Benjamini and Hochberg's false discovery rate (FDR)-controlling

method is applied to the problem of testing infinitely many contrasts

in linear models. Usual asymptotics for FDR-controlling methods fail

in this case, because the test statistics are highly dependent. An

alternative formulation using randomly sampled contrasts allows

direct application of the Glivenko-Cantelli theorem, and exact,

easily calculated critical values are derived, defining a new

multiple comparisons method for testing contrasts in linear models.

The new method makes no assumptions about the data-generating process

other than nonzero sample variance. The method is seen to be

adaptive, depending on the data through the usual ANOVA F-statistic,

like the Waller-Duncan Bayesian multiple comparisons method.

Comparisons with Scheffé's method are given, and the method is

extended to the simultaneous confidence intervals of Benjamini and

Yekutieli.