Spectral evidence is a form of evidence based upon dreams and visions. It was admitted in court during the Salem witch trials by the appointed chief justice, William Stoughton. The booklet A Tryal of Witches taken from a contemporary report of the proceedings of the Bury St. Edmunds witch trial of 1662 became a model for, and was referenced in the Trials when the magistrates were looking for proof that such evidence could be used in a court of law.
Spectral evidence was testimony that the accused witch's spirit (i.e. spectre) appeared to the witness in a dream or vision (for example, a black cat or wolf). The dream or vision was admitted as evidence. Thus, witnesses (who were often the accusers) would testify that "Goody Proctor bit, pinched, and almost choked me," and it would be taken as evidence that the accused were responsible for the biting, pinching and choking even though they were elsewhere at the time.
Thomas Brattle, a merchant of Salem, made note that "when the afflicted do mean and intend only the appearance and shape of such an one, say G. Proctor, yet they positively swear that G. Proctor did afflict them; and they were allowed to do so; as though there was no real difference between G. Proctor and the shape of G. Proctor."
Rev. Cotton Mather argued that it was appropriate to admit spectral evidence into legal proceedings, but cautioned that convictions should not be based on spectral evidence alone as it was possible for the Devil to take the shape of an innocent person. Robert Calef published More Wonders of the Invisible World to criticize Mather for this position. Calef also made libelous statements about Cotton and Increase Mather, suggesting that they sexually molested young girls. Upon reading the book, Increase Mather publicly burned the book in Harvard Yard. 
Rev. Increase Mather became an opponent of spectral evidence - though not until after the Salem hangings had taken place, and not on the basis that it was false testimony by witnesses, but that it might be a deception by demons. He published Cases of Conscience Concerning Evil Spirits Personating Men, Witchcrafts, infallible Proofs of Guilt in such as are accused with that Crime., in which he argued that "It were better that ten suspected witches should escape, than that one innocent person should be condemned".
See also 
- Geis, Gilbert; Bunn Ivan.; … (1997). A Trial of Witches: A Seventeenth-century Witchcraft Prosecution. New York: Routledge. ISBN 0-415-17109-1.
- Jensen, Gary F. (2006). The Path of the Devil: Early Modern Witch Hunts. Lanham: Rowman & Littlefield. ISBN 0-7425-4697-7.
- Bunn, Ivan. "The Lowestoft Witches". Retrieved 2007-12-29.
- Shadow of Doubt; Specter Evidence in Hawthorn's "In Young Goodman Brown", by David Levin, Standford University (@JSTOR)
- Richard F. Lovelace (1979). The American Pietism of Cotton Mather: Origins of American Evangelicalism. Washington D.C: Christian College Consortium. p. 22.
- Cases of Conscience concerning evil SPIRITS, by Increase Mather