The person conforms publicly as well as privately because they have identified with the group and feel a sense of group membership. Change or belief of a behaviour is often temporary.
People conform because they don't know what to do or think and they look to others for answers. They genuinely think the group is right. They need to be right. This leads to identification.
About norms or what is normal behaviour for a certain group. They want some reward, they do not want to be punished, they want to be accepted and part of the group. This leads to compliance.
Participants in Asch's study conformed due to fear of disapproval and desire to avoid rejection by the group. Conformity reduced when answers were private, highlighting the impact of normative group pressure.
Research support for ISI
Lucas et al. found that participants conformed more with incorrect answers on hard math problems, supporting ISI as an explanation for conformity.
Counterpoint
It's difficult to tell NSI from ISI. Asch saw conformity dip with a dissenting participant, weakening both NSI by offering support and ISI by giving alternative info. Both likely team up in real-life conformity scenes.
Individual differences in NSI
NSI varies in predicting conformity. nAffiliators tend to conform more, showing NSI affects people differently. Individual differences in conformity go beyond one theory.