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Level of measurement
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=== Nominal level === <!--Do not change this name. It is pointed to by other Wikipedia articles.--> A nominal scale consists only of a number of distinct classes or categories, for example: [Cat, Dog, Rabbit]. Unlike the other scales, no kind of relationship between the classes can be relied upon. Thus measuring with the nominal scale is equivalent to [[classifying]]. Nominal measurement may differentiate between items or subjects based only on their names or (meta-)categories and other qualitative classifications they belong to. Thus it has been argued that even [[dichotomy|dichotomous]] data relies on a [[constructivist epistemology]]. In this case, 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.<ref>Nominal measures are based on sets and depend on categories, a la Aristotle: {{cite web |url=http://www4.uwsp.edu/geo/faculty/gmartin/geog476/Lecture/BeySt.htm |title=Beyond Stevens: A revised approach to measurement for geographic information |first=Nicholas |last=Chrisman |date=March 1995 |access-date=2014-08-25}}</ref><ref>"Invariably one came up against fundamental physical limits to the accuracy of measurement. ... The art of physical measurement seemed to be a matter of compromise, of choosing between reciprocally related uncertainties. ... Multiplying together the conjugate pairs of uncertainty limits mentioned, however, I found that they formed invariant products of not one but two distinct kinds. ... The first group of limits were calculable ''a priori'' from a specification of the instrument. The second group could be calculated only ''a posteriori'' from a specification of what was ''done'' with the instrument. ... In the first case each unit [of information] would add one additional ''dimension'' (conceptual category), whereas in the second each unit would add one additional ''atomic fact''.", β pp. 1β4: MacKay, Donald M. (1969), ''Information, Mechanism, and Meaning'', Cambridge, MA: MIT Press, {{ISBN|0-262-63-032-X}}</ref> In a university one could also use residence hall or department affiliation as examples. 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 rank]]s below domains: kingdom, phylum, class, etc. * in [[software engineering]], type of [[Trap (computing)|fault]]: 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. If numbers are assigned as labels in nominal measurement, they have no specific numerical value or meaning. No form of arithmetic computation (+, β, Γ, etc.) may be performed on nominal measures. The nominal level is the lowest measurement level used from a statistical point of view. ====Mathematical operations==== [[Equality (mathematics)|Equality]] and other operations that can be defined in terms of equality, such as [[inequality (mathematics)|inequality]] and [[set membership]], are the only [[non-trivial]] [[operation (mathematics)|operation]]s that generically apply to objects of the nominal type. ====Central tendency==== The [[mode (statistics)|mode]], i.e. the ''most common'' item, is allowed as the measure of [[central tendency]] for the nominal type. On the other hand, the [[median]], i.e. the ''middle-ranked'' item, makes no sense for the nominal type of data since ranking is meaningless for the nominal type.<ref>{{cite journal|last1=Manikandan|first1=S.|title=Measures of central tendency: Median and mode|journal=Journal of Pharmacology and Pharmacotherapeutics|date=2011|volume=2|issue=3|pages=214β5|doi=10.4103/0976-500X.83300|pmc=3157145|pmid=21897729 |doi-access=free }}</ref>
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