Institute for Mathematical Behavioral Science, University of California, Irvine, Irvine, CA 92697-5100, USA.
Psychol Rev. 2010 Oct;117(4):1247-58. doi: 10.1037/a0020174.
Most studies concerning psychological measurement scales of intensive attributes have concluded that these scales are of ratio type and that the psychophysical function is closely approximated by a power function. Experiments show, for such cases, that a commutativity property must hold under either successive increases or successive decreases provided, e.g., all other independent dimensions are fixed. A good deal of data support this conclusion. However, little or no attention has been paid to whether or not such subjective intensity scales differ when an independent dimension such as frequency (pitch in audition, color in vision, etc.) is varied. Using a simple and favorably tested theoretical model for global psychophysics, the authors arrive at a necessary and sufficient cross-dimension, commutativity condition for a common intensity ratio scale to exist. For example, the data show that the loudness of a tone at frequency f and another tone at frequency g can each be viewed as arising from a common property of loudness over intensity/frequency pairs. Comparing one version of cross-dimensional commutativity with the corresponding 1-dimensional commutativity property discriminates between a general representation of the ratio scale property and a special case of it.
Does the theory extend to other intensive continua (prothetic attributes)? If so, which ones? And does it extend to cross-modal matching?
大多数关于密集属性心理测量量表的研究得出的结论是，这些量表属于比率类型，心理物理函数非常接近幂函数。实验表明，在连续递增或连续递减的情况下，如果其他所有独立维度都固定不变，则必须满足可交换性。大量数据支持这一结论。然而，几乎没有或根本没有关注当独立维度（如频率（听觉中的音高、视觉中的颜色等）发生变化时，这种主观强度量表是否会有所不同。作者使用一个简单且经过良好测试的全局心理物理学理论模型，得出了存在共同强度比率量表的必要且充分的跨维度、可交换性条件。例如，数据表明，频率为 f 的音调的响度和频率为 g 的另一个音调的响度都可以看作是来自响度在强度/频率对中的共同属性。比较跨维度可交换性的一个版本与相应的 1 维可交换性属性，可以区分比率量表属性的一般表示和其特殊情况。
该理论是否适用于其他密集连续体（拟态属性）？如果是，哪些可以？它是否适用于跨模态匹配？
