  We compare [O IV] 25.89 micron emission line luminosities with very hard
(10-200 keV) X-rays from Swift, Integral, and BeppoSAX for a complete sample of
89 Seyferts from the Revised Shapley-Ames sample. Using Seyfert 1s, we
calibrate [O IV] as a measure of AGN intrinsic luminosity, for particular use
in high-obscuration environments. With this calibration, we measure the average
decrement in 14-195 keV X-ray to [O IV] luminosity ratio for Seyfert 2s
compared to type 1s. We find a decrement of 3.1 +- 0.8 for Seyfert 2s, and a
decrement of 5.0 +- 2.7 for known Compton-thick Seyfert 2s. These decrements
imply column densities of approximately log N(H)=24.6 and 24.7 cm^-2,
respectively. Thus, we infer that the average Seyfert 2 is more highly obscured
and intrinsically more luminous than would be inferred even from the very hard
X-rays. We demonstrate two applications of the hard X-ray to [O IV] ratio. We
measure a column density for the extremely obscured NGC 1068 of log
N(H)=25.3-25.4 cm^-2. Finally, by comparing [O IV] luminosities to total
infrared luminosities for twelve bright ultraluminous infrared galaxies, we
find that four have substantial AGN contributions.
