There is a discrepancy in the birth year. Although the grave marker says 1896, (delayed) birth certificate, draft registration, his children and several census records all support 1897. [per Dodek13 FG#48358902]

Son-in-law of Herbert Soloman Whaley & Ivory Oreal Strickland Whaley. He is noted in the 1920 census in Ossineke, Alpena, Michigan living with his parents William H. & Maryette , siblings Sarah and Hazel.

Wm. A. Barrett in "Michigan, Marriages, 1822-1995"
Name: Wm. A. Barrett
Birth Date: 1897
Birthplace:
Age: 23
Spouse's Name: Celena Van Norman
Spouse's Birth Date: 1901
Spouse's Birthplace: Cass City
Spouse's Age: 19
Event Date: 23 Dec 1920
Event Place: Presque Isle, Michigan
Father's Name: Wm. Barrett
Mother's Name: Marreta Gooley
Spouse's Father's Name: Albert Whaley
Spouse's Mother's Name: Stricklain
Race:
Marital Status:
Previous Wife's Name:
Spouse's Race:
Spouse's Marital Status:
Spouse's Previous Husband's Name:
Indexing Project (Batch) Number: I02199-0
System Origin: Michigan-EASy, GS Film number: 965755, Reference ID: 182

The family is noted in the 1930 census as living in Muskegon County, Michigan
Head: Alfred Barrett M 33 Michigan
Wife: S Voylet Barrett F 28 Michigan
Son: Vern A Barrett M 8 Michigan
Daughter: Etta M Barrett F 6 Michigan
Son: Clifford G Barrett M 4 Michigan
Daughter: Clara A Barrett F 1 Michigan
Stepdaughter: Ivry VanNorman F 9 Michigan

Here the family is in the 1940 census, still in Muskegon County, Michigan (note that first name and middle initials are reversed in at least several pages of this census):
Head: A William Barrett M 43 Michigan
Wife: S Voylet Barrett F 35 Michigan
Daughter: M Etta Barrett F 16 Michigan
Daughter: I Clara Barrett F 11 Michigan
Daughter: E Doris Barrett F 9 Michigan
Son: A Perl Barrett M 8 Michigan
Daughter: D Sarah Barrett F 6 Michigan
Son: L Orson Barrett M 4 Michigan

His parents are noted in the 1940 census living in Alma, Alma County, Michigan as William, 69 and Marietta, 62 yrs