In the 1870 and 1880 censuses his name is given as Warren.
In the Federal Census of 1900, William and Barbara Remington are living at Hackberry, Labette Co., KS. They have two children, and apparently from the census data, had another child who died. With them or next door are Williams's two brothers and their families, as well as his mother Prudence Remington.
In 1910, the family is still at Hackberry. William & Barbara have six children, including apparently a set of twins.
In 1920, William is widowed and still living at Hackberry. There are four children in the household.