The sonification of data to communicate information to a user is a relatively new approach that established itself around the 1990s. To date, many researchers have designed their individual sonification from scratch. There are no standards in sonification design and evaluation. But researchers and practitioners have formulated several requirements and established several methods. There is a wide consensus that psychoacocustics could play an important role in the sonification design and evaluation phase. But this requires a) an adaption of psychoacoustic methods to the signal types of sonification and b) a preparation of the sonification for the psychoacoustic experiment procedure. In this method paper, we present a PsychoAcoustical Method for the Perceptual Analysis of multidimensional Sonification (PAMPAS) dedicated to the researchers of sonification. A well-defined and well-established, efficient, reliable, and replicable just noticeable difference (JND) experiment using the maximum likelihood procedure (MLP) serves as the basis to achieve perceptual linearity of parameter mapping during the sonification design stage and to identify and quantify perceptual effects during the sonification evaluation stage, namely the perceptual resolution, hysteresis effects and perceptual interferences. The experiment results are scores from standardized data space and a standardized procedure. These scores can serve to compare multiple sonification designs of a single researcher or even among different research groups. This method can supplement other sonification designs and evaluation methods from a perceptual viewpoint.