How do we know her name was Barbara?

1.  Marriage Record: 

2.  See his father's will, in which Andrew is named as eldest son. 

3.  1810 Census Index/Images (online at Ancestry.com; Image #2 of 9; extracted by Diana Gale Matthiesen):¤•

1810

PA

Northumberland Co.

Turbot Twp.

p. 15A/119

Ln. 13

A. Strout

10100-00100

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	9 or under	1800-1810	= Son
1 male	16-25	1784-1794	= Andrew (b. 1788)
1 female	16-25	1784-1794	= Barbara

Living four doors down from his mother, "Mrs. STROUT." 

4.  Anon.  1911.  Genealogical & Biographical Annals of Northumberland County.  J.L. Floyd & Co., Chicago. Biographical sketch of Andrew's nephew, Jacob STRAUB, and his kin. 

5.  Date information found by Frank Stroup at the Pennsylvania Historical Society in two folders of unpublished notes entitled Helen Gearhart Collection.  These notes were entirely undocumented, so caveat emptor; yet to the degree that they are accurate, they contain much valuable information, so are worth consulting. [See next source and search on "Gearhart."]

6.  Archives of the STRAUB-L mailing list (online at RootsWeb.com), including especially posts from Jim Burnell, Frank Stroup, and Garry Heagy.