Source : Webster's Revised Unabridged Dictionary (1913)

Nonconformity \Non*con*form"i*ty\, n.
   Neglect or failure of conformity; especially, in England, the
   neglect or refusal to unite with the established church in
   its rites and modes of worship.

Source : WordNet®

nonconformity
     n 1: lack of harmony or correspondence
     2: a lack of conformity [syn: {nonconformance}] [ant: {conformity}]
     3: unorthodoxy as a consequence of not conforming to expected
        standards or values
     4: failure to conform [ant: {conformity}]