As a general rule, it is
essential[/b] to note which
parish any of your people lived when you are trying to find out where a place is or was. Names of farms, like Backfield, can occur in many different parishes, and if you don't know which parish to look in, you can't be sure of finding the right place. You must know the parish, because the 1871 census, like all other available censuses, is arranged by parish.
There are two Backfields in the 1881 census, one in the parish of Glenbervie in the county of Kincardine, and the other in the parish of Dunbarney, so I would go along with the suggestion that it is Pitcaithly, more usually spelled Pitkeathly these days. The surnames listed at Backfield are Scott, Nairn, Robertson and Jackson.
Using the map catalogue at
www.nls.gov.uk I have found Backfield in the parish of Dunbarney. It looks as if it no longer exists, but it was south of the B935 road between Pitkeathly Wells and Mount Stewart. This is the URL of the map I found:
http://maps.nls.uk/os/6inch/view/?sid=74428189. You will need to zoom in and move around until you find it.
So assuming that your 1871 census listing was in the parish of Dunbarney, this is the place.