Noise and distortion reduce speech intelligibility and quality in audio devices such as hearing aids. This study investigates the perception and prediction of sound quality by both normal-hearing and hearing-impaired subjects for conditions of noise and distortion related to those found in hearing aids. Stimuli were sentences subjected to three kinds of distortion (additive noise, peak clipping, and center clipping), with eight levels of degradation for each distortion type. The subjects performed paired comparisons for all possible pairs of 24 conditions. A one-dimensional coherence-based metric was used to analyze the quality judgments. This metric was an extension of a speech intelligibility metric presented in Kates and Arehart (2005) [J. Acoust. Soc. Am. 117, 2224-2237] and is based on dividing the speech signal into three amplitude regions, computing the coherence for each region, and then combining the three coherence values across frequency in a calculation based on the speech intelligibility index. The one-dimensional metric accurately predicted the quality judgments of normal-hearing listeners and listeners with mild-to-moderate hearing loss, although some systematic errors were present. A multidimensional analysis indicates that several dimensions are needed to describe the factors used by subjects to judge the effects of the three distortion types.