Stable Variables and Variables Involved in Linguistic Change
(1) Stable variables:
A stable (sociolinguistic) variable is a variable which is not undergoing linguistic change. Such a variable exhibits the regular age pattern. A stable variable, thus, reflects change in the speech of the individual speaker as (s)he progresses through life.
An example for a stable (sociolinguistic) variable is (ng) with its prestige velar variant [ɪŋ] and its non-prestige alveolar variants [ɪn] or [ən]. Both the prestige and non-prestige variants show linguistic stability in that they have been described to occur regularly in the speech of the individuals in a speech community. The use of one or the other variant(s) differs with respect to age but there is no indication that the prestige variant is pushing out the non-prestige variant(s) or vice versa.
(2) Variables involved in linguistic change:
Apart from stable variables which are not involved in linguistic change, there are (sociolinguistic) variables which are affected by linguistic change in a speech community. Such variables do not show the regular U-curve-like age pattern and we find that a particular age group uses more or less standard or non-standard variants than is usually observed. This indicates that a change might be in progress in the speech community.
(r) is an example for a variable involved in linguistic change that was studied by William Labov in New York City (1966). (See here). At the time of the study, the variable (r) represented a change in progress in New York City. Traditionally, New York City had been r-less, but after World War II the pronunciation of /r/ gained prestige. Labov found that the pronunciation of /r/ was reintroduced by younger speakers into New York City speech as the prestigious variety. Variable (r) showed social and stylistic stratification and all speakers viewed the pronunciation of /r/ as prestigious by using higher frequencies of it in more formal styles.
Variable (r) in New York City is an example for a change from above.