England and Wales Census, 1881, database with images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/Q27B-9Q3Y : 2 September 2017), Robert Gardham in household of John Gardham, Storwood, Yorkshire,Yorkshire East Riding, England; from "1881 England, Scotland and Wales census," database and images, findmypast (http://www.findmypast.com : n.d.); citing p. 13, Piece/Folio 4732/10, The National Archives, Kew, Surrey; FHL microfilm 101,775,324. 
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It may be possible to confirm family relationships with Robert by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA test-takers in his direct paternal line.
Mitochondrial DNA test-takers in the direct maternal line: