Nominal scale
A characteristic scales nominally (from the Latin noun “ name ” from the Greek onoma; Pl . : noun, also noun ), if its possible manifestations can be differentiated, but do not have a natural ranking. A nominally scaling feature is made measurable by a description of categories , according to which each examination unit can be assigned (precisely) to a category. The result of such an operationalization is then called a nominal scale . Because of the lack of order, the scale (from Latin scalae , 'ladder, staircase') is actually not appropriate and should be seen in connection with the other scale levels .
Formal conditions
The formal conditions of a nominal scale are:

Reflexivity
Formally written: a = a. If I z. B. have an apple in front of me and look at it a second time, I should recognize it as identical . 
Symmetry
If a = b, then b = a. If I have a fruit a in front of me, describe it to someone who has a fruit b in front of him, and he recognizes the fruits as being the same, then the same result should come out if the fruits are exchanged. 
Transitivity
If a = b and b = c, then a = c. I hold an apple in my hand, see a picture of an apple and recognize it as being the same. Then I take the picture outside and recognize a fruit on the tree as being the same (b = c). Then a categorization, and thus a nominal scale, only makes sense if I recognize the apple in my hand and the one on the tree as the same (a = c). 
Homomorphism
The description of the categories must be such that the mapping defined thereby is structurepreserving (homomorphic), that is, that the same objects of the empirical relative are assigned to one category and unequal objects to different categories.
Examples
Examples of nominally scaled features:
 Vehicle registration number
 Family name: Müller , Schmidt , Schneider
 Gender: male , female , diverse
 blood type
 Tax class
 Postcodes or place of birth: Berlin , Hamburg , Heidenheim
 Numbers of the bus routes
 Religion: Buddhist , Christian , Hindu , Jewish , Muslim
Possible operations and transformations
The only structurepreserving transformations are renaming, which means that a new category is uniquely assigned to each category. Even if the categories can be coded by numbers (one then speaks of nominal numbers , example: occupation 1, occupation 2, ...), mathematical operations with these codes, e.g. B. a division "carpenter / baker", does not make sense. Likewise, size comparisons using nominally scaled features are not useful. However, it makes sense to determine the frequency of occurrence of the categories in a set of investigation units, which are then the subject of the statistics . Only the most frequent value, the socalled modal value, can be determined as the location parameter of such a frequency distribution .
See also
Individual evidence
 ↑ ^{a } ^{b } ^{c } ^{d } ^{e } ^{f} Herbert Büning, Götz Trenkler: Nonparametric statistical methods . Walter de Gruyter, 1994, ISBN 9783110163513 , p. 8 ( limited preview in Google Book search).