We use the dressed-atom formalism to calculate the frequency shift in a hyd
rogen maser induced by applied radiation near the Zeeman frequency, and fin
d excellent agreement with a previous calculation made in the bare-atom bas
is. The maser oscillates on the DeltaF=1, Deltam(F),=0 hyperfine transition
, while the applied field is swept through the F=1, Deltam(F)=+/-1 Zeeman r
esonance. We determine the effect of die applied field on the Zeeman levels
using the dressed-atom picture, and then calculate the maser frequency shi
ft by coupling the dressed states to the microwave cavity. Qualitatively, t
he dressed-atom analysis gives a simpler physical interpretation of this do
uble-resonance process, which has applications in precision hydrogen Zeeman
spectroscopy, e.g., in fundamental symmetry tests.