There are two widely recognized types of nonconformity: anti-conformity
and independence. From a social point of view, it is very important to
distinguish between independence and anti-conformity. The term
`independence' implying the failure of attempted group influence.
Independent individuals evaluate situations independently of the group
norm. On the contrary, anti-conformists are similar to conformers in the
sense that both take cognizance of the group norm - conformers agree with
the norm, anticonformers disagree. We show how the both types of
nonconformity can be introduced into opinion dynamics models with binary
opinions taking as an example the generalized voter model. We discuss the
differences and similarities between aniconformity and independence from
different perspectives -  simple physical microscopic models and social
reality.

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