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Fifteen sites is a small landscape genetics study, and a power of 74.5 per cent for a moderate effect is a useful number to have before designing one. The permutation test finds the real effect 74.5 per cent of the time with 15 sites, against 91 per cent for the ordinary test, and the ordinary test buys that difference with a false positive rate of 26.75 per cent. Fit one dataset of 18 sites where geographic distance has a coefficient of 0.55 and a barrier has 0.3. Draw one random ordering of the sites and apply it to the rows and the columns of the response matrix at once. Write the genetic distance between sites i and j as a site term plus a pair term.
Fifteen sites give 105 pairs but only 15 independent things were sampled, and every site appears in 14 of those pairs. In other words, the jury verdict required by the Sixth Amendment is a jury verdict of guilty beyond a reasonable doubt. It would not satisfy the Sixth Amendment to have a jury determine that the defendant is probably guilty, and then leave it up to the judge to determine (as Winship requires) whether he is guilty beyond a reasonable doubt. It is self evident, we think, that the Fifth Amendment requirement of proof beyond a reasonable doubt and the Sixth Amendment requirement of a jury verdict are interrelated. This beyond a reasonable doubt requirement, which was adhered to by virtually all common law jurisdictions, applies in state as well as federal proceedings. In his instructions to the jury, the trial judge gave a definition of "reasonable doubt" that was, as the State conceded below, essentially identical to the one held unconstitutional in Cage v. Louisiana, 498 U.S. 39 (1990) In closing argument, defense counsel argued that there was reasonable doubt as to both the identity of the murderer and his intent. You can decide when to allow embedded content to access your data for sites you trust.
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