Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and has since had a complex history, being adopted and extended in some disciplines and by some scholars, and criticized or rejected by others. Other classifications include those by Mosteller and Tukey, and by Chrisman.
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In this Dossier
- ⭐ Core Definition: Level of measurement
- Level of measurement in the context of Measurement
- Level of measurement in the context of Continuum (theory)
- Level of measurement in the context of Bivariate data
- Level of measurement in the context of ISO 668
- Level of measurement in the context of Statistical data type
Level of measurement in the context of Measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind.The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International Vocabulary of Metrology (VIM) published by the International Bureau of Weights and Measures (BIPM). However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.
Measurement is a cornerstone of trade, science, technology and quantitative research in many disciplines. Historically, many measurement systems existed for the varied fields of human existence to facilitate comparisons in these fields. Often these were achieved by local agreements between trading partners or collaborators. Since the 18th century, developments progressed towards unifying, widely accepted standards that resulted in the modern International System of Units (SI). This system reduces all physical measurements to a mathematical combination of seven base units. The science of measurement is pursued in the field of metrology.
Level of measurement in the context of Continuum (theory)
Continuum (pl.: continua or continuums) theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variation using qualitatively different states.
Level of measurement in the context of Bivariate data
In statistics, bivariate data is data on each of two variables, where each value of one of the variables is paired with a value of the other variable. It is a specific but very common case of multivariate data. The association can be studied via a tabular or graphical display, or via sample statistics which might be used for inference. Typically it would be of interest to investigate the possible association between the two variables. The method used to investigate the association would depend on the level of measurement of the variable. This association that involves exactly two variables can be termed a bivariate correlation, or bivariate association.
For two quantitative variables (interval or ratio in level of measurement), a scatterplot can be used and a correlation coefficient or regression model can be used to quantify the association. For two qualitative variables (nominal or ordinal in level of measurement), a contingency table can be used to view the data, and a measure of association or a test of independence could be used.
Level of measurement in the context of ISO 668
ISO 668 – Series 1 freight containers – Classification, dimensions and ratings is an ISO international standard which nominally classifies intermodal freight shipping containers, and standardizes their sizes, measurements and weight specifications.
The current version of the standard is the Seventh edition (2020), which integrates version E. The standard was prepared by Technical Committee ISO/TC 104: Freight containers, Subcommittee SC 1: General purpose containers.
Level of measurement in the context of Statistical data type
In statistics, data can have any of various types. Statistical data types include categorical (e.g. country), directional (angles or directions, e.g. wind measurements), count (a whole number of events), or real intervals (e.g. measures of temperature).
The data type is a fundamental concept in statistics and controls what sorts of probability distributions can logically be used to describe the variable, the permissible operations on the variable, the type of regression analysis used to predict the variable, etc. The concept of data type is similar to the concept of level of measurement, but more specific. For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale).