Abraham Dobson was born on Apr. 12, 1842 in Lafayette Township, Medina County, Ohio, to David Dobson and Elizabeth Lance. As the second son, he was likely named "Abraham", after his maternal grandfather, "Abram" Lance.

In the 1860 U.S. Census, Abe was living with his mother's sister (Mary "Polly" Lance) and her husband (Robert Eaken).
In the 1870 U.S. Census, Abram was living with his wife and first child (Franklin D. F. Dobson) and he gave his birthplace as Ohio, and there was no parents' birthplaces information required on that form.
In the 1880 U.S. Census, Abram gave his birthplace as Ohio, and both his parents' birthplaces as Ohio.
In the 1900 U.S. Census, Abram gave his birthplace as Ohio and both his father's birthplace as Unknown and his mother's birthplace as Ohio.
In 1910 U.S. Census, his final one, he gave his birthplace as Ohio and both his parents' birthplaces as Ohio.
In Abe's death certificate, his birthplace is Medina County, Ohio; his father is David Dobson, born in Wayne County, Ohio and his mother Becky Miller [Elizabeth Lance], born in Jefferson County, Ohio. Abe's daughter, Alta Irwin, was the informant.

Abraham Dobson married Mary Lance, his 2nd cousin (through shared great-grandparents, Christopher Lance & Sarah Johnson), on December 18, 1866.

Together they had three children:
Franklin D. F.,
Alta, and
Fred E.

Abraham died on November 2, 1914, at the age of 73 and he was survived by his wife, Mary; two children: Alta and Fred; and seven grandchildren: Clyde Irwin, Dewey Irwin, Lewis Irwin, Jay Dobson, Frank Dobson, Pearl Dobson and Ida Dobson.