Ellermeier W, Faulhammer G
Institut für Psychologie, Universität Regensburg, D-93040 Regensburg, Germany.
Percept Psychophys. 2000 Nov;62(8):1505-11. doi: 10.3758/bf03212151.
Stevens's direct scaling methods rest on the assumption that subjects are capable of reporting or producing ratios of sensation magnitudes. Only recently, however, did an axiomatization proposed by Narens (1996) specify necessary conditions for this assumption that may be put to an empirical test. In the present investigation, Narens's central axioms of commutativity and multiplicativity were evaluated by having subjects produce loudness ratios. It turned out that the adjustments were consistent with the commutativity condition; multiplicativity (the fact that consecutive doubling and tripling of loudness should be equivalent to making the starting intensity six times as loud), however, was violated in a significant number of cases. According to Narens's (1996) axiomatization, this outcome implies that although in principle a ratio scale of loudness exists, the numbers used by subjects to describe sensation ratios may not be taken at face value.
史蒂文斯的直接标度法基于这样一个假设，即受试者能够报告或产生感觉量值的比率。然而，直到最近，纳伦斯（1996年）提出的一种公理化方法才明确了这一假设的必要条件，这些条件可以进行实证检验。在本研究中，通过让受试者产生响度比率来评估纳伦斯的交换性和乘法性核心公理。结果表明，调整符合交换性条件；然而，在大量情况下，乘法性（即响度连续加倍和三倍应等同于使起始强度变为原来的六倍这一事实）被违反。根据纳伦斯（1996年）的公理化方法，这一结果意味着，虽然原则上存在响度的比率量表，但受试者用来描述感觉比率的数字可能不能只看表面价值。
