If you look at the original page of that census, Matthew's status is in fact Brother-in-Law.
Why do you think Matthew Miller is Matthew Hogg?
This Matthew Miller, and his daughter Elizabeth Ann can be found in 1861:
Reference RG09, Piece 3630, Folio 40, Page 14
Market Place, Easingwold
Miller, Matthew Head M 42 Grocer & Tea Dealer b South Otterington
Miller, Ann Wife F 48 b Borrowby
Miller, Elizabeth Ann, Daughter F 14 b Thornton-le-Street
Miller, William Sadler Son M 12 Scholar b Thornton-le-Street
Miller, John Henry Son M 8 Scholar b Easingwold
Miller, Mary Anna Daughter F 8 Scholar b Easingwold
And, in 1841, Matthew is here:
Reference HO107, 1234, 18/4, 6
West Side, Thornton-le-Street
Miller, William M 60
Miller, Mary F 60
Miller, Ann F 24
Miiler, Matthew M 22
Plews, Jane F 26
Plews, Charles M 1
Plews, Emela F 4 months All born in Yorkshire
And, can I be a little pedantic?

This was NOT taken from the 1881 British census, but the Census of England & Wales.

Scotland has it's own census, as does Ireland.
Confusing I know, but I wouldn't want people to be misled!!
