A qualitative variable expresses an attribute, a quality or a characteristic.
A variable , in the field of mathematics , is a symbol that can appear in a function, an algorithm, a proposition or a formula, adopting different values . By establishing links with other variables, they can contribute to the development of a theory or hypothesis, acquiring the name constructs .
It is possible to differentiate between different classes of variables depending on the context. Qualitative variables are those that allow the expression of a characteristic , a category , an attribute or a quality .
The etymology
It is interesting in this sense to know the etymological origin of the two words that make up the term in question. Thus, we can establish the following information:
-Variable comes from Latin, specifically from “variabilis” which is the result of the sum of two components: the verb “variare”, which can be translated as “change appearance”, and the suffix “-able”, which is used to indicate possibility.
-Qualitative, on the other hand, also derives from Latin. In his case of the word “qualitativus”, which is made up of two parts: the noun “qualitas”, which means “quality”, and the suffix “-tivo”. This is used to indicate a passive or active relationship.
Characteristics of a qualitative variable
We said that variables can take on different values . In the case of qualitative variables, if they can only adopt two values, they are classified as dichotomous . For example: a person can be “alive” or “dead” , there is no third option. This qualitative variable, therefore, is dichotomous.
If the qualitative variable can acquire a number of values greater than two, it is called polytomous . In this group , in turn, we can distinguish between nominal polytomous qualitative variables and ordinal polytomous qualitative variables.
There are different types of qualitative variables.
Classification according to type
Nominal polytomous qualitative variables take on values that cannot be ordered . A pair of pants can be “blue” , “black” , “green” , “red” , “yellow” or “pink” , to name a few possibilities, without there being a criterion or hierarchy that allows the ordering of the attribute (the color) . ).
In the same way, another example that can help us understand what nominal qualitative variables are is the one that refers to a person's marital status. Thus, this person can be single, married, widowed, divorced or separated without being able to establish any type of rank or hierarchy regarding these possibilities.
Polytomous ordinal qualitative variables , on the other hand, acquire values that can be ordered according to a scale . A sound can be “weak” , “moderate” or “intense” , three values that are ordered from lowest to highest (or vice versa) according to its characteristics.
Examples of qualitative variables
More examples of ordinal or quasiquantitative qualitative variables are the following:
-Within an athletics competition, three medals are awarded that follow a hierarchy as to who reached the finish line first, second and third. We are referring to gold, silver and bronze.
-With regard to an exam grade, these variables are also established with the corresponding order or hierarchy. Thus, a student may have obtained an outstanding, a notable, a good, a pass or a fail grade.