The marriage reference says her name was "Eliphalet Randall, d. of Job, of Cranston." (newenglandancestors.org) I think it likely that her name was Elizabeth, and was misread in the transcription.
A family tree at Rootsweb's Worldconnect has her name as Elizabeth Palmer Randall, so I have added her middle name as Palmer, pending verification. Her great-grandmother was Bethiah (Palmer) Randall (see notes for her). "Elizabeth P. Randall" is mentioned by name as a granddaughter in the 5 Jan 1835 will of Patience Randall of Cranston, RI. The will also mentions a son named Job. (RI Genealogical Register, Vol. 10, p. 52, Cranston Wills)