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The Howland will forgery trial was a U.S. court case in 1868 to decide Henrietta Howland Robinson's contest of the will of Sylvia Ann Howland. It is famous for the forensic use of mathematics by Benjamin Peirce as expert witness.

Sylvia Ann Howland died in 1865, leaving roughly half her fortune, of some USD 2 million, to various legatees with the residue to be held in trust for the benefit of Robinson, Howland's niece. The principal was to be distributed to various beneficiaries on Robinson's death.

Robinson produced an earlier will, leaving her the whole estate outright. To the will was attached a second and separate page, putatively seeking to invalidate any subsequent wills. Howell's executor, Thomas Mandell, rejected Robinson's claim, insisting that the second page was a forgery, and Robinson sued.

In the ensuing case of Robinson v. Mandell, Charles Sanders Peirce testified that he had made pairwise comparisons of 42 examples of Howland's signature, overlaying them and counting the number of downstrokes that overlapped. Each signature featured 30 downstrokes and he concluded that, on average, 6 of the 30 overlapped, 1 in 5. When the admittedly genuine signature on the first page of the contested will was compared with that on the second, all 30 downstrokes coincided, suggesting that the second signature was a tracing of the first.

Benjamin Peirce, Charles' father, then took the stand and asserted that the probability that all 30 downstrokes should coincide in two genuine signatures was 1 divided by 2,666,000,000,000,000,000,000. He went on to observe

So vast improbability is practically an impossibility. Such evanescent shadows of probability cannot belong to actual life. They are unimaginably less than those least things which the law cares not for. ... The coincidence which has occurred here must have had its origin in an intention to produce it. It is utterly repugnant to sound reason to attribute this coincidence to any cause but design.

The court ruled that Robinson's testimony in support of Howland's signature was inadmissible as she was a party to the will. The statistical evidence was not called upon in judgement.

The case is one of a series of attempts to introduce mathematical reasoning into the courts. People v. Collins is a more recent example.

One potential issue with regard to Peirce's line of argument is why the particular metric of overlapping downstrokes was chosen, rather than one of the many other ways of quantifying the similarity of two signatures. Did he look at the data and decide that downstroke matching would be a fruitful line of attack or did he decide on downstroke matching before seeing the data? In such situations, there is always a fear that analysts are, perhaps inadvertently, indulging in testing hypotheses suggested by the data, which can generate very impressive but utterly spurious p-values.

Posterior match rate distribution based on 42 signatures and a Beta(0.5,0.5) prior

In attempting to understand Pierce's argument more deeply it is helpful to try to replicate it using a modern statistical analysis. See the Talk page for details.

• Robinson v. Mandell, 20 F. Cas. 1027 (C.C.D. Mass. 1868) (No. 11,959)
• Menand, L. (2002) The Metaphysical Club: A Story of Ideas in America ISBN 0-00-714737-6, pp163-176
• Meier, P. & Zabell, S. (1980) "Benjamin Peirce and the Howland Will", 75 Journal of the American Statistical Association vol. 75 p497
• "The Howland Will Case", American Law Review vol. 4 p625 (1870)
• Eggleston, Richard (1983) Evidence, Truth and Probability ISBN 0-297-78263-0