Eysenbach, Mary Locke. "The Alcocks of Maine, Massachusetts and New Hampshire: John Alcock and His Wife Elizabeth Wrightman, Anne Alcock and Her Husband Nicholas Needham, and Katherine Alcock and Her Husband Gregory Belcher," New Hampshire Genealogical Record (April-July 2009) 49-56).
This article, to which we do not have ready access, apparently establishes the relationships among the individuals named in the title.