The research for that study measured the frequency response of 283 headphones over a wide range of pricing from $4 to over $5000 and found that the frequency response had a nearly insignificant correlation to the cost. In other words, just because you spend more money, doesn't mean you will get a pair of headphones with more linear or better frequency response characteristics. In-ear, supra-aural, and circumaural headphones were the headphone types that were examined, and the study also showed that there wasn’t even much of a correlation of frequency response to headphone type.
One of the reasons why this is surprising is because frequency response was found to be the major determinant of sound quality in headphones, based on previous research by Sean Olive and Todd Welti. Some might wonder if other attributes of sound reproduction play an equally important role as frequency response, but this does not appear to be the case. Nonlinear distortion like harmonic distortion can crop up when a headphone is driven hard enough, but most headphones seem to have enough headroom for that not to be an issue. We asked Dr. Sean Olive about how much nonlinear distortions would be a factor that could separate the sound quality of different headphones.
He replied, “Based on our research and others, I believe frequency response is the dominant factor that determines sound quality. We've done some experiments where we equalized the headphones to have the same frequency response so that listeners could focus on distortion differences. The headphones sounded sufficiently the same that listeners could not say they preferred one to the other except in 1 or 2 cases where the distortion was really high.” Time-related properties such as group-delay would also seem not to be an issue in headphones, since most headphones are minimum phase up to high-frequencies where it is not audible, and any changes in the phase response would necessarily cause a change in the frequency response.