1930 census, Prairie, Hot Spring, Arkansas Lester M Sandage 28 Iva L T Sandage 21 Dortha M Sandage 1 Steven A D Sandage 69 Martha E Sandage 65
1910 census, Cadron, Van Buren, Arkansas Steven A Sandage 49IN f IN m IN Martha E Sandage 45AR f TN m VA Andrew F Sandage 21 Charley E Sandage 15 Johnie S Sandage 13 Laurence J Sandage 10 Florence M Sandage 10 Marley L Sandage 8 Sallie B Sandage 7 Cora I Sandage 3
1900 census, Cadron, Van Buren, Arkansas Stephen A Sandage 39IN Martha E Sandage 36AR William S Sandage 15 Andrew F Sandage 11 Charles E Sandage 5 John S Sandage 3 Lawrence J Sandage 1 Florence M Sandage 1
Center Post, Cleburne, Arkansas Moses Sandage 44IN Parthnia e Sandage 47TN Martin G B Sandage 19 Mary L J Sandage 16 Jacob Sandage 12 Stephen A D Sandage 9 Tennessee M Sandage 6
Arkansas Death Index, 1914-1950 about Martha A Sandage Name: Martha A Sandage Death Day: 7 Death Month: Apr Death Year: 1938 County: Hot Spring Roll Number: 19341940 Page Number: 3043
You can get her death cert, it may list her parents
I can't find her on the 1870 or 1880 census
Are you sure that her maiden name is Tarkington? Could she have been married previously?