Jane's father was Jonathan Michener (who may have died about 1839 in Stark County, Ohio, per probate records; 1 Jul 1839 per the 1909 publication, "The Longstreth family records;" burial location unknown. Find A Grave record was created for him in 2023, but have not found evidence for his burial being there)

Jane's birth listed in that same publication was denoted as 19 Sep 1836. Sep 1838 taken from the 1900 U.S. Federal Census.

She married Samuel Allerton (d. ~1879; burial location unknown) on 12 Aug 1852 in Stark County, Ohio; they had 9 known children:
John W (died in infancy), Mary Eva, Emma A, Cora (died in infancy), Alice (died in infancy), Hannah M, Rachel C, Samuel Ellsworth and Percy P (died at about age 8 in 1877)

*Specific birth date, birth place and middle name reflected on memorial are per user John Carl Roloff, Jr (50965305) who received a transcript of Job Scott's family information, which stated that Jane was born in the home of Job's parents, Thomas Rockhill Scott and Filena Keller Scott. Filena, who was a midwife, delivered both Jane and her sister, Hannah.

1850 United States Federal Census
Name Jane Michner
Age 14
Birth Year abt 1836
Birthplace Ohio
Home in 1850 Lexington, Stark, Ohio, USA
Family Number 36
Household Members
Name Age
Margaret Michner 57
Joshua Garwood 25
Mary Garwood 22
Jane Michner 14
Hannah Michner 11

Ohio, County Marriages, 1774-1993
Name Jane G Michener
Gender Female
Marriage Date 12 Aug 1852
Marriage Place Stark, Ohio, USA
Spouse Samuel Allerton
Film Number 000897628

Not sure what the HAN on her headstone stands for. Possibly the fact she had a daughter named Hannah and did live with her at the time of the 1900 census (appears twice; once also with son). Maybe HAN was Hannah's nickname and perhaps she was "signing" her mother's marker as a way of indicating that she had lovingly had the marker made and placed.