# Nominal scale

A characteristic scales nominally (from the Latin nounname ” 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:

1. 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 .
2. 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.
3. 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).
4. Homomorphism
The description of the categories must be such that the mapping defined thereby is structure-preserving (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 structure-preserving 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 so-called modal value, can be determined as the location parameter of such a frequency distribution .