okay... I'm not sure which information you currently have on Wiley Washington Anderton (civil war soldier who died at Rock Island), so here is the information as was recorded in our family bibles and per my grandparents.
Our Wiley Washington Anderton had 3 brothers and 2 sisters as follows: Thomas Daniel Anderton b.Sep 22 1832 d.Jan 12 1863 m.Emilou Ray
Mary Elizabeth Anderton b.Jun 16 1836 m.J.Holt
James William Anderton b.Mar 14 1839 d.Sep 13 1913 m.Naomi Powell
Nancy Anderton b.Mar 19 1841 m.J.McManus
John Kimbro Anderton b.1847 m.Millie Farris
Unfortunately there were not brothers in this Wiley's family that would have been old enough to father your John Washington Anderton if he was born in 1838 (as per your 1880 census records).