue) zero. A common example given to illustrate this point involves the Fahrenheit and Celsius temperature scales. On both scales, zero degree does not indicate an absence of heat (or average kinetic energy), only a subjective point on which higher and lower heat values are determined. Meaningful differences between points on their respective scales can be found (e.g., 40° separates 80°F and 40°F), but ratios between those points cannot be established (e.g., 80°F does not indicate twice as much heat as a 40°F). Other [Page 969]examples include shoe sizes, calendar years, standardized exam scores, pH levels (acidity or alkalinity measure), and intelligence tests. In the social and behavioral sciences, most measurement scales are at the interval level, whereas the ratio level is more common in economics, business, and the physical sciences.

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