  Modern statisticians are often presented with hundreds or thousands of
hypothesis testing problems to evaluate at the same time, generated from new
scientific technologies such as microarrays, medical and satellite imaging
devices, or flow cytometry counters. The relevant statistical literature tends
to begin with the tacit assumption that a single combined analysis, for
instance, a False Discovery Rate assessment, should be applied to the entire
set of problems at hand. This can be a dangerous assumption, as the examples in
the paper show, leading to overly conservative or overly liberal conclusions
within any particular subclass of the cases. A simple Bayesian theory yields a
succinct description of the effects of separation or combination on false
discovery rate analyses. The theory allows efficient testing within small
subclasses, and has applications to ``enrichment,'' the detection of multi-case
effects.
