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.
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