Born 1 Dec 1759 to Peter Shaw and Elizabeth (Meachum) Shaw. 
An Elizabeth Meachum married John Green in 1776. (See Research Notes) 
An Elizabeth Meachum married Joshua Wyatt in 1784. (See Research Notes) 
Downey-1809: There are 2 Elizabeth Shaw's in FamilySearch. One married John Eason and the other married Joshua Wyatt. The one that married Joshua Wyatt has parents listed as Benjamin Shaw and Jerusha Brown. There is one that married John Green has parents listed as Peter Shaw and Elizabeth Meacham. FindAGrave lists spouse as Joshua Wyatt and parents as Peter Shaw and Elizabeth Meatchum so it doesn't agree with either of the FamilySearch profiles.
↑ "Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q29L-PR57 : 18 February 2020), Elisabeth Shaw, 01 Dec 1759; citing Birth, Beverly, Essex, Massachusetts, United States, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 004934217.
↑ "Massachusetts, Town Clerk, Vital and Town Records, 1626-2001," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QPC8-W73G : 31 October 2019), Joshua Wyatt and Elizabeth Shaw, 22 Feb 1784; citing Marriage, Danvers, Essex, Massachusetts, United States, Massachusetts Secretary of the Commonwealth, Boston; FHL microfilm 007011221.
Find a Grave, database and images (accessed 07 October 2020), memorial page for Elizabeth Shaw Wyatt (1 Dec 1759–7 Feb 1828), Find A Grave: Memorial #41321925, citing Amesville Cemetery, Amesville, Athens County, Ohio, USA ; Maintained by 47117651 (contributor 47117651) .
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It may be possible to confirm family relationships with Elizabeth by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Elizabeth: