  Applied researchers often find themselves making statistical inferences in
settings that would seem to require multiple comparisons adjustments. We
challenge the Type I error paradigm that underlies these corrections. Moreover
we posit that the problem of multiple comparisons can disappear entirely when
viewed from a hierarchical Bayesian perspective. We propose building multilevel
models in the settings where multiple comparisons arise.
  Multilevel models perform partial pooling (shifting estimates toward each
other), whereas classical procedures typically keep the centers of intervals
stationary, adjusting for multiple comparisons by making the intervals wider
(or, equivalently, adjusting the $p$-values corresponding to intervals of fixed
width). Thus, multilevel models address the multiple comparisons problem and
also yield more efficient estimates, especially in settings with low
group-level variation, which is where multiple comparisons are a particular
concern.
