I believe that I have found some information for you.
The child, Robert Tarpley, in the 1940 census is not John and Carrie's child, but rather their grandchild. Robert Yancey Tarpley (1931-2005) was the son of Ida M. West and Robert Tarpley, according to the Social Security Applications & Claims files.
Using Ida's name, I found the family in South Huntington, Westmoreland Co, PA in 1930. Her father is listed as Robert West and mother Carrie.
I may have found them in 1920 in Pond, Pike Co, KY. Here the head of household is Bob West, 24, coal miner, born GA, wife is Callie b. Alabama, and 2 children, Jessie 9 & Ida M. 6 both born in AL.
On John Robert West's death certificate it states that he was born in Americus, GA. His parents were listed as Charles B. West & Dorcus Warsaw.
In 1900 Charles West 53, Dorcus, 48, and 4 children were living in Leslie, Sumter Co, GA One of their children was Bobbie, age 13.
In 1910 Dorcus West is a widow. John Robert is not in the household, but her other children are.
Dorcus died in 1925 and on her death certificate her parents are listed as Tom and Anna Dassaw,
There was a small article in the Pittsburgh Post-Gazette (Pittsburgh, Pennsylvania) · 21 Oct 1949, Fri · Page 8 stating that Carrie West had filed suit for $152,000 against the American Steel & Wire Co for causing the smog that killed her husband. I was not able to insert an image of the article here.
Susannah, thank you so very much! This information is wonderful, and I so appreciate passing it along.
Dear Mr. McPhee,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located 21 Population Schedules in the Records of the Bureau of the Census (Record Group 29) that could contain information on John Robert West. Some of the schedules have been digitized in part or whole (for 1940 only). For access to the non-digitized schedules, please contact the National Archives at Washington, DC - Textual Reference (RDT1) via email at firstname.lastname@example.org.
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For information about the U.S. Census, see the Census Bureau technical documentation and questionnaires.
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We hope this is helpful. Best of luck with your research!