  We present empirical scaling relations for the significance of absorption
features detected in medium resolution, far-UV spectra obtained with the Cosmic
Origins Spectrograph (COS). These relations properly account for both the
extended wings of the COS line spread function and the non-Poissonian noise
properties of the data, which we characterize for the first time, and predict
limiting equivalent widths that deviate from the empirical behavior by \leq 5%
when the wavelength and Doppler parameter are in the ranges \lambda = 1150-1750
A and b > 10 km/s. We have tested a number of coaddition algorithms and find
the noise properties of individual exposures to be closer to the Poissonian
ideal than coadded data in all cases. For unresolved absorption lines, limiting
equivalent widths for coadded data are 6% larger than limiting equivalent
widths derived from individual exposures with the same signal-to-noise. This
ratio scales with b-value for resolved absorption lines, with coadded data
having a limiting equivalent width that is 25% larger than individual exposures
when b \approx 150 km/s.
